Multi-disciplinary Design Optimization of a Composite Car Door for Structural Performance, Nvh,...

59
1 MULTI-DISCIPLINARY DESIGN OPTIMIZATION OF A COMPOSITE CAR DOOR FOR STRUCTURAL PERFORMANCE, NVH, CRASHWORTHINESS, DURABILITY AND MANUFACTURABILITY M. Grujicic, G. Arakere, V. Sellappan, J. C. Ziegert International Center for Automotive Research, CU-ICAR Department of Mechanical Engineering Clemson University, Clemson SC 29634 USA F. Y. Koçer, D. Schmueser Altair Engineering Inc. 1820 E. Big Beaver Rd., Troy, MI 48083 USA Correspondence to: * Mica Grujicic, 241 Engineering Innovation Building, Clemson, SC 29634-0921; Phone: (864) 656-5639, Fax: (864) 656-4435, E-mail: [email protected] ABSTRACT Among various efforts pursued to produce fuel efficient vehicles, light weight engineering (i.e. the use of low-density structurally-efficient materials, the application of advanced manufacturing and joining technologies and the design of highly-integrated, multi-functional components/sub-assemblies) plays a prominent role. In the present work, a multi-disciplinary design optimization methodology has been presented and subsequently applied to the development of a light composite vehicle door (more specifically, to an inner door panel). The door design has been optimized with respect to its weight while meeting the requirements /constraints pertaining to the structural and NVH performances, crashworthiness, durability and manufacturability. In the optimization procedure, the number and orientation of the composite plies, the local laminate thickness and the shape of different door panel segments (each characterized by a given composite-lay-up architecture and uniform ply thicknesses) are used as design variables. The methodology developed in the present work is subsequently used to carry out weight optimization of the front door on Ford Taurus, model year 2001. * Keywords: Multi-disciplinary Optimization, Automotive Engineering; Composite Structures; Altair Engineering Inc.

Transcript of Multi-disciplinary Design Optimization of a Composite Car Door for Structural Performance, Nvh,...

1

MULTI-DISCIPLINARY DESIGN OPTIMIZATION OF A COMPOSITE CAR DOOR FOR STRUCTURAL PERFORMANCE, NVH, CRASHWORTHINESS,

DURABILITY AND MANUFACTURABILITY

M. Grujicic, G. Arakere, V. Sellappan, J. C. Ziegert International Center for Automotive Research, CU-ICAR

Department of Mechanical Engineering Clemson University, Clemson SC 29634 USA

F. Y. Koçer, D. Schmueser Altair Engineering Inc.

1820 E. Big Beaver Rd., Troy, MI 48083 USA

Correspondence to:* Mica Grujicic, 241 Engineering Innovation Building, Clemson, SC 29634-0921; Phone: (864) 656-5639, Fax: (864) 656-4435, E-mail: [email protected]

ABSTRACT Among various efforts pursued to produce fuel efficient vehicles, light weight

engineering (i.e. the use of low-density structurally-efficient materials, the application of

advanced manufacturing and joining technologies and the design of highly-integrated,

multi-functional components/sub-assemblies) plays a prominent role. In the present

work, a multi-disciplinary design optimization methodology has been presented and

subsequently applied to the development of a light composite vehicle door (more

specifically, to an inner door panel). The door design has been optimized with respect to

its weight while meeting the requirements /constraints pertaining to the structural and

NVH performances, crashworthiness, durability and manufacturability. In the

optimization procedure, the number and orientation of the composite plies, the local

laminate thickness and the shape of different door panel segments (each characterized

by a given composite-lay-up architecture and uniform ply thicknesses) are used as

design variables. The methodology developed in the present work is subsequently used

to carry out weight optimization of the front door on Ford Taurus, model year 2001.

* Keywords: Multi-disciplinary Optimization, Automotive Engineering; Composite Structures; Altair Engineering Inc.

2

The emphasis in the present work is placed on highlighting the scientific and

engineering issues accompanying multi-disciplinary design optimization and less on the

outcome of the optimization analysis and the computational resources/architecture

needed to support such activity.

I. INTRODUCTION With continuously rising environmental demands and ever-tougher emissions

standards, lightweight engineering for the automobiles is steadily gaining in importance

as a viable technological avenue. Current efforts in the automotive lightweight

engineering involve at least the following five distinct approaches [1]: (a) Requirement

lightweight engineering which includes efforts to reduce the vehicle weight through

reductions in component/subsystem requirements (e.g. a reduced required size of the

fuel tank); (b) Conceptual lightweight engineering which includes the development and

implementation of new concepts and strategies with potential weight savings such as the

use of a self-supporting cockpit, a straight engine carrier, etc.; (c) Design lightweight

engineering which focuses on design optimization of the existing components and sub-

systems such as the use of ribs and complex cross-sections for enhanced component

stiffness at a reduced weight; (d) Manufacturing lightweight engineering which utilizes

novel manufacturing approaches to reduce the component weight while retaining its

performance (e.g. a combined application of spot welding and adhesive bonding to

maintain the stiffness of the joined sheet-metal components with reduced wall

thickness); and (e) Material lightweight engineering which is based on the use of

materials with a high specific stiffness and/or high specific strength such as aluminum

alloys and polymer-matrix composites or a synergistic use of metallic and polymeric

materials in a hybrid architecture (referred to as polymer metal hybrids, PMHs).

The development of a vehicle body-in-white (BIW) and its bolt-on components is a

very complex process, as the fulfillment of various, often-conflicting, functional

requirements has to be considered. Today, the development of the BIW and its

components is greatly facilitated by the use of computational engineering analyses and

simulations. Such analyses and simulations are at the core of the Multi-Disciplinary

Optimization (MDO) and Design of Experiments (DOE) tools, used to support the

3

process of finding “the best” design. Since the iterative evolution of the design topology,

size and shape can be formulated mathematically as an optimization problem, the

results of the associated computational optimization analyses can be used to guide the

design and facilitate the decision-making process. This, in principle, can lead to

significant cost reductions in at least three different ways [2]: (a) the design cycle may be

shortened resulting in reduced development time and costs; (b) the tooling and

manufacturing costs may be lowered leading to higher profit margins; and (c) the costs

of ownership of the product may be reduced leading to more cost-competitive products.

In their current practice, automotive OEMs and suppliers employ the design

optimization analyses, yet such analyses are typically concerned with either a single

engineering discipline or deal with different disciplines independently. Once the optimal

design(s) have been found, they have to be reconciled across all the relevant disciplines.

In most cases this procedure leads to significant design changes and unwanted

compromises. Hence, it is desirable to employ simultaneously all the participating

disciplines in the optimization process. It should be noted that, in general, the use of

design optimization methods and tools by the automotive OEMs and suppliers is greatly

affected by the availability of efficient, user-friendly commercial software with adequate

user-support service. For the optimization problems relying on the use of linear statics

and dynamics analyses, such software is available and fairly well supported. However,

if crashworthiness or manufacturability need to be considered as part of an MDO effort,

no algorithms are currently available to perform the required non-linear sensitivity

analyses, like the ones conducted within the linear optimization routines. Alternative

approaches based on response surface techniques have been proposed, nevertheless, in

order to handle non-linear optimization analyses. There is a variety of such approaches

and they differ with respect to the type of response surface, the method used to sample

the design space, the number (fixed number of pre-defined vs. sequentially-created set)

of design alternatives considered, etc.

In the present work, a novel use of HyperWorks, commercial CAE/MDO

software from Altair Engineering Inc. [3] is demonstrated. The software is used to

carry out a multi-disciplinary design optimization of a light-weight composite

4

passenger-vehicle door with respect to meeting structural and (Noise, Vibration and

Harshness) NVH performance requirements, crashworthiness, durability and

manufacturability. The starting point for design optimization is an existing all-metal

(inner shell/outer-shell) door. In the new design, the inner (initially metal) shell (panel) is

replaced with a composite-laminate alternative. The existing inner reinforcements

initially attached to the inner panel have been removed and their functionality restored

by introducing a spatial variation in the composite-panel thickness and in the (0o, +45o, -

45o, and 90o) ply/lamina thicknesses and orientations. The design optimization of the

replacement composite inner panel is carried out in two steps: (a) In the (first)

conceptual step, based on the sole use of linear structural and NVH analyses, the

number of composite-laminate patches (each characterized by a uniform distribution of

the 0o, +45o, -45o, and 90o ply/lamina thicknesses) and tentative locations of inter-patch

boundaries are determined; and (b) in the (second) detailed-design step, fully multi-

disciplinary (structural, NVH, crashworthiness, durability and manufacturability) size

and shape optimization analysis is carried out to determine the final ply thicknesses and

the location of patch boundaries. A schematic of the two-step optimization process is

depicted in Figure 1.

In the first optimization step, the Free Element Sizing (FES) composite-laminate

architecture/thickness optimization technique, developed by Altair Engineering Inc. [4],

was employed. The FES technique is quite similar to the well-established topology

optimization method [5] except for the fact that the shell-elements’ thicknesses and ply

thicknesses for composite lay-ups are used as design variables, in place of the material

density. In the second optimization step, HyperStudy software from Altair Engineering

inc. [6] is used. This software allows the set-up and the highly automated execution of a

multi-disciplinary optimization problem. In addition, HyperStudy offers Design of

Experiments (DOE) methods which can be used for screening of the design space and for

generation of the approximation models based on the Response Surface Method (RSM)

[7]. Consequently, the software enables the application of the global or local, single or

multi objective, non-linear optimization techniques on either the original (highly

computationally demanding) analyses or on the approximate models. Finally, several

5

resource management systems are available for the parallel execution of the MDO

analyses.

The main objective of the present work is to introduce the aforementioned two-

step MDO procedure and apply it to the case of a passenger-vehicle door inner panel

made of a carbon-fiber epoxy-matrix composite-laminate material. Within the first

(conceptual-design) step, the local laminate thickness (as well as the thicknesses of the

individual 0o, +45o, -45o and 90o laminas within the laminate) are determined, as well as

the number of composite patches (each characterized by a nearly uniform distribution

of the lamina thicknesses). Within the second (detailed-design) step, a fully multi-

disciplinary single-objective (mass) size and shape optimization analysis is carried out in

order to establish the final locations of the inter-patch boundaries (“weld lines”) and ply

thicknesses within each patch while meeting the structural, NVH, crashworthiness,

durability and manufacturability functional requirements/constraints.

The organization of the paper is as follows: Brief descriptions of the geometrical

model and the functional/performance requirements for the car door are presented in

Sections II.1 and II.2, respectively. More specific accounts of the conceptual and

detailed design optimization methods used in the present work are provided in Section

II.3. The results obtained in the present work are presented and discussed in Section

III. The main conclusions resulting from the present work are summarized in Section

IV.

II. COMPUTATIONAL PROCEDURE II.1 Geometrical Model of the Car Door

Within the present work, the front door of the Ford Taurus Model Year 2001 has

been considered. The mesh model for this door was obtained from the National Crash

Analysis Center website [8]. The model consists of the following 13 parts: (a) an outer

body trim; (b) a sheet-metal outermost panel; (c) a sheet-metal inner lower panel; (d) a

sheet-metal inner panel upper frame; (e) an upper reinforcement inner panel; (f) a

plastics molded inner panel; (g) an inner panel reinforcement; (h) a tailor-welded blank

inner panel; (i) a lower hinge mount; (j) a lower hinge bracket/arm; (k) an upper hinge

mount; (l) an upper hinge bracket/arm; and (m) a door bracket.

6

Adjacent parts are joined by having them share nodes or by either spot welds or

seam welding/adhesive bonding. A summary of the door parts considered their shell

thicknesses and materials, as well as the finite-element mesh details are given in Table 1.

An exploded view of the door is displayed in Figure 2. For improved clarity, some of the

parts are omitted in Figure 2.

II.2 Performance Requirements for the Car Door In this section, a list of performance targets (constraints) for the light composite

vehicle door is defined. These targets are obtained by first carrying out a series of

structural, NVH, crashworthiness and durability analysis using the original door design.

The results of these baseline analyses were then used as the performance targets for the

new design. In other words the new door design had to be lighter than the original

design while performing at least as well as the original design. In the remainder of this

section a more detailed description is provided for each of the specific performance

targets.

II.2.1 Structural Performance Requirements

The structural performance requirements for a car door typically include the

conditions which the door must meet with respect to its frame rigidity and sag

resistance. The two requirements pertain to the ability of the door to withstand without

excessive outward deflection of an interior/exterior pressure difference associated with

aerodynamic effects at high vehicle speeds and the ability of the door to withstand its

weight, respectively without excessive downward deflection.

To define quantitatively the two structural requirements for the door, the

following two linear structural finite-element analyses were conducted: (a) The closed

door has been fixed on one side at the locations of its hinges and on the other at the

location of its lock and a uniform pressure of 5.8kPa applied over the interior surface of

the door. The pressure of 5.8kPa was obtained in a separate CFD (Computational Fluid

Dynamics) analysis in which the outer shell of the entire (rigid) body of the Ford Taurus

(model year 2001) was moving in the forward direction at a speed of 100 km/h. No

further details of this analysis will be provided; and (b) the door is fixed only at the

7

locations of its hinges and subjected to the gravitational load. In both cases the

maximum displacements were recorded. In case (a), a maximum deflection in y-

direction of 15mm was found, while in case (b) a maximum displacement in the z-

direction of 0.18mm was found. These values are then used as the optimization

constraints for the composite car door. The coordinate system used throughout this

paper was defined as follows: x-direction coincides with the length, y-direction with the

width, z-direction with the height of the vehicle. The results obtained for the structural

analyses (a) and (b) are summarized in Figures 3(a)–(b), respectively.

II.2.2 Noise Vibration Harshness (NVH) Requirements

The noise, vibration and harshness requirements for the car door were defined by

determining the lowest natural vibrational frequency for the door in the close position.

Toward that end, an eigen-value analysis of the closed car door was conducted and the

eigen-modes and their corresponding eigen-frequencies obtained using the Lanczos

numerical eigen-solver [10]. The lowest natural frequency for the closed door was found

to be 30.7Hz and the corresponding modal shape is displayed in Figure 4. The lowest

natural frequency for the composite car door is then required to be at least 30.7Hz.

II.2.3 Crashworthiness

The crash worthiness functional requirement for the car door pertains to the

door’s ability to protect the driver/passenger in the case of a side impact collision.

Typically these requirements are defined as a maximum inward intrusion allowed under

different side-collision scenarios, and there are a number of regulations (in US, Europe,

Japan, etc.) mandating and defining in detail the side-collision crash requirements for

the door. Since the emphasis of the present work is on demonstrating the potential of

the MDO approach and not on complying with specific vehicle-safety regulations, a

simple “single-scenario” (i.e. one crash loading case) crashworthiness analysis was

carried out. In such an analysis, the bumper of the same vehicle (with an addition mass

of 1,500kg attached to it) is driven into the car door at an incident angle of 30 degrees

and at an initial velocity of 25km/h. The maximum inward intrusion at the interior

panel of the car door was found to be 223.5mm and this (maximum intrusion) value is

defined as the crashworthiness functional requirement for the composite-laminate car

8

door. An example of the results obtained in the crashworthiness analysis is displayed in

Figure 5.

II.2.4 Durability Requirements

While durability of an automotive component/sub-assembly is generally

controlled by either the damage inflicted to it or by corrosion of failure due to

cyclic/fatigue loading, only the fatigue-controlled durability will be considered in the

present work. This is justified by the fact that the component in question is an inner

door panel and, thus, is not usually exposed to common corrodants (rain, snow, road

salt, etc.). In addition, as is generally observed, durability of the inner door panel will be

assumed to be controlled by fatigue–induced failure of its spot welds to the connecting

door components and not by the failure of the panel itself. The durability of the metal

door inner panel will, hence, be defined by the number of loading cycles before the first

evidence of fatigue-induced failure is observed in any of its spot welds.

Resistance spot welding is nowadays the predominant joining technique in the

automotive industry. The components of the BIW are typically made of thin sheet metal

that are connected using spot-welded joints (i.e. spot welds). To create a spot weld, two

or more sheet-metal components are pressed between two electrodes and an electric

current is passed through. The resulting Joule resistance heating and the pressure

applied via the electrodes give rise to local fusion/welding. No filler material is used in

the spot welding process. Three distinct regions with different material properties can

generally be identified in a spot weld: (a) a cylindrically- shaped weld nugget; (b) a

surrounding heat-affected zone; and (c) the base sheet metals. Due to the applied

pressure by the electrodes, the thickness of the nugget is generally smaller than the

combined thicknesses of the spot welded components. The change in weld thickness at

the edges of this so-called “nugget indentation” typically gives rise to stress

concentrations at the indentation edges. In addition, stress concentrations are present at

the root of the notch created by spot welded components. The places associated with

stress concentrations are likely places where the initiation of durability-controlling

fatigue cracks takes place.

Two spot-weld fracture modes are generally observed: (a) “Interfacial or nugget

9

fracture”, i.e. fracture of the weld nugget along the plane of the weld (predominantly

observed in small (<2mm) diameter spot welds; and (b) “Nugget pullout” or “sheet

fracture” which involves fracture of the sheet metal around the weld that leaves the

nugget intact (predominantly observed in large-diameter spot welds). Since small-

diameter spot welds are quite deficient relative to their load-carrying and energy-

absorbing capabilities, large-diameter (ca. 5mm) spot welds are typically used in

automotive industry. Spot welds of this diameter are used in the present work.

A review of the literature shows numerous fracture-mechanics [e.g. 28],

structural-stress analysis [e.g. 29] and numerical analysis [e.g. 30] based efforts aimed at

fatigue-life predictions for spot welded joints. The predictions of these efforts were

subsequently correlated at different levels of success with experimental fatigue-test

results. Fatigue durability of the spot welds is modeled in the present work using the

equivalent structural stress approach proposed by Kang [27]. Within this approach, the

maximum equivalent (von Mises) structural stress at the edges of the weld nugget,

σeq,max (MPa), is directly related to the fatigue life of the spot welded joint, Nf (cycles), as:

Nf = 2.8·1019σeq,max-5.94.

Cyclic loading experienced by a car door is quite complex and depends on a

number of factors such as: (a) the source of loading, e.g. engine vibrations, wheel

vibrations, etc.; (b) vehicle driving speed; (c) surface condition of the road; (d) the way

the door is mounted to the BIW frame, since the loads diffuse into the door through its

contacts with the frame; etc. A detailed (multi-scenario) fatigue-based durability

analysis is beyond the scope of the present work. Instead, a single-scenario (i.e. a single

loading case) analysis is carried out in order to include durability into the MDO

analysis. Within this approach, the door is fixed at the locations of its hinges and twisted

along an axis parallel with the x-direction and passing through the center point of its

lock. Contour plots displayed in Figures 6(a)-(b) are provided to help understand the

nature of the cyclic loading used in the present work.

Since the present door design has passed the durability requirements, these are

replicated by computing the total number of loading cycles experienced by the car door

during its lifetime. In such calculations it was assumed that: (a) the vehicle at hand has

10

six cylinders; (b) total mileage=270,000km; (c) average vehicle speed=80km/h; (c)

average engine speed=2500rpm. The computation yielded 1.5 billion cycles. From the

fatigue-life equation given above, the maximum equivalent stress corresponding to this

fatigue life is computed as σeq,max=54MPa. Next, a static finite element analysis is carried

out to determine the torsional angle which has to be applied to the all-metal car door so

that the maximum value of the equivalent stress at the most highly-stressed spot weld is

equal to this value. The analysis was conducted using Abaqus/Standard finite-element

code [15] since this software enables the definition of spot welds as deformable

connectors with their own material properties and the range of influence in the

surrounding sheet metal. To account for the fact that the yield strength in the nugget

may be up to three times higher than in the base metal, a conservative increase of 50%

in the yield strength was used for the spot welds. A torsional angle of 3 degrees is

obtained. Finally, the durability requirement for the composite-laminate car door is

defined as the condition that the door must endure 1.5.109 cycles of torsional loading

described above without failing when subjected to the 3-degree torsion.

II.2.5 Manufacturability Requirements

Since in the present MDO analysis, the replacement of the initially metal inner

panel with a composite-laminate alternative is considered, the original all-metal door

design can not be used to define the manufacturability requirements for the new design.

Instead, it is recognized that the composite inner panel will be made by a Resin Transfer

Molding (RTM) process and that it will be made of an epoxy-matrix composite material

reinforced with 50-60% carbon-fiber plies/laminas. Furthermore, it is recognized that

the local composite-laminate thickness and architecture affect the permeability of the

carbon-fiber preform with respect to resin flow through it during the mold-filling stage

of the RTM process.

Taking all these facts into consideration and assuming that the “standard” RTM

processing conditions (the specification given in Section II.3.2) is used,

manufacturability requirements are defined as: (a) the filling stage of the RTM process

should result in a completely filled preform and (b) the RTM weld lines (places where

the converging resin flow fronts meet) located in the areas where the stress-levels

11

experienced by the panel during the crashworthiness analysis are the lowest (to ensure

that the detrimental effect of RTM weld lines on the inner-panel crashworthiness

performance is minimal).

II.3 Multi-disciplinary Design Optimization of the Car Door The design-optimization process for the light composite car door has been divided

into two distinct steps: (a) a conceptual design step whose main objective was to help

identify the number of composite patches(each patch is characterized by a unique set of

four (0o, +45o, -45o and -90o) composite-ply thicknesses and to define preliminary

boundaries (“weld boundaries”) between the patches; and (b) a fully-multi-disciplinary

size and shape detail design optimization step used to define the final set of ply

thicknesses within each patch and the final position of patch boundaries. A schematic of

the two-step optimization procedure used in the present work is depicted in Figure 1. In

the remainder of this section, a more detail account is provided for the two design

optimization steps.

II.3.1 Conceptual-design Optimization Step

Within this step, the free element sizing (FES) technique implemented into the

linear optimization computer program OptiStruct from Altair Engineering Inc. [9] has

been used. Within the FES technique, the thicknesses for each of the four (0o, +45o, -45o

and 90o) ply thicknesses for each shell element are considered as design variables.

However, the optimization procedure implemented in the FES technique does not

consider single-ply thicknesses in different elements as completely independent

variables, since such an approach would make the optimization procedure intractable

due to a large number of design variables. Instead, the variation of each of the four ply

thicknesses is represented using a continuous (field) functions, and the coefficients in

these functions are, in fact, used as design variables. The number of these function

coefficients is substantially smaller than the number of shell elements making the FES

optimization procedure not only feasible but also computationally very efficient. To

further clarify the FES technique, it could be stated that it is essentially analogous to the

well established topology optimization method [5] except that ply-thicknesses are used as

12

design variables in place of the material density. While the FES technique implemented

in OptiStruct is highly computationally efficient, it can currently be utilized only for the

optimization problems relying on the linear computational analyses. Consequently, only

the (linear-analyses based) structural and NVH functional requirements could be

considered within the conceptual design stage. The remaining (crashworthiness,

durability and manufacturability) requirements are addressed in the detailed design

step. In the remainder of this section, a more detailed account is provided for the FES

technology.

As stated above, within the conceptual design stage, the FES technique [4] is

utilized to determine the local composite-laminate make-up (i.e. the thickness of 0o, +45o,

-45o and 90o laminas) and the boundaries between different laminate patches, where a

patch is defined as a segment of the laminate which contains a nearly uniform

distribution of the thicknesses of laminas of a given (0o, +45o, -45o and 90o) type.

Furthermore, the FES method utilizes the concept of a super-ply (a subset of plies

located within the same element and having the same 0o, +45o, -45o or 90o orientation).

The super-ply concept thus significantly reduces the number of plies in the model. Also,

as the super-ply thicknesses are varied in the conceptual-design optimization step, the

process of ply addition or removal is simulated. Moreover, the solver package

OptiStruct [9] within which the FES method is implemented allows a shell-element

formulation which effectively homogenizes the stiffness matrix associated with each

super-ply uniformly throughout the element thickness. This process is analogous to

dividing each super-ply into infinitely-thin plies and mixing the infinitely-thin plies into

a homogeneous ply-less composite material. A schematic of the super-ply concept and

the subsequent homogenization process is depicted in Figure 7.

The results obtained in the conceptual-design optimization step are shown in

Figures 8(a)-(d) in which distributions of the four (0o, +45o,-45o and 90o) ply thicknesses

are displayed, respectively. It should be noted that unlike most of the previous figures,

Figures 8(a)-(d) show only the composite-laminate inner panel (and not all the door

components). The results displayed in Figures 8(a)-(d) are next used to partition the

composite-laminate inner panel into a number of patches (within each of which, the

13

thickness of individual plies will be kept constant). While this process requires

subjective engineering judgment and a larger number of patches more realistically

approximate the conceptual-design optimization results, seven patches were selected in

the present work in order to keep the number of design variables reasonable. The

partitioning of the composite-laminate inner panel into seven patches is displayed in

Figure 9.

II.3.2 Detailed-design Optimization Step

Within the detailed design step, the final-design (size and shape) optimization

procedure is applied to the car-door composite-laminate inner panel. As stated

earlier, the objective of this optimization procedure was to minimize the car-door

weight, while meeting all the structural, NVH, crashworthiness, durability and

manufacturability requirements, as defined in Section II. 2. To carryout the MDO

analysis at hand, the HyperStudy optimization toolbox from Altair Engineering Inc.

[6], was used. HyperStudy enables the set-up of an MDO analysis through the

definition of design variables (and their ranges) as well as of the system responses

(used to define the objective function(s) and the constraints). In addition, a Design of

Experiments (DOE) analysis can be carried out within HyperStudy in order to

either: (a) identify the design variables which have a minor to negligible effect on the

system responses and could be, hence, eliminated from the design-variables list used

in the MDO analysis; and/or (b) to construct approximate models (i.e. the response

surfaces) for the system responses.

Within HyperStudy, the HyperOpt module was used in the present work.

HyperOpt enabled automatic execution of the highly-complex MDO analyses

employing the following solvers: (a) OptiStruct [9] to carry out structural and NVH

analyses; (b) Radioss, a transient non-linear dynamic finite-element program from

Altair Engineering Inc. [11] to conduct the crashworthiness analysis; (c) Matlab, a

general-purpose mathematical package from MathWorks Inc. [12] and

Abaqus/Standard, a non-linear finite-element program from Abaqus Inc. [15] to

execute an in-house developed durability analysis program; and (d) Moldflow

14

Plastics Insight, a general purpose plastics processing program from Moldflow Inc.

[13] to carry out resin transfer molding of the car-door inner panel. The execution

of the MDO analyses was orchestrated by HyperStudy in such a way that the design

variables are varied automatically (following directions of a pre-selected

optimization algorithm) to optimize the car-door composite inner panel with respect

to its (minimal) weight, while ensuring that all the (structural, NVH,

crashworthiness, durability and manufacturability) constraints are met. The overall

geometry of the composite inner panel is kept identical to its metal counterpart,

except for the (local) patch thicknesses and geometries. In other words, the patch

thicknesses (more specifically the four laminas thicknesses within each patch are

defined as the design size variables while the weld boundaries (the boundaries

separating neighboring patches) are defined as the shape variables. To define the

weld boundaries as the design shape variables, HyperMorph module within

HyperMesh pre-processing program from Altair Engineering Inc. [14] was used.

This module enables the weld boundaries to be defined as shape functions while the

number of nodes (but not their coordinates) and the nodal connectivity are retained.

In other words, as the boundaries between the patches are repositioned during the

MDO analysis, the same (initial) finite-element mesh is morphed to prevent excessive

distortions of the elements. The shape variables applied to the composite-laminate

patch boundaries consist of both linear and harmonic shape variables. The

HyperMorph tool within HyperMesh enables the user to specify a family of harmonic

functions [14] which can be superimposed to allow increased generality of the evolved

geometry.

The starting point in the detailed MDO analysis is the conceptual design

obtained in Section II.3.2. When the complete set of multi-disciplinary analyses was

applied to this design, the so-called base-line (also known as the “nominal run”)

response of the system was obtained. Then, an Adaptive Response Surface

optimization algorithm is employed to guide the search of the design space in the

attempt to continue to improve the design of the card door. A flow chart of the

15

detailed design optimization step is given in Figure 10.

In the remainder of this section, more details are provided regarding each of

the five analyses used in the MDO procedure.

Structural Analysis

Structural analysis of the car door was conducted in the present work using

the standard small-strain linear-elastic finite element analysis as implemented in

OptiStruct. Within such an analysis, the meshed finite-element model is subjected to

boundary conditions, concentrated and/or distributed loads and the resulting system

of linear algebraic equations (defining the mechanical equilibrium) solved for the

nodal displacements and reaction forces. In the two structural analysis carried out

in the present work, surface (in the case of frame-rigidity analysis) and

(gravitational) volume (in the case of door-sagging analysis) distributed loads were

used.

NVH Analysis

As mentioned earlier, the NVH analysis entailed determination of the lowest

natural frequency of the car door. This was accomplished by using the Lanczos

algorithm, an iterative algorithm that is an adaptation of power method for finding

eigen-values and eigen-vector of a square matrix or the singular value decomposition of

a rectangular matrix [e.g. 16]. The power method is first used for finding the largest

eigen-value of a matrix. After the first eigen-vector/value is obtained, the algorithm is

successively restricted to the null space of the known eigen-vectors to get the other

eigen-vector/values. In practice, this simple algorithm does not work very well for

computing a large number of the eigen-vectors because any round-off error will tend to

degrade the accuracy of the computation. Also, the basic power method typically

converges slowly, even for the first eigen-vector. Lanczos algorithm is a modification of

the basic power algorithm in which each new eigen-vector is restricted to be orthogonal

to all the previous eigen-vectors. In the course of constructing these vectors, the

normalizing constants used are assembled into a tri-diagonal matrix whose most

significant eigen-values quickly converge to the eigen-values of the original system.

16

Crashworthiness Analysis

The crashworthiness analysis of the car door has been carried out using the

dynamic-explicit non-linear finite element method as implemented in Radioss [11].

The analysis was conducted by prescribing zero-velocity boundary conditions to the

car door at the locations of door hinges and the lock. The (other vehicle) bumper

(with a 1,500kg added mass) was rotated about the vertical z-axis and its vertical

plane of symmetry position at an angle of 30 degrees with respect to the longitudinal

vertical plane of symmetry of the vehicle and imparted an initial velocity of 25km/h.

To model the contact and friction between the bumper and the outer panel as well as

between various parts of the door during crash, a parts interaction option is used.

For each pair of contacting parts, the interaction option is based on the definition of

a master surface (belonging to one part) and slave nodes (belonging to the other

part). The master surface and slave nodes are used to compute the interaction gap

between the contacting parts, and can both belong to the same part for modeling self-

interactions. Standard values for the part-interaction parameters are used [17] and

sensitivity of the crashworthiness results to variations in these parameters was not

investigated. Particular attention was given, however, to developing and using the

appropriate material models which can capture materials behavior under dynamic,

large strain conditions involving plasticity and damage initiation and evolution. A

detailed account of the material models used in the crashworthiness analysis is

presented in the Appendix.

Durability Analysis

While the predominant joining mode in all-metal car door is spot welding

(supplemented by seam welding), the introduction of a composite-laminate inner panel

in the new door-design will necessitate the use of alternative joining technology,

primarily adhesive bonding and riveting. Durability of metal/composite adhesively-

bonded and mechanically-fastened joints is an area of intensive current interest [e.g. 18].

Fatigue life predictions of such joints are based on either interfacial fracture

mechanics approach [e.g. 18] or using a cohesive-zone formalism [e.g. 19]. In the present

17

work, the cohesive-zone formulation is adopted and the effect of rivets is included only

implicitly. In other words, joints between the composite-laminate inner panel and thread

joining components will be treated as adhesively bonded, but the cohesion-zone stiffness

and strength parameters of the joint will be increased in order to account for the effect

of the rivets. Such an approach was developed in our recent work [20] and hence, will

not be discussed in great details here.

The composite/metal joints have been modeled in the present work using the

“cohesive zone framework” originally proposed by Needleman [21]. The cohesive zone is

assumed to have a negligible thickness when compared with other characteristic lengths

of the problem, such as the composite-laminate/sheet-metal wall thicknesses, or the

characteristic lengths associated with the stress/strain gradients. The mechanical

behavior of the cohesive zone is characterized by a traction–displacement relation,

which is introduced through the definition of an interfacial potential. The perfectly

bonded composite-laminate/sheet-metal joint is assumed to be in a stable equilibrium, in

which case the interface potential has a minimum and all tractions vanish. For any

other configuration, the value of the potential is taken to depend only on the

displacements discontinuities across the joint interface. The interface potential initially

proposed by Socrate [22] is used in the present work. Within the finite-element

durability analysis carried out here, cohesive elements available in Abaqus/Standard

were used to represent the adhesive-bonded composite-laminate/sheet-metal joints. A

detailed account of this approach including the assessment of the initial (intact) cohesive

zone parameters and their finite element implementation can be found in our recent

work [20].

To assess fatigue-induced reduction in stiffness and strength of the cohesive zone,

a detailed finite element study of composite-laminate/sheet-metal adhesively-bonded

double cantilever beams was carried out in our recent work [20] and the results

compared with the experimental cyclic-loading data from Ref. [18]. To obtain a fatigue

life vs. maximum joint-interface equivalent stress relation, the joint is assumed to have

failed when the crack length exceeds 1 cm, and the interface has failed locally when the

composite-laminate/sheet-metal normal separation exceeds 100μm. The fatigue-life

18

predictions are found to be affected by the choice of these two parameters, but the effect

was relatively weak. A more detailed account of the procedure used to quantify fatigue-

controlled durability of adhesively-bonded composite-laminate/sheet-metal joints can be

found in Ref. [20]. While the procedure presented in Ref. [20] was found to yield

realistic results, it was not implemented in the present work due to its high

computational cost. Instead, a simpler procedure (producing comparable results)

presented below is used.

The interface potential used in the present work contains four parameters: (a) a

(normal) decohesion strength, σn ; (b) a (normal) critical interface separation distance, δn

; (c) an interface shear strength σs: and (d) a critical interfacial displacement, δs.

Following our previous work [20], σn /σs ratio is assumed to remain constant as the

adhesion bonding degrades with time, while δn and δs remain constant. Consequently,

only a fatigue-induced decrease of σn needs to be specified in order to account for the

loss of interfacial strength of adhesively-joined components with time in service.

Following the analysis presented in our previous work [20], the following recursive

relation was adopted: ( ) 7.14nnnn FC σσσ =Δ , where nσΔ is a loss of adhesion strength

per one loading cycle, C is a constant and nF normal interface traction. The formula is

solved for nF , subjected to the constraint that failure (defined by the condition nnF σ= )

will occur after 1.5 billion cycles. For the initial value MPan 40=σ (includes

contributions of the adhesive and the rivets), it was found that if MPaFn 7.12≤ , the

adhesively-bonded joint sill survive 1.5 billion cycles. Consequently, MPaFn 7.12≤ (in

any of the interfacial cohesive elements) was defined as the durability requirement for

the composite-laminate car door.

Manufacturability Analysis

As mentioned earlier, the composite-laminate door inner panel analyzed in the

present work is expected to be fabricated using Resin Transfer Molding (RTM). RTM

is a liquid thermosetting-polymer composite molding process in which the chemical

reaction in the resins are thermally activated by heat from the mold wall and fiber mat

19

(preform). The reaction rate in RTM processes is relatively slow allowing a longer fill

time at lower injection pressure. The resulting light-weight, high-strength material is

widely used in variety of automobile components. In the RTM process, dry fiber

reinforcements, or fiber preform, is packed into a mold cavity which has the shape of

the desired part. The mold is then closed and resin is injected under pressure into the

mold where it impregnates the preform. After the mold-fill cycle, the cure cycle begins,

during which the mold is heated and resin polymerizes to become rigid plastic.

The greatest benefit of RTM relative to other polymer-based composite

manufacturing techniques is the separation of the injection and cure stages from the

fiber-preform fabrication stage. In addition, RTM also enables high levels of

microstructural control and part complexity compared with processes like injection

molding and compression molding. Additional benefits offered by RTM include: low

capital investment, good surface quality, tooling flexibility, large and complex shapes,

relatively large range of reinforcements.

Fabrication of the car inner panel using the RTM process has been modeled in

the present work using the Reactive Molding module of the Moldflow Plastics Insight

6.1 [13]. Reactive Molding provides important information used to detect various

molding problems and to optimize part, mold, and molding process. Specifically,

insights can be gained into how the mold fills in the presence of fiber reinforced

preforms, whether short shots due to pre-gelation of the resin can occur, the locations of

potential air traps or weld lines, selection of the proper molding machine size, and

evaluation of different reactive resins.

Within Reactive Molding module, mold filling in the presence of fiber mat

reinforcements is modeled by Darcy's Law [e.g. 13]. Darcy's Law states that the flow

velocity at a given point, in a given direction, is proportional to a negative of the

component of pressure gradient in that direction. The proportionality constant is a

ratio of permeability of the porous medium and viscosity of the fluid, where

permeability quantifies the ability of a fluid to flow through a porous medium. The

numerical method used is based on a hybrid finite-element/finite-difference method for

solving the governing mass, momentum and energy conservation equations for pressure,

20

flow rates, and temperature, and a control-volume method is used to track moving resin

fronts. Resin viscosity is calculated as a function of temperature, the extent of cure and

shear rate. Resin curing kinetics is also included in both the calculations dealing with

flow dynamics and with temperature.

In the RTM process involving preform, resin is forced to flow through the porous

preform. Since the composite laminates used in the present work are expected to be

stitched or woven, the preform structure will generally be two-dimensional and

anisotropic. Consequently, in terms of the pore-area distribution, the preform will show

a maximum in one in-plane direction and a minimum in the direction at right angles to

the first direction. When resin flows through such a preform, the flow in the direction of

maximum pore area advances more quickly, because it encounters less resistance. In

other words, permeability will be larger in the first than in the second direction.

Consequently, permeability becomes a 2 by 2 [K11 K12; K21=K12 K22] matrix quantity.

In the RTM computational analysis carried out in the present work, un-filled

epoxy resin EMC CEL-9200-XU (LF) from Hitachi Chemical [13] was used. The

following general and thermal properties of this material were adopted: density -

1.23g/cm3; specific heat - 975J/kg.K and thermal conductivity-0.97W/m.K in the

analysis, a reactive viscosity model [23] was used which states that:

( )( )α

ααα

τγη

ηγαη21

1

*0

0

)(1

)(,,CC

g

gnT

TT+

− ⎟⎟⎠

⎞⎜⎜⎝

−⎟⎠⎞

⎜⎝⎛+

=&

& (1)

)exp()(0 TTBT b=η (2)

where η is the viscosity (Pa·s); γ& the shear rate (1/s), T the temperature (K), α the

degree of cure (0-1) and n, t*, B, Tb, C1, C2, and ag (gelation conversion) are material-

specific coefficients whose values for EMC CEL-9200-XU (LF) are given in Table 2.

To calculate the curing behavior of EMC CEL-9200-XU (LF), the N-th order

(Kamal's reaction) kinetics model [24] is used. Within this model, the reaction kinetics

is defined by the following relations:

21

dα/dt = (K1 + K2αm) (1 - α)n (3)

K1 = A1exp(-E1 / T) (4)

K2 = A2exp(-E2 / T) (5)

where α is the degree of cure (0-1), T temperature (K), t time (s), and m, n, A1, A2, E1 and

E2 are material-specific constants. The model also includes induction time (i.e. the period

before curing starts to take place) which is calculated using the following equation:

tz = B1exp(B2/T) (6)

where tz is the induction time, B1 (s) and B2 (K) material-specific constants. A summary

of the reaction kinetics model parameters for EMC CEL-9200-XU (LF) is given in Table

3.

The RTM analysis was carried out under the following recommended processing

conditions: (a) initial resin temperature - 323K; (b) mold surface temperature - 453K;

(c) ejection conversion - 0.5; (d) cooling rate- -0.3333 K/s; (e) nominal injection time - 5s;

(f) curing time - 30s; (g) maximum machine injection pressure - 20MPa; and (h)

intensification ratio - 10.

In the present work it was assumed that individual plies are made of carbon

roving (consisting of 6000 439THTA fibers from Cramer) weaved into a 5H satin fabric

and stitched using Titre 150 polyester thread. Such plies were investigated in the work

of Talvensaari et al. [25], who measured their permeability as a function of the stitching

pattern, ply-stacking sequence, and stitching-thread tension level. The following typical

permeability values corresponding to 0o plies, cross-stitched at a 10mm x 10mm line

spacing and an average thread tension of 5N obtained in Ref. [25] were used:

K11=1.4.10-11 m2, K22=0.9.10-11m2 and K12=K21=0 m2.

II.3.3 Optimization and Parameter Study

The multi-disciplinary optimization problem studied in the present work falls

into a class of engineering optimization problems in which the evaluation of an objective

function(s) or constraints requires the use of structural and manufacturing-process

simulation analyses. The design objectives for structural (load-bearing) automotive

22

components are the fulfillment of certain expectations with respect to the components’

weight, cost, functionality and appearance. The design problem can, for example, be

formulated as weight minimization subject to the cost, performance, manufacturability

and aesthetics constraints. In a compact form, the optimization problem can be

symbolically defined as:

• Minimize the objective function f(x),

• subject to the non-equality constraints g(x)< 0,

• to the equality constraints h(x) = 0, and

• to the condition that design variables x belong to a domain (design space) D.

where, in general, multiple non-equality and equality constraints are present making

g(x) and h(x) vector functions. The design variables x form a vector of parameters

usually describing the geometry and/or the material(s) of a product. For example, x,

f(x), g(x) and h(x) can be product dimensions, product weight, a stress condition defining

the onset of plastic yielding, and constraints on product dimensions, respectively.

Depending on the nature of design variables, its domain D can be continuous (e.g. a

continuous range of the length of a bar), discrete (e.g. the standard gage thicknesses of a

plate or the existences of structural member in a product), or the mixture of the two.

Furthermore, an engineering optimization may have multiple objectives, in which case

the objective function, f(x), becomes a vector function. Objective and constraints are

evaluated using different (multi-disciplinary) computational analyses.

The solution of an optimization problem involves multiple iterations through the

following steps:

1. An initial design is first selected;

2. The initial design is analyzed by evaluating its objective function(s) and

constraints;

3. Fulfillment of the constraints is examined and if the requirements are not met,

changes are made in the design and the procedure repeated starting with step 2.

Otherwise, an optimal design has been found and the optimization procedure is

terminated.

23

The selection of a new design in Step 2 is usually done using one of the following

two approaches:

(a) Design variables are updated along a “search direction” in the design space.

The search direction is obtained using the design sensitivities (partial derivatives of the

objective and constraints functions with respect to the design variables at a given point

in the design space). Such design sensitivities are typically computed as part of the

multi-disciplinary analyses used to evaluate the objective and constraints functions. In

this approach, the objective and constraints functions are essentially linearized around

the current design and it is assumed that only small changes in the design occur in each

optimization iteration. Typically very few evaluations of the objective and constraints

functions are necessary and the result is a local “optimal” design; and

(b) Higher-order algebraic-function approximations (typically referred to as

“Response Surfaces”) are constructed to represent functional relationships between the

objective and the constraints equations, on one end, and the design variables, on the

other. Response surfaces are normally obtained by employing a parametric study (i.e.

the Design of Experiments approach) in which design variables (i.e. designs) are selected

by sampling the design space in accordance with a given sampling scheme [31] and the

objective and constraints functions are evaluated for each design. In response surface

functions, the terms depending on the value of a single design variable are commonly

referred to as “effects” while those depending on the values of two or more design

variables are referred to as “interactions”. Once response surfaces are generated for

the objective and constraints equations, they can be treated as a proxy for the design

model at hand and used in the multi-disciplinary optimization procedure. The

optimization problem is then solved using mathematical programming and the result

represents an approximate solution. This approach enables identification of the optimal

design in a very efficient manner with out a need for running additional

computationally-expensive multi-disciplinary analyses (beyond those used in the

construction of the response surfaces). The response surface approach is usually

employed for the highly non-linear problems and/or in the cases in which the design

space is too large. After response surfaces for the objective and constraints functions

24

are constructed, they are examined and, if necessary, the search/design domain is

redefined. Then a parameter study procedure can be invoked again the whole

procedure repeated until convergence is reached. An alternative response-surface

method called “The Adaptive/Sequential Response Surface Method” [2] (used in the

present work) is also available, Within this method, the response surface is updated

after each optimization iteration which, typically, results in a smaller number of

functional evaluations relative to that needed in the ordinary response-surface method,

making the former approach computationally more efficient.

In addition to helping create the response surfaces, parameter studies are also

useful in reducing the number of design variables to be used in the optimization

analysis. Reducing the number of design variables to no more than ten is highly critical

since some computational analyses, like crashworthiness analyses, are associated with

computational times of several hours. To reduce the number of design variables, the so-

called “Screening Design of Experiments” approach can be employed to identify the

design variables which have large effects on the objective and constraints functions and,

hence, should be considered in the optimization analysis.

In the present work, (Screening) Design of Experiments approach, parameter

studies and the Adaptive Response-Surface method are combined within HyperStudy to

carry out multi-disciplinary optimization of a car door with respect to meeting the

weight, structural, NVH, crashworthiness, durability and manufacturability

requirements. As explained earlier, HyperStudy provides interfaces to different solvers

enabling multi-disciplinary optimizations to be performed.

III. RESULTS AND DISCUSSION III.1 Conceptual Design

As mentioned earlier, within the conceptual design, the car-door composite-

laminate inner panel is optimized with respect to its weight while meeting the structural

(frame-rigidity and sagging-resistance) and NVH requirements as defined in Sections

II.2.1 and II.2.2, respectively. The FES optimization method was used within which the

thicknesses of the four (0o, +45o, -45o and 90o) ply-types within each inner-panel finite

25

element were used as design variables. The results of this optimization step are

displayed in Figures 8(a)-(d) in which the spatial distributions of the four-ply

thicknesses are shown. It should be recalled that composite-laminate lay-out (i.e. the

stacking sequence of the plies) is not considered. Rather, plies are homogenized into a

monolithic composite laminate. The conceptual design for the car-door inner panel

represented by the ply-thicknesses distributions displayed in Figures 8(a)-(d), meets all

the structural and NVH requirements while having a ~16% lower mass than its metal

counterpart. The computational analysis employed was found to be quite efficient and a

typical conceptual-design optimization run took about 20min to complete and entailed 7

iteration steps.

The conceptual design displayed in Figures 8(a)-(d) needs to be modified before it

can be subjected to the detailed design optimization procedure. More specifically, the

regions of the inner-panel characterized by nearly uniform ply thicknesses of the four

plies are defined as composite patches. In the detailed-design optimization step, the plies

within each patch will have uniform thicknesses. These thicknesses are used as size

design variables while the boundaries between the adjacent patches are used as shape

variables within the detailed design optimization step. Furthermore, to ensure an

orthotropic character of the composite laminate, the thicknesses (i.e. the numbers) of the

+45o and -45o plies are constrained to remain the same.

To keep the number of design variables in the detailed-design optimization step

relatively low, the composite-laminate inner panel is partitioned into 7 patches. The

shapes of the initial patches are depicted in Figure 9.

III.2 Detailed-design Optimization As explained earlier, within the detailed design optimization step, not only the

structural and NVH requirements, but also crashworthiness, durability and

manufacturability requirements are considered. These requirements were identified in

Sections II.2.3 through II.2.5 and II.3.2. The position of the composite-laminate inner-

panel inter-patch boundaries obtained at the end of the detailed-design optimization

step is displayed in Figure 11. The thicknesses of the three (0o, +45o/-45o and 90o) plies in

each of the composite patches are also displayed in this figure. The extent of adjustment

26

of the inter-patch boundaries can be obtained by comparing the results displayed in

Figure 11 with the starting inner-panel design shown in Figure 9.

The optimal design displayed in Figure 11 needs all the structural, NVH,

crashworthiness, durability and manufacturability requirements. This can be seen in

Figures 12-14.

In Figures 12(a)-(b), it is seen that the maximum y-displacement resulting from

the 5.8kPa pressure is lower than 15mm (the frame-rigidity requirement), while the

gravity-induced z-component is lower than 0.18mm (the sagging-resistance

requirement). In order to help visual comparisons between the results displayed in

Figures 3 and 12, the same displacement contour levels were used.

The lowest natural frequency of the door was found to be 30.8Hz and is, thus,

effectively identical to its counterpart in the all-metal door. In other words, the final

design of the composite-laminated inner panel was controlled by the condition that the

NVH requirement must be met. This finding is consistent with the fact that the low

density of the composite-laminate material reduces the structural frequencies.

The results presented in Figure 13 show that the maximum inward intrusion

resulting from the crash is lower than 223.5mm (the crashworthiness requirement).

Again, in order to help visual comparison between the results displayed in Figures 5 and

13, the same displacement contour levels were used.

The maximum normal traction nF was found to satisfy the durability

requirement MPaFn 7.12≤ . Furthermore, since in a number of cohesive elements nF

was found to be ca. 12.5MPa, it appears that the durability requirement also plays a

dominant role in controlling the final design of the composite-laminate inner panel.

Finally, as can be seen in Figure 14(a), under the standard RTM processing

conditions, the infiltration of the carbon-fiber perform is complete. Thus the

manufacturability constraint is also satisfied. The corresponding orientation of the 0o

plies in the panel is displayed in Figure 14(b). The results displayed in Figure 14(a) also

show that the resin flow is balanced (ensuring minimal post-curing distortions), that the

weld lines are equally spaced (ensuring a fairly uniform distribution of potential resin-

infusion flaws) and that the number of (undesirable) air traps is relatively small. All

27

these findings suggest that the optimized composite-laminate inner panel is not only

manufacturable under the standard process conditions, but also that its structural

integrity and performance/reliability should be quite high.

The weight of the composite laminate inner panel resulted from the detailed-

design optimization process is 5% lower than its metal counterpart. This weight

reduction is somewhat lower than that obtained at the end of the conceptual design

stage. This finding is consistent with the fact that the detailed-design optimization is

subjected to additional constraints i.e., crashworthiness, durability and

manufacturability constraints and the number of design variables is lower (due to the

fact that the thickness of each ply within a given patch was kept uniform and that the

numbers of the +45o and -45o plies was kept the same within a given patch).

The present detailed-design multi-disciplinary optimization problem was solved

on a PC with 16GB RAM and two four-core CPUs (each having a 3GHz clock speed).

Upon the completion of the optimization-study set up, it took around 11 hours to obtain

the final optimal design, Figures 11-14. As mentioned earlier, however, the multi-

disciplinary optimization analysis presented in this work is highly simplified since single

scenarios (i.e. single loading conditions) are used to describe particular functional

requirements (e.g. frame rigidity) and the definition of crashworthiness, durability and

manufacturability were greatly oversimplified. Nevertheless, in the present work an

attempt was made to identify and model some of the most critical scientific and

engineering phenomena and concepts which currently limit the viability of the MDO

analyses (e.g. consideration of component-joints fatigue controlled durability, proper

modeling of materials under large deformation/high strain-rate conditions and

consideration of manufacturability within the design process. While there are many

examples of the MDO analyses applied to automotive components, they are mostly

concerned with NVH and crashworthiness requirements and with all-metal components.

Inclusion of the additional concepts presented in the present work in the multi-

disciplinary design optimization of structural automotive components is considered by

the present authors as highly critical before the MDO can be expected to become a

viable design alternative.

28

IV. SUMMARY AND CONCLUSIONS Based on the results obtained in the present work, the following summary and

main conclusions can be made:

1. A two-step multi-disciplinary optimization procedure is proposed and

applied to the design of a car-door composite-laminate inner panel. Within the first

(conceptual-design) step, the free element sizing method is used while, within the second

(detailed-design) step, an adaptive response surface method is used to obtain a weight

optimized design which meets specific structural, NVH, crashworthiness, durability and

manufacturability constraints.

2. The work revealed the variety and the complexity of concepts (particularly

those related to components joining, durability and manufacturability) which must be

included into comprehensive multi-disciplinary optimization analysis.

3. The use of HyperStudy computer program is demonstrated in setting up and

running in an automatic manner a multi-disciplinary optimization analysis which

employs a large number of linear and non-linear structural-mechanics finite-element

codes, durability prediction algorithms and manufacturability-process simulation

software.

4. While some of the aspects of the multi-disciplinary optimization were

oversimplified, the approach showed, nevertheless, the potential of composite materials

to reduce the weight of automotive structural components.

V. ACKNOWLEDGEMENTS The material presented in this paper represents an extension of the work

conducted as a part of the project “Lightweight Engineering: Hybrid Structures:

Application of Metal/Polymer Hybrid Materials in Load-bearing Automotive

Structures” which was supported by BMW AG, München, Germany.

29

APPENDIX: MECHANICAL MATERIAL MODELS For the structural, NVH and durability analyses carried out in the present work,

mechanical response of the materials at hand could be handled using simple (isotropic,

in the case of metals and plastics, or orthotropic, in the case of composite laminates)

linear elastic material models. In the case of crashworthiness analysis, however,

material non-linearities associated with plastic deformation and damage had to be taken

into account. Toward that end, material-specific relations between the flow variables

(pressure, stress, mass density, internal energy density, etc.) had to be specified. These

relations typically involve: (a) an equation of state; (b) a strength equation; and (c) a

failure equation for each material. These equations arise from the fact that, in general,

the total-stress tensor can be decomposed into a sum of a hydrostatic-stress (pressure)

tensor (which gives rise to a change in the volume/density of the material) and a

deviatoric-stress tensor (which is responsible for the shape change of the material). An

equation of state is used to define mass-density (specific volume) and internal energy

density (temperature) dependencies of the pressure. A strength model, on the other

hand, combines yield criterion (the condition which must be met for elastic deformation

to take place), a (plastic) flow rule (an equation defining the relative amounts of the

plastic strain components) and a constitutive (strength) relation (an equation which

defines the effect of plastic strain, the rate of deformation, and the temperature on

material strength). Material degradation and failure are governed by a failure material

model which describes the (hydrostatic or deviatoric) stress and/or strain conditions

which, when met, cause the material to fracture and lose (abruptly, in the case of brittle

materials or gradually, in the case of ductile materials) its ability to support tensile and

shear stresses. In the following, a brief description is given of the models for the

materials utilized in the present work, i.e. steel, short glass-fiber reinforced

thermoplastics and carbon-preform reinforced epoxy-matrix composite.

A.1 Steel and Reinforced Thermoplastics The material models for various grades of steel and reinforced thermoplastics

includes a linear equation of state, a von Mises yield criterion, the Prandtl-Reuss

30

associated flow rule, a Johnson-Cook strength model, and a Johnson-Cook ductile-

failure model. Since a detailed account and parameterizations of these material models

was given in our recent work [32], no further details will be presented here.

A.2 Carbon-preform Reinforced Epoxy-matrix Composite Laminates

Before the material model for the carbon-preform reinforced epoxy-matrix

composite laminates is presented, it should be noted that this material is assumed to be

orthotropic (i.e the numbers of +45o and -45o plies are equal) with the three principal

material directions coinciding with the in-plane 0o-direction, the in-plane 90o-direction,

and the through-the-thickness direction, respectively. The model presented in the

remainder of this section is an extension of the material model for E-glass reinforced

ply-vinyl-ester-epoxy composite laminates developed in our recent work [33]. The

development of this model includes two distinct steps: (a) the development of the

mechanical model for a single ply/lamina; and (b) the development of the composite-

laminate material model using a homogenization procedure and the material model

developed in (a).

A.2.1 Material Model for a Single Ply

Equation of State

A polynomial equation of state is used whose functional form is:

( ) ( ) ( )

( ) d

dd

CCC

CCCCCCeBBAAKP

33332313

22322212113121110103

32

2

31

31

31

ε

εερμμμμ

++−

++−++−−+−+−= (A1)

where P is pressure, K the bulk modulus, 0

1ρμρ

⎛ ⎞≡ −⎜ ⎟

⎝ ⎠ the compression, ρ density, ρ0

initial density, e mass-based internal energy density, Cij’s the material stiffness

coefficients (coefficients of the material 6x6 stiffness matrix), dije ’s the components of the

deviatoric strain matrix, and A2, A3, B0, B1 are material-specific parameters. The last

term on the right hand side of Eq. (A1) represents the coupling between pressure and

the deviatoric strain and is absent in isotropic materials.

31

For an orthotropic material, the bulk modulus K is defined as:

( )[ ]312312332211 291 CCCCCCK +++++−= (A2)

Furthermore, the mass-based internal energy density e is defined as:

( )v refe C T T= − (A3)

where Cv is the constant-volume specific heat, T is temperature and Tref is a reference

temperature.

Strength Model

While the equation of state allows the computation of the pressure evolution

during loading, the strength material model enables the entire stress tensor to be

updated during the loading. During each computational time increment, a material can

undergo either elastic deformation or a combination of elastic and plastic deformations.

A yield criterion is used to assess if the material’s response is elastic or elastic/plastic.

The yield criterion used in the present work is based on a total-stress nine-parameter

parabolic yield function in the form:

Raaa

aaaaaaf ij

=+++

+++++=21266

23155

22344

33111333222322111223333

22222

21111

222

222)(

σσσ

σσσσσσσσσσ (A4)

where σij’s represent stress components, while aij’s and R represent material specific

parameters.

It should be noted that one of the parameters in Eq. (A4) can be set

independently. It is customary to let a22=1 so that R is numerically equal to the square

of in-plane transverse yield (flow) stress of the composite material. As indicated in Eq.

(A4) parameter R can, for strain-hardening materials, increase with an increase in the

magnitude of the equivalent plastic strain, p

e .

To determine if the material’s response will be elastic or elastic/plastic during a

given time step, the following procedure is implemented:

32

(a) First it is assumed that the material’s response is purely elastic, and the

corresponding increments in the stress components are given by the linear elastic

relationship in the form:

⎥⎥⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢⎢⎢

ΔΔΔΔΔΔ

⎥⎥⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢⎢⎢

=

⎥⎥⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢⎢⎢

ΔΔΔΔΔΔ

12

31

23

33

22

11

66

55

44

332313

232212

131211

12

31

23

33

22

11

000000000000000000000000

eeeeee

CC

CCCCCCCCCC

σσσσσσ

(A5)

where Δ is used to indicate incremental quantities, and eij’s represent (total) strain

components;

(b) The stress increments are added to the corresponding stress components and

Eq. (A4) is used to evaluate the yield function f; and

(c) If 0f < , the material response is elastic and the updated stress components

are retained. Otherwise, the material response is elastic/plastic and the updated stress

components are used as “elastic predictors” for the new material stress state.

To update the stress components during an elastic/plastic loading time step, a

procedure based on the Prandtl-Reuss associated flow rule is utilized, according to

which the increments in the plastic-strain components are defined as:

pij

ij

fde d δλδσ

= (A6)

where the scalar parameter dλ is generally referred to as “plastic strain-rate multiplier”.

It should be noted that according to Eq. (A6), the vector of the incremental plastic strain

is normal to the surface defined by the yield function f.

The procedure for updating the stress state during an elastic/plastic loading

increment involves the following steps:

(a) A yield surface is constructed through the “elastic predictor” stress state;

(b) The stresses are relaxed along a direction which is orthogonal to the yield

surface defined in (a), in accordance with the normality plastic flow rule, Eq. (A6). The

extent of this stress relaxation is proportional to the magnitudes of the incremental

33

plastic-strain components, which according to Eq. (A6), scale with dλ ;

(c) Simultaneously, the original yield surface is expanded due to associated effect

of strain-hardening on the magnitude of ( ) ( )p p p

oR e R e de= + , where subscript o is used to

denote a quantity at the end of the previous time step. It can be readily shown that the

increment in the effective plastic strain, p

e , is defined as:

( )228

3p

de fdλ= (A7)

Since both the magnitude of the stress relaxation and the size of the yield surface

depend on dλ , an iterative procedure is set up to determine dλ for which the relaxed

stress state lies on the updated yield surface. The increase in the magnitude of ( )p

R e

with an increase in the magnitude of the effective plastic strain is defined in the present

work using a piece-wise linear strain-rate insensitive material constitutive relation; and

(d) When the relaxed stress state falls on the updated yield surface, the final

stress state for an elastic/plastic loading step is attained.

In summary, the strength material model for the carbon-preform reinforced

epoxy-matrix composite laminates involves a total-stress six-parameter parabolic yield

criterion, an associated plastic flow rule and a piece-wise linear strain-rate invariant

material constitutive relation.

Failure Model

Once a material reaches the condition for damage initiation, the stress state in

such elements is subsequently updated using a failure model rather than a strength

model. The orthotropic softening failure model used in the present work, however, has a

lot of mathematical similarities with the strength model discussed in the previous

section. That is the orthotropic-softening failure model includes: (a) a failure initiation

criterion; (b) a (damage) flow rule; and (c) a material degradation constitutive relation.

Twelve material-specific parameters (6 failure initiation stresses and 6 corresponding

fracture energies) are used to define the failure model at hand. The six stress/fracture-

energy components are associated with the six basic failure modes: tensile failure in 11,

34

22 and 33 directions, and shear failure in 23, 31 and 12 directions. The relationship

between the failure stress and the corresponding fracture energy, Gf, for a single mode

of failure is shown schematically in Ref. 34, Figure 2.

Past the point of failure initiation, the relationship between the stress and strain

is assumed to be linear. Consequently, a maximum “crack strain” maxcre is defined as a

ratio 2 /f fG Lσ , where L is the characteristic dimension of the computational-cell

undergoing fracture [34]. In other words, a crack strain is introduced which defined the

extent of material (damage induced) deformation past the point of failure initiation. The

ratio max/cr cre e for a given mode of failure is generally denoted as the extent of material

damage, D, and D=0 at failure initiation and D=1.0 at complete failure.

The damage initiation (continuation) criterion is defined separately for the three

principle-direction material planes as:

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

2 2 2

2 1311 1211,

11, 11 12, 12 13, 13

2 2 2

2 2322 1222,

22, 22 12, 12 23, 23

2

2 33 2333,

33, 33 23, 23

11 1 1

11 1 1

1 1

ff f f

ff f f

ff f

gD D D

gD D D

gD D

σσ σσ σ σ

σσ σσ σ σ

σ σσ σ

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + + ≥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟− − −⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= + + ≥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟− − −⎝ ⎠ ⎝ ⎠ ⎝ ⎠

⎛ ⎞ ⎛= +⎜ ⎟ ⎜⎜ ⎟− −⎝ ⎠ ⎝ ( )

2 2

31

31, 31

11f D

σσ

⎞ ⎛ ⎞+ ≥⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟−⎠ ⎝ ⎠ (A8)

A flow rule analogous to that and in the strength model is used to define the

components of the crack-strain increments as;

,ij crij

gde dλσ∂

=∂ (A9)

To update the stress state at the end of a time increment for a “failed” material

element, a similar iterative procedure to that discussed in the previous section is used to

determine the value of dλ. That is, the elastic-predictor stress state is relaxed along a

direction which is orthogonal to the corresponding failure surface (the surface passing

through the point associated with the elastic-predictor stress state). Simultaneously, the

35

failure surface is updated (shrunk) due to a damage-softening effect. That is, for a given

value of dλ, components of the crack strain increments are calculated using Eq. (A9),

and used to update the corresponding crack-strain components. The latter are, in turn,

used to update the corresponding damage parameters, Dij’s. The updated Dij’s are

finally used in Eq. (A8) to determine the new location of the failure surface. At this

point the relaxed stress state lies on the updated failure surface as required. A

schematic of this procedure for the 11-plane type failure is depicted in Ref. 34, Figure 3.

In summary, the orthotropic-softening damage model for the carbon-preform

reinforced epoxy-matrix composite laminates includes parabolic stress-based damage

initiation criteria (one criterion for each material principal direction), a normality flow

rule and a linear damage-induced softening constitutive relation for each failure mode.

A.2.2 Material Model for the Composite Laminate

Once the mechanical model for the individual plies is developed, it is used to

define the corresponding material model for the composite laminate. Within the

approach used in the present work, the effect of the number of 0o, +45o, -45o and 90o

plies is taken into account but not their stacking sequence. Since the details of such

“homogenization” procedure can be found in our recent work [34], only the main points

will be discussed here. The procedure used is as follows:

(a) Since the thicknesses of all types of plies are assumed to be the same, they can be

used to determine the corresponding, volume fraction of each ply;

(b) For scalar quantities (e.g. P), a simple volumetric rule of mixture is used to

determine such quantities for the composite laminate from the corresponding quantities

of the individual plies; and

(c) Tensorial quantities (e.g. the (6x6) elastic stiffness matrix, [C], the (6x6) matrix of

yield-function coefficients, aij, etc.) are first transformed as:

[ ] [ ] [ ][ ])()(1)()( kkkk TCTC −= (A10)

where )(kT is a (6x6) transformation matrix which is a function of the orientation

relationship between the laminate and the k-th ply, and [ ])(kC and [ ])(kC are the stiffness

matrices of the k-th ply before and after the transformation. After the transformation is

36

imposed to all types of plies, the volumetric rule of mixture is applied to [ ] sC k ')( .

In the present case, there are only four types (0o, +45o, -45o and 90o) of plies and,

in order to ensure that the composite laminate behaves as an orthotropic material, the

volume fractions (i.e. the numbers) of +45o and -45o plies are kept the same.

A.3 Parameterization of Material Models The values of the material parameters for various steel grades and reinforced

thermoplastics are summarized in Table 1. As far as the material model for the carbon-

preform reinforced epoxy-matrix composite laminates is concerned, it was

parameterized using a variety of available experimental data. The material-model

parameterization procedure used as well as the values of the parameters obtained will

be reported in a future correspondence.

37

REFERENCES 1. M. Grujicic, V. Sellappan, G. Arakere, N. Seyr and M. Erdmann, " Computational

Feasibility Analysis of Direct-Adhesion Polymer-To-Metal Hybrid Technology for Load-Bearing Body-In-White Structural Components," Journal of Materials Processing Technology, accepted for publication, May 2007.

2. U. Schramm, “Multi-Disciplinary Optimization for NVH and Crashworthiness,” Altair Engineering Inc., Troy, MI, 2007.

3. “HyperWorks, User Manual”, Altair Engineering, Inc. www.altair.com 4. P. Cervellera, M. Zhou, U. Schramm, “Optimization Driven Design of Shell

Structures Under Stiffness, Strength and Stability” 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janerio, 30 May - 03 June, 2005, Brazil.

5. K. Suzuki and N. Kikuchi, “A Homogenization Method for Shape and Topology Optimization,” Comput. Methods Appl. Mech. Eng., 1991, 9(3), pp. 291-318.

6. “ HyperStudy, User Manual”, Altair Engineering Inc., Troy, MI, 2007. 7. E. Taguchi, Introduction to Quality Engineering. (White Plains, 1986). 8. National Crash Analysis Center. www.ncac.gwu.edu. 9. “OptiStruct, User Manual”, Altair Engineering Inc., Troy, MI, 2007. 10. B. N. Parlett, “The Symmetric Eigen value Problem”, Prentice-Hall, Englewood

Cliffs, New Jersey, 1980. 11. “Radioss 5.1, User Manual”, Altair Engineering Inc., Troy, MI, 2007. 12. “Matlab 8.0, User Manual”, MathWorks Inc., www.mathworks.com . 13. “Moldflow Plastics Insight 6.1, User Manual”, MoldFlow Corporation,

www.moldflow.com 14. “Altair HyperMesh, User Manual”, Altair Engineering Inc., Troy, MI, 2007. 15. “Abaqus 6.6, User Documentation”, ABAQUS Inc., Rising Sun Mills, Providence,

RI, 2006. 16. C. Lanczos, “An Iteration Method for the Solution of Eigen Value Problem of Linear

Differential and Integral Operators,” J. Natn. Bur. Stand., 45, 255-282, 1987. 17. M. Grujicic, B. Pandurangan, I. Haque, B. A. Cheeseman and R. R. Skaggs, " A

Computational Analysis of Mine Blast Survivability of a Commercial Vehicle Structure," Multidiscipline Modeling in Materials and Structures, accepted for publication, February 2007.

18. R. Yuuki, J. Liu, J. Xu, T. Ohira and T. Ono, “Evaluation of the fatigue strength of adhesive joints based on interfacial fracture mechanics,” Japan Society of Materials Science, 41, 467, 1299-1304.

19. A. D. Crocombea, Y. X. Hua, W. K. Loh, M. A. Wahab and I. A. Ashcroft,

38

“Predicting the residual strength for environmentally degraded adhesive lap joints” International Journal of Adhesion and Adhesives, 26, 5, 325-336, 2006.

20. M. Grujicic, V. Sellappan, M. A. Omar, N. Seyr and A. Obieglo, "Computational Analysis of Injection-molding Residual-stress Development in Direct-adhesion Polymer-To-Metal Hybrid Body-In-White Components," Journal of Automobile Engineering, submitted for publication, July 2007.

21. A. Needleman, "A Continuum Model for Void Nucleation by Inclusion Debonding ,” J. Appl. Mech., 54, 525-531, 1987.

22. S. Socrate, “Mechanics of Microvoid Nucleation and Growth in High-strength Metastable Austenitic Steels,” PhD thesis, Massachusetts Institute of Technology, 1995.

23. C. W. Macosko, RIM: Fundamentals of Reaction Injection Molding, Hanser Gardner Publications, New York, April 1989.

24. S. Sourour, and M. R. Kamal, “Differential Scanning Calorimetry of Epoxy Cure: Isothermal Cure Kinetics,” Thermochimica Acta, 14, 1976, 41-59.

25. H. Talvensaari, E. Ladstätter and W. Billinger, “Permeability of Stitched Preform Packages Composite Structures,” Composite Structures, 71, 3-4, 371-377, December 2005.

26. M. Grujicic, G. Arakere, L. Mears, N. Seyr and M. Erdmann, " Application of Topology, Size and Shape Optimization Methods in Polymer Metal Hybrid Structural Lightweight Engineering," Multidiscipline Modeling in Materials and Structures, submitted for publication, April 2007.

27. H. T. Kang, “Fatigue Prediction of Spot Welded Joints Using Equivalent Structural Stress,” Materials & Design, 28, 3, 837-843, 2007.

28. Y. Chao, “Ultimate strength and failure mechanism of resistance spot weld subjected to tensile, shear or combined tensile/shear loads,” J. Eng. Mater. Tech.-Trans. ASME, 125, 125–132, 2003.

29. S. V. Thillo, “Puntlasmodelleringen voor structuurdynamische analyses,” Master's Thesis, Department of Mechanical Engineering, Katholieke Universiteit Leuven, Division PMA, Leuven, Belgium, June 2004.

30. M. Palmonella, M. Friswell, J. Mottershead and A. Lees, “Finite element models of spot welds in structural dynamics: review and updating,” Comput. Struct., 83, 8-9, 648-661, 2005.

31. D. M. Grove, and T. P. Davis,, Engineering, Quality and Experimental Design. (Longman, 1997).

32. M. Grujicic, B. Pandurangan, I. Haque, B. A. Cheeseman and R. R. Skaggs, "A Computational Analysis of Mine Blast Survivability of a Commercial Vehicle Structure," Multidiscipline Modeling in Materials and Structures, accepted for publication, February 2007.

39

33. M. Grujicic, B. Pandurangan, U. Zecevic, K. L. Koudela and B. A. Cheeseman, "Ballistic Performance of Alumina/S-2 Glass Fiber-Reinfoced Polymer-Matrix Composite Hybrid Light Weight Armor Against Armor Piercing (AP) and Non-AP Projectiles," Multidiscipline Modeling in Mateials and Structures, 3, pp. XXX-XXX, 2007.

34. M. Grujicic, W. C. Bell, L. L. Thompson, K. L. Koudela and B. A. Cheeseman, "Ballistic-Protection Performance of Carbon-Nanotube Doped Poly-Vinyl-Ester-Epoxy Composite Armor Reinforced with E-glass Fiber Mats ," Material Science and Engineering, accepted for publication, May 2007.

40

Table 1. Geometry, Mesh and Materials Used in the Original Ford Taurus Model Year 2001 Front Left Door: E -Youngs Modulus (GPa), ν – Poisson’s Ratio; σy – Yield Strength (MPa)

Number of Shell Elements Material Thickness

mm Part Number Part Name

3-Node 4-Node

1 Outer Body Trim 5 346 Thermoplastics: E=2.8; ν=0.3; σy=45 2.0

2 Sheet-metal Outermost Panel 54 5826 Steel:

E=210; ν=0.3; σy=240 1.1

3 Sheet-metal Inner Lower Panel 423 4761 Steel:

E=210; ν=0.3; σy=300 1.2

4 Sheet-metal Inner Panel Upper Frame 22 970 Steel:

E=210; ν=0.3; σy=300 1.2

5 Upper

Reinforcement Inner Panel

140 1562 Thermoplastics: E=2.8; ν=0.3; σy=45 4.8

6 Plastics Molded Inner Panel 247 4585 Thermoplastics:

E=2.8; ν=0.3; σy=45 2.31

7 Inner Panel Reinforcement 15 153 Thermoplastics:

E=2.8; ν=0.3; σy=45 2.9

8 Tailor-welded Blank Inner Panel 196 1854 Steel:

E=210; ν=0.3; σy=340 1.2

9 Lower Hinge Mount 3 47 Steel: E=210; ν=0.3; σy=300 4.4

10 Lower Hinge Bracket (Arm) 4 69 Steel:

E=210; ν=0.3; σy=300 4.4

11 Upper Hinge Mount 5 73 Steel: E=210; ν=0.3; σy=300 4.4

12 Upper Hinge Bracket (Arm) 6 73 Steel:

E=210; ν=0.3; σy=300 4.4

13 Door Bracket 1 35 Steel: E=210; ν=0.3; σy=300 1.14

41

Table 2. Reactive Viscosity Model Parameters for EMC CEL-9200-XU (LF) Epoxy Resin from Hitachi Chemical

Parameter

Unit Value

n N/A 0.6941

τ Pa 7.327.10-5

B Pa.s 0.3812

Tb K 5366

D3 K/Pa 0.0

C1 N/A 0.108

C2~ N/A 3.332

Gelation Conversion N/A 0.5454

42

Table 3. N-th Order Reaction Kinetics Model Parameters for EMC CEL-9200-XU (LF) Epoxy Resin from Hitachi Chemical

Parameter

Unit Value

H J/kg 0.6941

m N/A 0.07329

n N/A 1.103

A1 1/s 10000

A2 1/s 1.227.108

E1 K 26820

E2 K 9790

43

FIGURE CAPTIONS

Figure 1. Two-step multi-disciplinary optimization procedure used for redesign of the Ford Taurus model year 2001 front left door. Figure 2. Exploded view of the Ford Taurus model year 2001 front left door. Figure 3. Linear structural finite element analysis results obtained for (a) y-component of the displacement(used to define the door frame-rigidity functional requirement and (b) z-component of the displacement(used to define the door sagging resistance). Figure 4. The shape mode associated with the lowest natural frequency. Figure 5. (a) Simple collision analysis used to quantify the car-door crashworthiness; and (b) y-component of the displacement used to quantify inward intrusion during side collision. Figure 6. (a) Von Mises stress amplitude field plot projected onto the un-deformed door and (b) y-displacement field plot projected onto the (cyclic-loading) deformed door. Figure 7. (a) Initial laminate lay-out; (b) Super-plies; (c) Homogenized composite laminate. Figure 8. Distribution of ply thicknesses obtained in the conceptual-design optimization step of the inner panel: (a) 0o; (b) +45o; (c) -45o; and (d) 90o. Blue=0.3mm, Yellow=0.6mm, Red=0.9mm. Figure 9. Seven composite-panel patches defined after analyzing the results displayed in Figures 8(a)-(d). Figure 10. A flow chart of the detailed-design multi-disciplinary optimization procedure used in the present work. Figure 11. Seven composite-panel patches obtained after the application of the detailed-design optimization analysis. The numbers (e.g. 0.6/0.3/0.9mm) refer to the thicknesses of 0o, *45o/-45o and 90o plies rounded off to the nearest multiple of 0.3mm (the single-ply thickness). Figure 12. Detailed-design optimization results pertaining to the: (a) frame rigidity and (b) sagging resistance of the composite-laminate car door. Figure 13. Detailed-design optimization results pertaining to the crashworthiness of the composite-laminate car door. Figure 14. Detailed-design optimization results pertaining to manufacturability of the composite-laminate inner panel using the standard resin transfer molding process: (a) a mold-filling time contour plot (with weld lines and air traps indicated) and (b) orientation of the 0o plies throughout the composite laminate.

44

Figure 1. Two-step multi-disciplinary optimization procedure used for redesign of the Ford Taurus model year 2001 front left door.

Conceptual Design Step • Free Element Sizing Optimization Method • Element Ply Thickness Used as Design

Variables • Objective- Minimal Mass

Structural FEM Analysis - Optistruct

NVH Analysis - Optistruct

Structural FEM Analysis - Optistruct

NVH Analysis - Optistruct

Crashworthiness Analysis- Radioss

Durability Analysis - In-House Computer Program Implemented in Matlab and Abaqus

Manufacturability Analysis - Moldflow Plastics Insight

Detailed Design Step • Adaptive Response Surface Optimization

Method • Patch Ply Thickness and Weld Line Shapes

Used as Design Variables • Objective- Minimal Mass • HyperStudy Used to Automate MDO

45

Figure 2. Exploded view of the Ford Taurus model year 2001 front left door. Please see Table 1 for components identification.

2 3

4

5

6

7

8 9

10

11 12

4

2

3 6

5

7

9 10

11 12

8

46

Figure 3. Linear structural finite element analysis results obtained for (a) y-component of the displacement(used to define the door frame-rigidity functional requirement and (b) z-component of the displacement(used to define the door sagging resistance).

(a)

(b)

47

Figure 4. The shape mode associated with the lowest natural frequency.

(a)

(b)

30.7Hz

48

Figure 5. (a) Simple collision analysis used to quantify the car-door crashworthiness; and (b) y-component of the displacement used to quantify inward intrusion during side collision.

(a)

(b)

Bumper Door

49

Figure 6. (a) Von Mises stress amplitude field plot projected onto the un-deformed door and (b) y-displacement field plot projected onto the (cyclic-loading) deformed door.

(a)

(b)

50

Figure 7: (a) Initial laminate lay-out; (b) Super-plies; (c) Homogenized composite laminate.

(a)

(b)

0o

0o

0o

0o

90o- 45o

- 45o

+ 45o

+ 45o

0o

90o

- 45o

+ 45o

51

Figure 7. (Continued).

(c)

52

Figure 8. Distribution of ply thicknesses obtained in the conceptual-design optimization step of the inner panel: (a) 0o; (b) +45o; (c) -45o; and (d) 90o. Blue=0.3mm, Yellow=0.6mm, Red=0.9mm.

(a)

(b)

53

Figure 8. (Continued).

(d)

(c)

54

Figure 9. Seven composite-panel patches defined after analyzing the results displayed in Figures 8(a)-(d).

55

Figure 10. A flow chart of the detailed-design multi-disciplinary optimization procedure used in the present work.

Study Setup • Creation of a Study • Creation of the MDO Models • Identification of Design Variables • Execution of the Nominal Run • Identification of the Responses • Linking of the Design Variables • Sensitivity Analysis

Design of Experiments (DOE) • Creation of a DOE Study • Identification of Controlled Variables and

Interactions • Identification of Uncontrolled Variables and

Interactions • Selection of Responses • Execution of the DOE Runs • Extraction of the Responses • Post Processing

Approximation Models • Selection of the Type of Approximation • Definition of the Input Matrix • Definition of the Validation Matrix • Creation of the Approximation • Computation of the Residuals • Definition of the Trade-offs • ANalysis Of Variances (ANOVA)

Optimization Analysis • Definition of Design Variables • Identification of the Constraints • Identification of the Objective Function(s) • Post Processing

56

Figure 11. Seven composite-panel patches obtained after the application of the detailed-design optimization analysis. The numbers (e.g. 0.6/0.3/0.9mm) refer to the thicknesses of 0o, *45o/-45o and 90o plies rounded off to the nearest multiple of 0.3mm (the single-ply thickness).

0.9/0.6/0.6mm

0.6/0.9/0.9mm

0.9/0.9/0.9mm

0.6/0.9/0.9mm

0.6/0.6/0.9mm

0.6/0.3/0.6mm

0.9/0.6/0.6mm

57

Figure 12. Detailed-design optimization results pertaining to the: (a) frame rigidity and (b) sagging resistance of the composite-laminate car door.

(a)

(b)

58

Figure 13. Detailed-design optimization results pertaining to the crashworthiness of the composite-laminate car door.

59

Figure 14. Detailed-design optimization results pertaining to manufacturability of the composite-laminate inner panel using the standard resin transfer molding process: (a) a mold-filling time contour plot (with weld lines and air traps indicated) and (b) orientation of the 0o plies throughout the composite laminate.

(a)

(b)

Injection Port

Injection Port

Injection Port

Weld Line

Air Trap

Air Trap

0o Ply Orientation