Detail Part Optimization on the F-35 Joint Strike Fighter

American Institute of Aeronautics and Astronautics

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Detail Part Optimization on the F-35 Joint Strike Fighter

Robert M. Taylor*, Jason E. Thomas†, and Nicholas G. Mackaron‡ Lockheed Martin Aeronautics Company, Fort Worth, Texas, 76137

Shawn Riley§ Northrop Grumman Corporation, El Segundo, California, 90245

Martin R. Lajczok** Lockheed Martin Space Systems Company, Denver, CO, 80201

The F-35 Joint Strike Fighter (JSF) faced a substantial weight challenge during the design phase of the Short Take-off and Vertical Landing (STOVL) variant. Among the many weight reduction trade studies and initiatives executed during STOVL variant design, the F-35 Program applied structural optimization tools and methods to optimize load paths and sizing of structural detail parts to realize weight savings. The program applied topology, shape, and sizing optimization through finite element tools and focused on reducing the weight of compact fittings and flat metallic web panels. Parts with sufficient design freedom benefited substantially from methodical optimization. This paper outlines the optimization process employed on F-35 and its impact, providing several examples to illustrate process details.

I. Introduction The F-35 Joint Strike Fighter (JSF) faced a substantial weight challenge during the design phase of the Short

Take-off and Vertical Landing (STOVL) variant. The JSF Program Office (JPO), Lockheed Martin, and JSF partner companies aggressively pursued weight reduction initiatives to bring the design within weight targets because decisions made during aircraft development will be significant drivers of cost and performance through the life cycle of the aircraft. Major weight reduction trade studies executed during 2004 and 2005 addressed every aspect of the aircraft, including structural arrangement, materials, and requirements.

Pursuit of weight reduction has continued at the detail part level, where substantial effort has been made, through rigorous structural analysis and optimization, to understand load paths and weight-driving design parameters in each component. The F-35 Program instituted application of structural optimization tools and methods to optimize load paths and sizing of structural detail parts to realize weight savings.

The objective of this paper is to demonstrate the application of finite element based structural optimization tools to design of components on the F-35 Joint Strike Fighter and discuss the value, challenges, and opportunities for improvement that have been discovered through its application. Rather than dealing with more theoretical aspects of optimization algorithm and tool development, this paper focuses on the issues involved in implementing optimization tools and methods in a production aircraft development environment. First, the paper outlines issues in realizing the potential benefits of optimization and the authors’ view of how optimization fits into the structural design process. Next, the paper discusses the application of optimization tools and methods to F-35 structural components, providing specific examples to illustrate the processes used. Finally, the paper examines the downstream impact of the optimization process.

* Aeronautical Engineer, P.O. Box 748, MZ 6527, Fort Worth, TX 76101, AIAA Senior Member † Aeronautical Engineer, P.O. Box 748, MZ 6522 Fort Worth, TX 76101, AIAA Member ‡ Aeronautical Engineer, P.O. Box 748, MZ 6527 Fort Worth, TX 76101 § Aeronautical Engineer, One Hornet Way M/S 9A32/C3, El Segundo, CA 90245, AIAA Member ** Senior Staff Engineer, P.O. Box 179, Denver, CO 80201

47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Confere1 - 4 May 2006, Newport, Rhode Island

AIAA 2006-1868

Copyright © 2006 by Lockheed Martin Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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II. Realizing the Potential of Optimization While formal mathematical programming methods have existed for greater than a century and computational

implementations of these methods date to 19601, the practical application of optimization methods to reduce weight in real aircraft development still does not live up to its potential. A search of the Compendex database found 6103 titles containing the words “structural” and “optimization” published between 1969 and 2005. The literature is replete with studies applying optimization methods and technologies to hypothetical aircraft and aircraft components that demonstrate the weight saving or other performance benefits of using these methods and technologies. Conversely, comparatively few cases can be found of optimization methods and technologies applied to the development of actual flight hardware, although they have increased significantly in recent years. If the benefits are real, as evidenced by the large body of related literature professing such, why have optimization tools and methods not been institutionalized in production aircraft development processes?

Before addressing this question, it should be noted that significant progress in application of optimization methods and tools has been made in recent years. In 1981, Ashley2 surveyed literature, friends, colleagues, and specialists and found that the number of examples where optimization had been applied to work that had been incorporated in an actual flight vehicle “was painfully, perhaps shockingly small.” Ashley listed specific aeronautical applications of formal optimization, including aerodynamic and vehicle configuration, flight trajectories, air-to-air combat, guidance and control, static structures, and structural synthesis with dynamic and aeroelastic constraints.

Since the time of Ashley’s survey, computing capability and awareness of optimization methods have increased. Indeed, optimization has directly contributed to the success of actual flight vehicles in recent years and design tools now exist that facilitate the application of optimization methods. In particular, optimization methods have found application in meeting aeroelastic and aeroservelastic constraints and in taking advantage of these interactions. The field of multidisciplinary design optimization has attracted much research interest. For example, the X-293,4 used an aeroelastic tailored graphite epoxy forward swept wing, designed by advanced analytical and optimization tools. Recent years have seen development of tools for multidisciplinary configuration optimization, such as SBAAT.5

Successful aeronautical structural optimization application has been predominately sizing optimization.6 The work of Engelstad, Barker, and Ellsworth, unable to be cited in this paper, provides a good example. Topology and shape optimization have only recently seen application.7

While these examples show that progress is being made, they are far from fulfillment of the potential value to be gained from broad-based application of optimization tools and methods in production development processes. The major barriers to unlocking the value of optimization are now cultural and managerial in nature. Successful optimization in a production development environment, or value-added optimization, requires effective and efficient man-machine interaction, effective and efficient structural analyst-designer interaction, and process organization that promotes successful optimization.

First, value-added optimization requires effective and efficient man-machine interaction. Optimization works well when the problem is not too complex, when there is an overarching goal such as weight, and when the problem can be completely captured mathematically. The time-consuming nature of capturing a finite element based mathematical model demands an effective and efficient preprocessor, something that has been lacking until recent years, in order to be practical in a schedule driven development program. In reality, the problem can never be completely reduced to a determinate mathematical statement. Engineering judgment is always required to capture and apply non-analytical constraints and simplify the problem to make it tractable. Consequently, all optimization is inherently multidisciplinary; the optimizer must have knowledge of all constraints, either explicitly or implicitly, to arrive at a feasible solution. The human must ensure constraints not explicitly enforced in the optimization have been enforced implicitly through variable limits, through geometric definitions, or simply through application of good engineering judgment. Omission or poor formulation of even one constraint leads to undesirable effects and dismissal of the results as irrelevant.

Second, value-added optimization requires effective and efficient structural analyst-designer interaction with the optimization toolset. The true potential of optimization tools as applied to structural components is to achieve a lightweight part in a shorter time span. An experienced designer and structural analyst can probably do about as well in achieving minimum weight without using optimization tools. However, an effective optimization toolset will get to the minimum weight part faster. Culturally, structural analysts and designers are hesitant to give up control of part configuration and sizing to an automated tool, which they perceive happens with optimization tools. In fact, optimization tools give engineers a lever to more rapidly apply their knowledge, learn about the component, and make decisions to drive the part to minimum weight. Furthermore, the aerospace industry has developed a cultural impediment to value-added optimization since most aerospace companies grow specialized structural


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analysts and designers along different career paths, as necessitated by ever more sophisticated design and structural analysis toolsets. Effective optimization requires bridging these skills and toolsets, either through tight optimization interaction between the designer and structural analyst or development of individuals with more integrated skills and knowledge.

Finally, value-added optimization requires development process organization that takes advantage of optimization capability. Structural optimization is a synthesis activity and requires a cultural and process change to bring structural analysts into a synthesis role as optimizers. Optimization must be planned for at the right time in the development process or else it will not add value, will conflict with structural analysis work, duplicate effort, and will be resisted by all. This cultural and process requirement highlights Whitney’s observation that design is both an organizational and a technical process.8

III. Optimization in the Structural Design Process Realization of the potential value of optimization requires an understanding of the design process and where

optimization fits in this process. This section presents a simplified model of the aircraft structural design process, the optimization techniques available, and introduces the optimization strategy followed on the F-35 Program.

A. Structural Design Process For the purposes of this paper, the airframe structural design process can be represented in a simplified form by

three stages, as shown in Figure 1. At the upstream system level, layout and design entails determination of global structural configuration, preliminary sizing, and internal loads, all with a minimum level of detail. During downstream component final structural analysis, every part must be fully defined geometrically and checked at critical locations against criteria for static strength, stability, stiffness, durability and damage tolerance (DaDT), and any significant environmental or special considerations. In the middle is a stage where the detail component design is matured to arrive at a full geometric definition. During this phase, it is expected that the final part configuration is determined and preliminarily sized, although the sizing will be adjusted during component final analysis. If a required change to the configuration is discovered later during the component final structural analysis, it typically requires a lengthy iteration and can impact surrounding structure and systems.

Static Strength Stability

Durability & Damage Tolerance

ConfigurationPreliminary Sizing

Global Load PathsInternal Loads

Environmental Criteria

Global Synthesis TaskLoad Path Optimization

Analysis TaskOptimization LimitedCost High, Impact Low

Local Synthesis TaskComponent Configuration Optimization

System Level Layout and Design Component

Design MaturationComponent

Final Structural Analysis

Iterate from Parametric to Preliminary Sizing & Weight

Iterate from Parametric to Preliminary Sizing & Weight

Stiffness Criteria

Figure 1: Structural Design Process Stages

Optimization is inherently a synthesis activity and, ideally, optimization methods should be applied during the component design maturation phase when part synthesis occurs. During this phase, preliminary loads are available,


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critical constraints can be addressed while simplifying for detail driven criteria that can be addressed downstream (e.g. fillet radii driven by DaDT). Topology, shape, and sizing optimization methods can generate component configurations that have low risk of future configuration change, as required to complete the component design maturation phase. These optimization methods cannot of themselves be the final structural analysis because they include simplifying assumptions and are driven by finite element results, which, while frequently meaningful to the process, are not directly used for writing final margins.9 Additionally, the inclusion of constraints ordinarily not addressed until final structural analysis means that the sizing, and consequently the weight estimate, produced through the optimization process is of higher fidelity and will reduce the risk of expensive downstream iterations. The final component structural analysis that follows is, therefore, more likely to be a verification process rather than, as is typical, an iterative redesign process. This reduction of late cycle iterations yields reduced cycle time during component final structural analysis.

Optimization applied during the final component structural analysis phase may still save weight but, because optimization is a synthesis activity, it essentially recreates work already completed during the component design maturation phase. Consequently, much of the potential for cycle time reduction evaporates and organizational resistance to late cycle design changes impedes acceptance of potentially lighter weight components.

B. Optimization Techniques Three different optimization techniques, topology, shape, and sizing, have been applied to JSF parts and found to

be effective, each in its own way. Figure 2 shows notional examples of these three techniques. Topology optimization, shown in Box a) of Figure 2, seeks to determine the best arrangement of a limited volume of structural material within a given spatial domain to maximize some performance metric, typically stiffness. The Topology optimization employed on JSF uses the density method10,11, incorporated within commercial finite element software tools, wherein element density is treated as a design variable for each designable finite element. Through an iterative procedure, regions with high strain energy are allocated greater densities and regions with low strain energy have their densities reduced, thereby producing variable density results within the structural domain that indicate preferred structural layout.

t1

t3

t2

w

h

a)

b)

c)

Figure 2: Optimization Techniques

Shape and Size optimization methods used in this work employ gradient-based optimization algorithms12 incorporated within commercial finite element software tools. Shape optimization, shown in Box b) of Figure 2, adjusts boundary definitions in order to improve some performance metric, which is typically weight in structural


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optimization. The method employed on JSF involves definition of shape basis vectors by means of mesh morphing in the finite element preprocessor. These shape basis vectors are then used as design variables within the gradient-based optimization algorithm.

Size optimization, shown in Box c) of Figure 2, adjusts entries on finite element property cards to improve the weight performance metric. In this work, the thickness entry is primarily used to define design variables and reduce weight through the gradient-based algorithm. Because many aeronautical structures consist of built up shell configurations, this type of optimization has been most easily applied and has received the greatest application in the industry.

The general process of optimization followed on JSF involves the application of each of these three optimization techniques. Typically, the process begins with topology optimization to determine the load paths and configure the structure along these load paths. In topology optimization the standard objective is to minimize compliance while constraining allowable volume within a package space, which bounds the volume usable for structural material. This optimization technique typically does not address strength and stability constraints so no sizing is inferred, only relative stiffness trends that guide efficient material distribution. Subsequently, shape and sizing optimization are applied to adjust geometry and address strength and stability. As will be discussed, various iterations and combinations of these techniques have been used to address different types of parts in different environments and stages of maturity.

C. Applications of Optimization Methods on JSF On JSF, these optimization techniques have been applied primarily to metallic compact fittings but also to some

frames, brackets, and shell structures. These part classes were chosen after a 6-week investigation of optimization tools found that they could most conclusively and efficiently benefit from optimization. The key to enabling the use of optimization has been the availability of a preprocessing tool to reduce the overhead associated with optimization model setup.

Compact fittings benefit primarily from the application of topology optimization to study load paths within a compact structural domain. Use of topology optimization to determine the stiffest configuration results in more efficient use of material and a lighter weight part. The package space is tight and the loads and boundary conditions are relatively simple. Built-up shell structure is generally more difficult from a topology perspective because the resulting load paths are quite sensitive to surrounding stiffnesses and geometric connections (which were predetermined as of this stage of work). Additionally, optimization methods have some difficulty dealing with the buckling critical nature of built-up shell structure. Topology optimization algorithms have difficulty addressing buckling constraints13, which are often critical in built-up shell structure, and sizing optimization often requires the use of inertia relief, which precludes the application of buckling constraints, in order to balance internal loads.

Topology, shape, and sizing optimization of compact fittings on JSF has primarily used the Altair HyperWorks tool suite, developed by Altair Engineering Inc. Within this suite, the HyperMesh preprocessor provides efficient preprocessing facilities for the setup of optimization models and the OptiStruct linear finite element solver includes optimality criteria for topology optimization and gradient-based optimization algorithms for shape and size optimization. Additionally, limited sizing optimization has been executed using MSC NASTRAN.

IV. Optimization Processes Employed The optimization techniques described previously have been applied to numerous parts on JSF using various

combinations and iterations. The primary combinations of techniques used, in terms of the type of finite elements (solid or shell) and optimization technique (topology, shape, or size), are as follows:

Optimization Process 1: Solid Topology Optimization Process 2: Solid Topology, Shell Shape and Size Optimization Process 3: Solid Topology, Solid Shape Optimization Process 4: Shell Topology, Shell Shape and Size Optimization Process 5: Shell Size

While each of these processes aims to reduce weight and time, many factors influence which process is most appropriate for the part. The primary factor is the nature of the part. Prime candidates have complex geometry and load paths that are not visually obvious. A part highly constrained by surrounding parts and stay-out zones has its configuration determined for it. Since topology optimization cannot change these constraints, fewer interfacing parts essentially equates to a greater design space. The nature of the part also drives simplifying assumptions that can be made. F-35 has used shell model part representations whenever possible, even if the shell idealization is not valid in some local regions of the part, because of the far greater efficiency in running optimization studies using


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shell elements. Where necessary, these shell approximations are followed by solid finite element models to verify results. Another significant factor is the maturity of the part. Topology optimization adds value when engineers are looking for guidance either early on to configure the part or later in a part’s evolution to identify localized regions of material not heavily used. Shape and size optimization apply either as a downstream process after topology optimization or as a starting point when part maturity or constraints preclude any sort of reconfiguration from topology optimization. Finally, the personnel involved influence the process that is used. More experienced engineers may have an intuitive sense of load paths within a part’s package space, nullifying the value offered by topology optimization.

Examples of these five optimization processes are outlined in the sections that follow. All of the examples are compared against baseline part definitions as of the start of optimization to determine a weight savings. While there are variations in the level of maturity of each part prior to the start of optimization, the effort spent in optimization in all cases is three to four man weeks and the part leaves the optimization process with a preliminary design that has high probability of being at minimum weight.

A. Optimization Process 1: Solid Topology For schedule constrained compact fittings, focused topology optimization has been the simplest and quickest

tool. In these cases, a basic topology optimization provides insight into load paths within the package space and is followed by conventional methods for sizing the part by experience and manual analysis iteration. In the interest of time, no subsequent shape or size optimization is performed.

The example fitting shown in Figure 3 illustrates this process. After extensive part configuration work, as shown in Box 1 of Figure 3, the baseline part weight did not meet the weight target set for the part. The topology optimization model was set up by defining a package space, as shown in Box 2 of Figure 3, with solid tetrahedral elements. For solution efficiency, the topology optimization model uses first order tetrahedrons. This element choice is justified because the model’s goal is to provide relative stiffness trends rather than converged stress results, which would call for second order tetrahedrons. Loads and boundary conditions applied to this model were identical to those applied to the baseline configuration. This model used the typical topology optimization objective and constraint, which is to minimize global compliance subject to a volume fraction constraint.

11 22 33 44

1

2 3

4 5

Figure 3; Example of Optimization Process 1: Solid Topology


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Box 3 of Figure 3 shows the results from the topology optimization. As these results show, topology optimization does not generate a usable, sized part; rather, it provides load path information to guide part configuration, indicating where structural connections should be made and where material can most effectively be removed. For this fitting, the topology results suggested feet with bathtub fittings that had not been considered previously. The configuration suggested by these results was interpreted and developed into a new solid model definition, as shown in Box 4, using rule-of-thumb sizing.

Finally, a p-version finite element analysis, the results of which are shown in Box 5 of Figure 3, of the new configuration quickly identified regions that required additional material and gave an indication of the realization factor that needed to be applied to the results to account for downstream modifications that would add weight back in to the part. In a case such as this where no strength optimization is performed, the realization factor can be significant. This model showed additional sizing work was needed to address local fillet radii for DaDT considerations during downstream activities, an issue that did not impact the configuration results developed during the topology optimization.

Total optimization time for this quick and focused study was 4 days, resulting in a weight reduction of 30% (before realization factor) from the lightest baseline configuration and a higher average part stress, indicating more efficient material use.

B. Optimization Process 2: Solid Topology, Shell Shape and Size The next category of optimization studies that have been executed consists of a process of solid finite element

topology optimization for stiffness-optimized part configuration followed by shell element shape and size optimization for strength, stability, and stiffness constraints. The example presented to illustrate this process is a large bracket used to mount internal equipment, the baseline for which is shown in Box 1 of Figure 4. Like many other examples, this problem seeks to maximize stiffness, which in this case is controlled by a constraint placed on the normal vibration modes of the part. Much of the optimization performed on F-35 seeks to identify most efficient load paths and then sizing based on strength criteria. Whereas identifying the best load paths is not always intuitive, identifying the normal modes of a structure is even less so. The modal constraint on this part required that no normal modes occur below 70 hertz. Two 67 lb canisters hanging from the middle of the part, rather than the part itself, drove the mode shapes. Topology optimization saved both time and weight during the design process.

1 2

3 4

5 6

1 2

3 4

5 6

Figure 4: Optimization Process 2—Solid Topology, Shell Shape and Size


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Structural analysis of this part began with a shell model of the initial layout, as shown in Box 2 of Figure 4, at which point the part was far from meeting the stiffness constraint. Consequently, geometric features were added to increase stiffness against the resulting modes and the model was subsequently run using sizing optimization to determine gauge thicknesses. This process was iterated and would have achieved a working solution, but not the best solution due to two limitations that prevented realization of a minimum weight part. First, by dictating the topology and optimizing on size only, the optimization process did not realize the full design space. Second, the modes driving the weight shifted. Changes made to resist one particular mode did little to resist another. Although each iteration produced a part closer to meeting the constraint, reducing the weight significantly from the starting point, the final weight would have been much higher than the acceptable target. Therefore, it was deemed necessary to take the time to start over with a clean slate in order to get to a lighter solution.

The clean slate began with a topology model, using a solid volume of 4-node tetrahedral elements to fill in the available package space across the top central portion of the part, as shown in Box 3 of Figure 4. Because mature surrounding structure constrained most of the part’s perimeter regions, the package space for the topology optimization consisted of only interior regions. Neither the topology returned by the solver, shown in Box 4, nor the interpretation of it, shown in Box 5, bore resemblance to the original part geometry.

At first comparison the final part design shown in Box 6 of Figure 4 bears little resemblance to the results in Box 4. The locations of fasteners, which can be seen in Box 4, made interpretation of the results somewhat challenging and relied on good engineering and design judgment as an important factor. Stiffeners are shown growing directly toward and around fastener locations, which is logical since this is where loads are introduced into the plate. The resulting stiffener pattern is an attempt to surround the fasteners with load paths that will support load normal to the plane of the plate and minimize the distance over which the out of plane loads must be carried.

Keeping the many geometry constraints in mind, the topology results were interpreted into a new solid CAD model, which was then used to construct a new shell finite element model. Again an iterative process began with the shell model, making geometry changes based on engineering judgment and then resizing with the optimizer. This time however the geometry changes were much more subtle, the number of iterations required was few, and, most importantly, the end weight of the part was significantly lower. Estimated weight savings was over 25% of the baseline part weight.

This example shows that topology optimization can be a highly beneficial step in achieving weight saving goals, and should be implemented as early as possible in the design process. While not as beneficial for weight reduction on this part, shape and size optimization did add value. Based on experience with the process, the topology optimization removes weight, but shape and size optimization keep the weight minimum while fully realizing the part.

C. Optimization Process 3: Solid Topology, Solid Shape Shape optimization with solid elements requires additional time and effort that has not, in general, been justified

on F-35 parts. The example presented here comes from the case studies initially used to evaluate optimization tools on the F-35 program. Because the optimization study was conducted after the part was released, the results shown here were not used on the actual part. Nevertheless, the study heavily influenced subsequent optimization studies.

This optimization process, which is outlined in Figure 5, starts with definition of the package space, which fills the full region where the part was allowed to have material. This package space was meshed using 4-noded tetrahedral elements and fixed at the base of the fitting. The appropriate loads were introduced at the lug, which was held as nondesignable because it was sized using standard lug sizing procedures. The topology optimization identified preferred load paths within the package space. In this case the results highlighted that a gusset should be angled and that material was not needed in the base between the lugs. These two indications led to a new fitting design 30% lighter than the baseline part. The topology optimization was relatively quick, requiring only a few days of work.


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1 2

3 4

5 6

1 2

3 4

5 6

Figure 5: Optimization Process 3—Solid Topology, Solid Shape

Following the topology optimization, design variables were defined from shape basis vectors that were applied to gusset thicknesses, base thickness, and hole locations. The shape optimization yielded only a slight weight improvement, about another 1%, and took significant effort, about twice as long as the topology optimization. The definition of shape basis vectors on tetrahedral elements can be quite difficult, since these elements can collapse with only slight morphing of the mesh. This effort can be substantially reduced if a hexahedral mesh can be obtained.

Despite the effort involved and the seemingly low weight savings achieved, the shape optimization produced a very important benefit. The initial design had poor fastener load distribution and several negative bolt margins. The shape optimization produced a design that satisfied all of the applied SPC force constraints (i.e. fastener loads), thus eliminating weeks of downstream iteration between design and structural analysis.

D. Optimization Process 4: Shell Topology, Shell Shape and Size The next process discussed uses shell element models for topology, shape, and size optimization. A shell

element idealization is used wherever possible instead of solids because it is easier to construct the optimization model and computationally more efficient given the iterations inherent in optimization. Topology optimization using shell elements is an efficient way to gain insight on stiffening configurations in shell parts that are not driven by buckling, which is not considered in the topology optimization. While this is an admittedly small class of problems it can still provide useful guidance in some cases. Definition of design variables is considerably easier with a shell model, which allows for more variables to be studied. Two examples follow.

The first example, a door hinge, achieved significant weight savings by using this process, shown in Figure 6, of topology optimization results to guide stiffener layout and size optimization to produce flange profiles and thicknesses.


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1 2

34

Figure 6: Optimization Process 4—Solid Topology, Shell Shape and Size, Example 1

The baseline configuration, shown in Box 1 of Figure 6, had a large section where stiffeners had been arbitrarily located that was targeted with topology optimization. The clevis area and the lower section were left as is due to existing interfaces with other parts. If these areas were to change then the interfacing parts would have had to change with them. Since the design area for topology had primarily constant thickness and loads primarily in-plane, the finite element model used shell elements, as shown in Box 2. Element size could be small because run times were relatively short for this small model.

The topology model used a basic load envelope capturing max positive and negative hinge moments at the door hinge line. This model had an objective to minimize the compliance of the entire structure and a constraint on the volume fraction of the design area. Additionally, this optimization set a control parameter on minimum member size, which controls the size of the members produced by topology optimization. This parameter was adjusted to get the most realistic and manufacturable stiffener layout. The topology optimization results, shown in Box 3 of Figure 6, suggested a clear stiffener pattern.

Being a door hinge, stiffness considerations drove sizing. Consequently, a baseline for part stiffness, based on strain energy and max displacement, was developed using an existing shell element hinge model, which was known to provide acceptable overall door stiffness.

The minimum gauges for each cap, stiffener, and web of the hinge were found by extracting element moments and forces from several critical load cases and using them in strength hand calculations, which are preferred for stress over finite element stresses. These minimum gauges were then applied to the baseline shell model. The original baseline FEM and the FEM with the strength minimum thickness were then both run with the worst moment at the hinge line, which was the critical load case. Comparing the total strain energy and maximum displacement of the two models showed the new model to be insufficiently stiff.

Consequently, a gauge optimization model was developed, as shown in Box 4 of Figure 6, in order to meet the stiffness requirements. By using strength minimum thickness for the lower bounds in gauge optimization no attention to stresses was needed, as this was now strictly a stiffness problem. Gauge variables were set up for all thicknesses excluding the clevis thickness, which was sized with hand calculations. The optimization constrained total strain energy of the hinge, which could not exceed that of the baseline FEM, and had an objective to minimize mass. The results from the gauge optimization showed a significant reduction in weight with the total strain energy not exceeding that of the baseline. The maximum displacement of the optimized FEM was also checked and less than the baseline.

The optimization results showed a 4% weight reduction. The total strain energy was equal to that of the baseline FEM and the maximum displacement was reduced by 6%. Time consumption for this optimization was minimal with total time spent approximately 2 days.

The second example, a beam, which is outlined in Figure 7, starts with an existing design that lent itself to shell finite element representation. The part was meshed, as shown in Box 1, with thin shell elements based on assumed initial thicknesses. Non-designable regions were defined as described in Optimization Process 3. A higher mass fraction (ratio of optimized mass to original mass) was used as the optimization goal since the initial layout of the part was assumed close to the final design layout. Running shell topology optimization was relatively quick in comparison to shell size and shape optimization. With minimal set-up time the structural analyst can leverage an


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existing FEM, or FEM that will be subsequently used for size and shape optimization, to determine if stiffeners are being efficiently utilized or if portions of a part are grossly oversized. Results from the shell topology optimization, shown in Box 2, saved an approximate 1-2% off of the baseline part weight for this example.

Figure 7: Optimization Process 4— Shell Topology, Shell Size, and Shell Shape, Example 2

After incorporation of topology optimization results, size optimization, shown in Box 3 of Figure 7, determined appropriate thicknesses based on stress, buckling, and deflection constraints. This portion of Optimization Process 4 is very similar to standard FEA sizing performed by a structural analyst, although the optimization solver streamlines the process. The structural analyst can approximate the final sizing, which will likely include some sort of non-linear analysis, by adjusting the allowable stress levels used in the size optimization, instead of incorporating time intensive non-linear analysis in the optimization. It can be surmised that the optimizer is used as an aid to get to minimum weight quicker than by iterating manually, and the results should not be considered the final releasable sizing data. In the case of this example, size optimization saved an approximate 10% off of the initial weight and considerable time in thickness iteration.

The final step in Optimization Process 4 is shape optimization, which is shown in Box 4 of Figure 7. This step is often optional since it takes a considerable amount of time to set-up, but can be useful if part geometry has cut-outs where dimensions can be varied, stiffener or part geometry profiles that can be adjusted, or fastener patterns that would benefit from more equal load distribution. Shape optimization can also be completed in tandem with size optimization, which can yield a lighter more efficient design, but requires additional solution time when compared to size optimization alone. In the case of this example, shape optimization was not utilized since adjacent parts limited the fastener pattern, topology and size optimization adequately optimized stiffener geometry, and the part is devoid of cut-outs. Box 5 shows the resulting optimized part.

An additional complication in this part was the load application method of enforced displacements. Since the overall load distribution could not change significantly without affecting surrounding parts, optimization was approached less aggressively than for a less constrained part with more direct load application.

E. Optimization Process 5: Shell Size Shell sizing optimization, treating shell thicknesses as design variables, has been applied in numerous instances

to both save weight and time. For parts with a fixed configuration, having either insufficient time or space for adjustment (a common occurrence), topology optimization offers no value and shell sizing optimization alone has


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been used through general FEA solvers and pre-and post-processors developed by the MacNeal-Schwendler Corp and Altair Engineering.

An example of this optimization process, outlined in Figure 8, is a frame that serves to react large wing bending loads, support pressure loads on an access cover, and support jacking loads. The process started with an existing design, shown in Box 1, that lent itself to shell finite element representation. The part was meshed with thin shell elements based on assumed initial thicknesses, but only size optimization was utilized due to the complex surrounding geometry and load path. The finite element model, shown in Box 2, consisted of the frame plus additional members to adequately represent the flexibility of the surrounding geometry.

1 2 3

Figure 8: Optimization Process 5—Shell Size

Initially a fully stressed analysis provided the starting thicknesses for the members. This approach assumed that the load was fixed and the member thicknesses were adjusted so that the maximum allowable stress was attained. Since the effect of Frame thickness iterations on the surrounding structure needed to be minimized, free body loads from critical load cases, with inertia relief, were used to optimize the size of the members based on stress constraints. It was also evident that large changes in stiffness in the Frame would not be accounted for in using the baseline enforced displacements from a global FEM, which further verified the need for a free body/inertia relief approach to the initial size optimization (excluding buckling). Since a large percentage of airframe sizing is stability driven, once the member sizes were optimized for strength, the enforced displacements were obtained at the load application points for the most severe compressive load case to run a linear buckling analysis. The member sizes were then adjusted in the buckling analysis until an eigenvalue of one was obtained. This process required several inertia relief analyses to obtain updated enforced displacements for subsequent linear buckling analyses, until a converged solution was reached. After this manual iteration, the final member sizes were used as a lower bound in a final fully stressed analysis. It is conceivable that the inertia relief static analysis and enforced displacement buckling analysis runs could be coupled in a user-defined program, but time constraints prohibited a more automated solution. The application of size optimization alone resulted in a 42% weight reduction, and although time intensive to set-up, this sizing method saved the structural analyst several weeks of manual thickness iteration. The resulting part, having the same configuration as the baseline, is shown in Box 3 of Figure 8.

V. Impact on Final Structure As shown previously in Figure 1 and evidenced by the examples presented herein, optimization should not and

can not be the end point in part maturation. Final detail structural analysis must follow in order to determine all critical margins of safety. Therefore, component optimization must have the objective to improve the structural analyst’s ability to execute final detail structural analysis, achieving minimum weight at minimum cost and schedule. While optimization inherently seeks to minimize weight, the objective of minimizing downstream cost and schedule is highly sensitive to the details of when and how optimization is applied and how it interfaces with loads, other parts, and other design and analysis disciplines.

Optimization results should provide a good preliminary component design. That is, optimization results should define a part configuration that has a very low probability of change downstream and sizing that, while it may need to be adjusted slightly to meet final margin requirements, is very close. Optimization should ensure that final detail structural analysis is primarily a verification process, checking all the boxes, as opposed to the start of late cycle configuration changes that typically occur when some aspect of the part is found to not satisfy requirements. Optimizers must take care to ensure that the increased complexity that typically results from optimization, particularly topology optimization, is manageable by the downstream structural analysis process.


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Because optimization models typically make use of simplifying assumptions, realization factors must be applied in many cases to the optimized weight. The extent to which optimization results carry through to the final part impacts the acceptance of the method. If all of the weight savings is consumed once the simplifying assumptions are removed in the final structural analysis then optimization of detail parts adds no value. These simplifying assumptions include, for example, use of finite element results to size features (which are typically sized by forces and moments resolved on section cuts) and exclusion of local details driven by DaDT that do not impact gross area sizing. Realization factors in this work ranged from 0 to 10% of the optimized part weight.

A key limitation that has prevented broader application of optimization on F-35 is the need to use breakout models with balanced freebody loads to analyze local regions of structure. In these models, loads are extracted from the global loads finite element model for specific load cases in equilibrium. Use of optimization with such models faces two challenges. First, any change in model geometry driven by the optimizer immediately unbalances the load case, necessitating the use of inertia relief to artificially balance the loads. Use of inertia relief, however, precludes the use of buckling constraints, which are primary drivers of the built-up shell structure that comprises the bulk of an airframe. The hierarchical approach suggested by Schramm, et al.,13 whereby buckling is checked after optimization, is the necessary, but not necessarily optimal, workaround process. Second, and perhaps more significant, optimization using breakout shell models has the potential to change part stiffnesses sufficient to alter load paths and invalidate the global loads model. Boundary stiffness and forces must be checked and either constrained or otherwise accounted for during any optimization using a local breakout model.

VI. Conclusion The F-35 JSF program has found weight savings and expedited the maturation of numerous structural

components by applying finite element-based structural optimization tools. To date, these tools have been applied primarily to compact fittings and some frames and shell structure. While experienced engineers performing standard structural analysis and design iterations may get to minimum weight over time, optimization is a tool to get there faster if an effective optimization toolset can be employed at the appropriate phase of the development process.

Optimization is a multifaceted tool. It is an educational tool to give young engineers insight into load paths. It is a design tool to aid in part configuration. It is a weight saving tool to meet performance targets. It is a requirements management tool to ensure that a wide array of technical and manufacturing constraints are met. It is an efficiency tool to reduce cycle time and cost. All of these aspects are only potential and realization of this potential depends greatly on how the tool is applied.

While optimization is indeed a powerful tool, algorithms alone do not add value. If optimization’s potential value is to be realized, aircraft structural engineers and tool developers must work together to overcome the challenges that remain. Aircraft structural engineers must work to overcome the separation of design and structural analysis disciplines and define methods for applying optimization appropriately within the production development environment. Tool developers must help to develop methods to further integrate optimization methods into the process of aircraft structural design and analysis, addressing the complex nature of aircraft loads and constraints and reducing the overhead associated with execution of optimization methods.

Acknowledgements The authors wish to acknowledge the support and contribution of numerous F-35 program personnel that

contributed design, structural analysis, process, and moral support in the development of the processes and methods described in this paper. The authors are grateful for the contribution of Adam Brinkman to examples presented herein and to Altair Engineering for technical assistance with much of this work.

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Detail Part Optimization on the F-35 Joint Strike Fighter

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