Post on 15-Jul-2018
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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2
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
4
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