On the Methods and Examples of Aircraft

Impact Analysis

Bulgarian Atomic Forum

Varna

30 May – 01 June 2012

Jorma Arros

MMI Engineering

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Presentation Outline

Concerns with Aircraft Impact to NPP

Methods for aircraft impact

Modeling – spatial discretization method

Dynamics – time discretization and integration algorithm

On material modeling

Demands on software

Software today

Plane modeling

Examples – analysis results and animations – Verification – LS-DYNA

– Riera force histories

– Missile/target examples

– Smooth particle hydrodynamic example – LS-DYNA

Conclusions

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Concerns with Aircraft Impact to NPP

Structural integrity - perforation

– Hit to control room, fuel pools, safety equipment

– Fuel ingress – fire effects

Shock loading – transmitted through connected buildings

– Effect on safety equipment

– Safety train redundancy/physical separation

– Equipment qualification for the shock loading

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Method: Riera Force History

Suitable when target deformation is small

Reasonable estimates for Pc and µ must be

available

lengthunitpermass

forcecrushing

velocityinitial

where

)()(

0

2

0

c

c

P

v

dtvPdttFMv

Load description computed based on simple

momentum equation:

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Method: Missile/Target Interaction

Both the target structure and the aircraft explicitly

modeled, e.g., with finite elements

Problem treated as a large deformation contact/impact

dynamic problem in a single response run

M/T method must be used when large deformation

or perforation occur

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Method: Uncertainties

Because of the nature of the problem, significant

uncertainties exist in ACI analysis

– Type of plane

– Impact velocity and angle

– Mass of the plane at time of impact – payload, amount of fuel

– Data on plane construction details

– Other significant modeling uncertainties

Analysis approach and detail should be “balanced” -

commensurate with the uncertainties

– Do not “over-do” details of some parts of the model (e.g., the

plane) and the analysis

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Spatial Discretization

Finite element method

– Well developed

– Dominates commercial software today

Meshless/particle based methods

– Newer development

– May be beneficial for large deformation concrete “punching shear”

analysis – potentially solves the “element erosion” problem

associated with FE

– Not generally implemented yet in major commercial software

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Explicit vs Implicit Time Integration

Explicit time integration Typically required for highly nonlinear large deformation impact

problems

Typically with missile-target interaction method

Typically based on the central difference method

Time step size limited by numerical stability condition, often in the order on nE-05 sec – may have to use mass scaling

To control run time must simplify element computations – use reduced element integration – may induce hourglassing issues

High demands on concrete material model fidelity

Comprehensive contact modeling features required, including eroding contact

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Explicit vs Implicit Time Integration

Implicit time integration For smaller deformation problems not involving perforation

Typically with Riera force history method

Typically unconditionally stable – can use longer time steps determine by required level of accuracy and required higher frequency capture

Typical example is the Newmark-β method

Typically fully integrated elements – no hourglassing problems

More expensive element computations & must solve large coupled matrix equations – tends to increase run times

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On Material Modeling - Concrete

Concrete Concrete material/constitutive modeling is a challenge

– Cracking and crushing

– Cyclic response – crack closure

– Shear retention

– Rate effects

Examples of concrete models in the major software

LS-DYNA: – WINFRITH_CONCRETE – MAT84 with rate effects and

MAT85 with no rate effects – CSCM_CONCRETE - MAT159 – CONCRETE_DAMAGE_REL3 – MAT072R3

ABAQUS/Explicit: – Concrete damaged plasticity – Cracking model for concrete

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On Material Modeling - Steel

Steel Well developed metal plasticity models are available in the

major software

– Mises and Hill yield surfaces

– Associative flow rules

– Kinematic and Isotropic hardening

– Rate effects

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The following aspects must be well developed: Element or meshless formulations for large displacement, large

strain modeling

Adequate material models particularly for concrete

Contact formulations meeting the requirements posed by the problem

Time integration algorithm suitable for the problem category – implicit/explicit

Verification

Demands on Software

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Software Today – Finite Elements

FE methods and software dominate today – decades of development and experience – all the above aspects well developed

Explicit codes: – LS-DYNA – ABAQUS/Explicit – Autodyn – ADINA and others

Implicit codes: – ANSYS – ABAQUS/Standard – ADINA and others

In today’s FE codes, for many large deformation problems element erosion (elimination) is used to achieve “realistic” response

Element erosion is a mathematical construct – typically based on computed element strain measures – it is not based on the physics of the problem

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Software Today – Finite Elements

As such it tends to be problem dependent – it is not possible to define the erosion “threshold parameters” that work consistently acceptably for varied problems

Possible solution: particle methods – smooth particle hydrodynamics (SPH) already commercially (LS-DYNA) implemented or lattice discrete particle method (LPDM) – these do not use erosion

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Software Today – Meshless & Particle Based

Meshless/particle based methods are being developed

Examples: smooth particle hydrodynamics (SPH), lattice discrete particle method (LDPM), diffuse element method (DEM), element free Galerkin method (EFGM), and others

Mesh distortion insensitivity

Mesh alignment insensitivity

Circumvent the “erosion issue” associated with severe deformation concrete impact

Computational cost may be higher than FE

Commercially developed codes not available – except SPH implemented in LS-DYNA

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Plane Modeling

Actual geometry

Finite element model of the plane to be as simple as possible

Actual total mass

Reasonable mass distribution

Crushing force Pc can be quite approximate – studies have shown that the impact force history is quite insensitive to Pc distribution - can be computed as follows:

3lbs/in0.1 astakenbemay density,weightmaterialaircraft

areaunitpermass

areasectioncrossmaterialfuselage

50,000psie.g.,estress,compressivultimatematerialaircraft

where

1.01.0

i

i

i

cui

iicuiicuici

A

f

gfAfP

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Plane Modeling – Boeing 767-400ER

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Verification – Liquid filled Cylinder

Impact Test

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Verification – Liquid filled Cylinder

Impact Test

WS1 Displacement Histories

-7

-6

-5

-4

-3

-2

-1

0

0 0.05 0.1 0.15 0.2 0.25

Time [sec]

Dis

pla

cem

en

t [i

n]

D6 - Test

D8 - Test

D6 - ALE Model

D8 - ALE Model

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Verification – Concrete Slab Flexure – Soft

Missile – IRSN-VTT Tests

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Verification – Concrete Slab Flexure – Soft

Missile – IRSN-VTT Tests - Rebar

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Verification – Concrete Slab Flexure – Soft

Missile – IRSN-VTT Tests

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Verification – Concrete Slab Flexure – Soft

Missile – IRSN-VTT Tests

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Verification – Concrete Slab Flexure – Soft

Missile – Computed Displacement

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Verification – Concrete Slab Flexure – Soft

Missile – Max Reinforcing Strain

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Verification – Concrete Slab Flexure – Soft Missile –

Reinforcing Effective Plastic Strain

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Verification – Winfrith 85

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – IRSN-VTT Tests

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Verification – Meppen Test

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Verification – Meppen Test

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Verification – Meppen Test

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Verification – Meppen Test

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Verification – LS-DYNA vs ABAQUS/Explicit

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Verification – LS-DYNA vs ABAQUS/Explicit

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Missile-Target Interaction Method

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Riera Force History – Boeing 747

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Missile-Target Interaction Method

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Missile-Target Interaction Method

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Riera Force History – Boeing 747

FORCE TIME HISTORY

0.00E+00

2.50E+07

5.00E+07

7.50E+07

1.00E+08

1.25E+08

1.50E+08

1.75E+08

2.00E+08

2.25E+08

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

Time [sec]

Fo

rce

[lb

s]

RIERA

LS DYNA

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Riera Force History – Boeing 747

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Riera Force History – Boeing 747

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Riera Force History – Boeing 747

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Response Spectrum – Missile Target

Interaction

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Linear Shell Model - Riera

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Response Spectrum – Linear Model -

Riera

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Discrete Rebar in Impact Area

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Aircraft Impact – B747 vs VVER

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Aircraft Impact to Protective Earth Berm

Earth Berm protecting a critical building modeled with Smooth Particle

Hydrodynamics (SPH) formulation – LS-DYNA

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HELB Whip Analysis

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HELB Whip Analysis

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HELB Whip Analysis

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HELB Whip Analysis

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HELB Whip Analysis

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Conclusions

Aircraft impact analysis can be performed today within feasible run

times using PCs and available advanced commercial finite element

software tools

Adequate element and material model technologies exist

Explicit time integration enables analysis of very large deformation

Missile/Target impacts

Meshless/particle based methods may be beneficial for large

deformation concrete “punching shear” analysis – potentially solves the

“element erosion” problem associated with FE, but are not generally

implemented yet in major commercial software

Verification of the complicated modeling technologies continues to be a

challenge

Not much work has been done yet on ACI shock loading – redundant

and physically separated safety trains key to success

Analysis approach and detail should be “balanced” - commensurate

with the significant uncertainties - do not “over-do” details of some

parts of the model (e.g., the plane) and the analysis

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