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Finite Elements in Analysis and Design 45 (2009) 324--332

Contents lists available at ScienceDirect

Finite Elements in Analysis and Design

jo ur na l ho me pa ge: w w w . e l s e v i e r . c o m / l o c a t e / f i n e l

CAE (computer aided engineering) driven durability model verification for the

automotive structure development

Dong-Chan Leea, b, Chang-Soo Han a,

aDepartment of Mechanical Engineering, Hanyang University, Sa-1 dong, Sangnok-gu, Ansan, Kyeonggi-do 425-791, KoreabSPACE Solution Co. Ltd., Republic of Korea

A R T I C L E I N F O A B S T R A C T

Article history:Received 28 November 2007

Received in revised form 1 October 2008

Accepted 13 October 2008

Available online 2 December 2008

Keywords:

Vehicle body design

Durability

VPG (virtual proving ground)

CAE (computer aided engineering)

EMBS (elastic multi body simulation)

Test/analysis correlation, in the refinement of finite element models to accord with test results of themodeled structure is an emerging field in the today's automotive industries. The accuracy of finite element

analysis predictions in the linear and nonlinear specifications becomes more and more important and

directly influences the competitiveness of the product. In particular, fatigue or durability is traditionally

a test based activity. The drawback with testing is that it can be performed only after the prototype has

been built and should design problems surface it would be difficult to redesign, as the design by then is

finalized. For this reason, FEA (finite element analysis) based fatigue analysis is increasingly popular and

the input loads used for these predictions are derived from test or CAE-predicted virtual prototype. In this

point, the well-correlated model is very necessary for the feasible evaluations of structural performances.

To perform and process the correlation analysis between durability test and simulation, the FE model

updating techniques were developed and implemented into the existing FE software and optimization de-

sign. This paper gives a design reference for the durability specifications and model updating techniques.

2008 Elsevier B.V. All rights reserved.

1. Introduction

The durability of automotive body structure has two major spec-

ifications: structural strength and fatigue resistance. The structural

strength is the capacity of a system/subsystem/component to main-

tain function when subjected to the peak loads. Fatigue resistance is

the ability to maintain function while subjected to repetitive cyclic

loading. The loads associated with fatigue occur many ties during the

life time. Fatigue damage caused by slow but gradual microstructure

degradation may occur under cyclic loading, even if the maximum

stress is lower than the material yield. Loads, geometry, material

and manufacture process plus environmental conditions determinesystem/subsystem/component durability. Thee factors interact with

each other and make the durability design a very complex and chal-

lenging task. In order to reduce the product development time, re-

duce prototypes, optimize weight and costs, the automotive makers

have established their systematic durability design and verification

process. The customer correlated proving ground test is a represen-

tation of actual customer usage. By setting up various test track road

surfaces, the proving ground can replicate the more severe events

Corresponding author: Tel.: +8231 4155255; fax: +82 31406 6242.

E-mail addresses: [email protected] (D.-C. Lee), [email protected],

[email protected] (C.-S. Han).

0168-874X/$- see front matter 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.finel.2008.10.004

encountered by the customer which contributes most of the fatigue

damage. The advantage of leveraging CAE is to drive the design

to more mature levels by interactions far ahead of hardware or

prototype's availability. This virtual development lays the founda-

tion for shortening development time, optimizing the design and

reducing cost and weight. Potential risks and failure modes are

predicted and prevented much earlier in the development stage

[14]. The model elaboration with its respective elements is based

in turning a real complex component into a concept mode, de-

termining the geometric dimensioning parameters, stiffness and

elasticity modulus. This way to a new development the methodol-

ogy to be used at each phases will be explained as follows; verifyit the new project has the same characteristics of the previous

one such as weight of vehicle, distance between axles, classified

considering the type of vehicle, whether compact, standard, sedan

or van and kind of engine, whether longitudinal or transversal.

Select the similar characteristics of the previous project including

the design departments and their estimations of the dimension-

ing, stiffness and elasticity modulus. Adopt the hypothesis to the

model creation with the finite element representations for the

mathematical reasons, the elasticity modulus and yield stress which

are not related to the material but to the individual components.

The automotive development process using CAE (computer aided

engineering) is shown in Fig. 1. As the stages from the concept

verification plan to development verification plan are preceded,
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D.-C. Lee, C.-S. Han / Finite Elements in Analysis and Design 45 (2009) 324-- 332 325

Nomenclature

[K] conventional stiffness matrix

[K0] initial stiffness matrix due to preloading

{u} displacement vector

{F} external force vector

[B] differentiation operator of shape function

[S] stress matrix due to preloading

U0 strain energy due to preloading

U strain energy

p design variable

{P} design variable variation

{R} response error vectors

[Q] structural sensitivity matrix

x static response

y dynamic response

displacement assurance criterion normalized static displacement dynamic displacement assurance criterion normalized dynamic displacement

Fig. 1. Development process of automotive structure using CAE.

the dependencies on the CAE get larger and the model correlations

with test get more important. Engineering data in the development

process can be divided into three domains: requirements domain

gathering requirements related to product performance and behav-

ior, product domain gathering product information, and simulationdomain gathering data related to product/manufacturing environ-

ments and enabling the analysis and validation of product definition

regarding the set of identified requirements.

This paper presents the optimization process for the model corre-

lation concerning the nonlinear structural stiffness and strength with

material strain-hardening and tangent stiffness. The minimization of

strain difference between test and simulation is chosen as the objec-

tive function and the corrections of design parameters are based on

the various configuration parameters of panel-based structure. The

constraints are the dimensional variations of configuration parame-

ters. The optimization problem is formulated by the integrated de-

sign process and iteratively solved by the NewtonRaphson method

for the nonlinear static analysis and the sequential quadratic pro-

gramming [5,6]. The integration design procedure in the paper canbe considered that one of the bottlenecks in product design is the it-

erative process of selecting design alternatives and making changes

to files to execute those alternatives. The VPG model was developed

for improving the efficiency of the load acquisition process by simu-

lating the real tie running of a vehicle driven on the proving ground.

A complete body FE model is combined with a multi-body dynamic

model.

2. Theoretical considerations for the durability equations [710]

For the nonlinear equilibrium equation of the mechanical struc-

tures with the material and geometric nonlinearities, we can state

the incremental description as

[K]{u} = {F} (1)

where [K] is known as thetangentstiffnessmatrix which is calculated

by adding the elastic material matrix and the second PiolaKirchhoff

stress matrix to the straindisplacement transformation matrices:

[K]=[KL]+[KNL]=

V[BL+BNL]T[D][BL+BNL] dV

=

V

[BL]T[D][BL] dV+{

V

[BL]T[D][BNL] dV

+

V

[BNL]T[D][BL] dV +

V

[BNL]T[D][BNL] dV} (2)

[KL] denotes the small displacement stiffness and [KNL] denotes the

large displacement and nonlinear material behaviors. The strain ten-

sor is defined with respect to the initial coordinates of the body

ij =1

2

juijxj

+juj

jxi+jukjxi

jukjxj

(3)

{} = [B]{u} = ([BL] + [BNL]){u} (4)

The residual between the external and internal forces is represented

by {F} as follows:

{F} =

V

fBuB dV +

SfSuSdV

V[BL + BNL] dV (5)

where is the stress tensor in the iterative nonlinear process result-ing in the internal forces.

Consider the nonlinear force-deformation relationship shown in

Fig. 2. We imagine that the tangent stiffness can be composed of

the linear term [KL] and the nonlinear term [KNL] that affect the de-

formations with geometric and material nonlinearities. In the force-

deformation relationship, [KL] and [KNL] are known as the functions

of {u} relative to the structural rigidities due to the geometric di-

mensions and therefore, {F} can also be calculated in terms ofgeometric dimensions.
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326 D.-C. Lee, C.-S. Han / Finite Elements in Analysis and Design 45 (2009) 324-- 332

F

u

KNL < 0

KL

KNL > 0

KNL = 0

Fig. 2. Forcedeformation relationship in the effect of nonlinear tangent stiffness.

One can take the view that external forces change the stiffness of

a structure under the preloading condition. If the forces reverse some

physically possible deformation mode, the stiffness of the structure

increases or decreases. The effects of preloading are accounted for bya matrix that augments the conventional stiffness matrix. The matrix

due to these effects is called the stress stiffness matrix and is defined

by an element's geometry, displacement field and stress state. The

stress stiffness matrix is independent of elastic properties. Including

the stress stiffness matrix under preloading, the forcedisplacement

relationship for the structure is given by

([K] + [K0]){u} = {F} (6)

where {u} is the displacement vector, {F} is the external force vec-

tor, [K] is the conventional stiffness matrix concerning the elastic

properties, and [K0] is the initial stress stiffness matrix.

[K0] =e=1

[k0]e (7)

Let the element displacement field be given by {u}=[N]{d} and {u}=

[N]{d}= [B]{d}. The element's stress stiffness matrix can be given by

[k0]e =

Ve

[B]T[S][B] dV (8)

where [B] is obtained from shape function, [N] by appropriate dif-

ferentiation and [S] contains the stress level due to the preloading.

[N] is the shape function matrix.

[S] =

S 0 00 S 0

0 0 S

, [S] =

x0 xy0 zx0xy0 y0 yz0zx0 yz0 z0

(9)

The stored strain energy due to the preloading is given by

U0 =

V

( 12 (u2,x+v

2,x+w

2,x)x0 + + (u,xu,z + v,xv,z+w,xw,z)zx0) dV

=

V

{}T{0} =12 {u}

T[K0]{u} (10)

where {}T = {xy zx}, {0}T = {x0y0 zx0}.

To design a stiffening structure under a given loading, mean com-

pliance is chosen as the objective function, which is defined as the

least amount of displacement and the minimum mean compliance.

Thus, optimization involves not only minimizing the mean compli-

ance or elastic strain energy of the structure, but also minimizing the

effect of external forces. The compliance of a structure with stress

stiffness under a given loading can be written as

U= 12 {u}T([K] + [K0]){u}. (11)

Taking the derivatives of Eq. (11) with respect to the design param-

eter gives

dU

d= U =

1

2

du

d

T([K] + [K0]){u}

+1

2{u}T

dK

d

+

dK0d

{u} +

1

2{u}T([K] + [K0])

du

d

= 12

{u}T([K] + [K0]){u} +12

{u}T([K] + [K0]){u}

+1

2{u}T([K] + [K0]){u

}

= {u}T([K] + [K0]){u} +1

2{u}T([K] + [K0]){u} (12)

Eq. (11) can be rewritten by

U = {u}T{F} + 12 {u}T([K] + [K0]){u}. (13)

Assuming that the coordinates under a given loading are only

considered in the work done by the external forces and that the

coordinates in the free domain are not under loading, the following

may be defined:

{u}T{F} =

duT

f

d

duTed

0

Fe

=

dued

T{Fe}

= ({ue}T{Fe})

= 2U (14)

where uf is the displacement field that is not under a given loading

and ue is the displacement field under a given loading.

Using Eq. (14), the sensitivity of compliance from Eq. (11) is given

by the following expression

U = 12 {u}T([K] + [K0]){u} = U

e + U

0 (15)

where Ue and U0 are the strain energy sensitivities due to external

forces and preloading. [K

] and [K0] defined on an element level can

be given by the material densities of elements relative to the stress

ratio. The full stress scaling is used for the preloading. The deriva-

tive of the stress stiffness matrix depends on the initial stress {0}.If these stresses remain constant, [K0] is zero. But the topological

distribution or geometric dimensions of structure under preloading

may change on the design domain and in structural rigidities:

[K0] =d

d

e=1

Ve

[B]T[S][B] dVe =e=1

Ve

[B]T[S][B] dVe (16)

where [S] is the derivatives of initial stress with respect to the topo-

logical distribution and geometric dimensions of the structure.

Thus, we can assume the tangent stiffness matrix, incremen-

tal deformation and load unbalance as a function of dimensional

parameters:

[K] = [K(p)]

{u} = {u(p)}

{F} = {F(p)} (17)

For design optimization of nonlinear structural performance, the

sensitivity analysis is given by Eq. (1):

d

dp([K]{u}) =

d

dp{F}

[K]j{u}

jpk=jF

jpkj[K]

jpk{u} (18)

where j{u}/jpk is the unknown displacement sensitivity coeffi-cients, j{F}/jpk is the external loads not dependent on structural

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Fig. 3. Design procedure of automotive structure through the model correlation.

properties, j[K]/jpk is the derivative of the system stiffness matrix

with respect to the parameter.

j[K]/jpk =[K(pk +pk)] [K(pk)]

pk

The geometric parameters can be defined by setting the basis vector

of grid point changes to the directions normal to the surfaces as

follows:

{G} = [T]{p} (19)

where {G} is the set of grid point changes, [T] is the set of shape

basis vectors and {p} is the set of scaled design parameter changes

in the shape dimension.

3. Sensitivity based correlations between test and simulation

3.1. Static response correlation

In the static analysis, the response error vector {Rn} consists

of the n-th normalized displacement of configuration and DAC

(displacement assurance criterion), :

{Rn} =

xn

n

(20)

where

xn =xn

xntest=

xntest xnanalysis

xntest(21)

n=1n = 1

({ntest}

T{nanalysis})2

({ntest}T{ntest})({

nanalysis}

T{nanalysis})

(22)

ntest and

nanalysis represent the n-th normalized static displacement

vector of the test and analysis. The sensitivity sub-matrices can be

given by

[Qn] =

jxn

jP

jn

jP

(23)

3.2. Dynamic response correlation

In the dynamic response analysis, the response error vector {Rn}

can be given by

{R} =

{R1}

{R2}...

{Rn}

=

y1

1

y2

2

...

yn

n

(24)

where the error vector {Rn

} consists of the n-th independent vari-able and DDAC (dynamic displacement assurance criterion), under

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unit dynamic loading:

yn =yn

yntest=

yntest ynanalysis

yntest(25)

n=1 n=1

({

ntest}

T{nanalysis})

2

({ntest}T{ntest})({

nanalysis}

T{nanalysis})

(26)

yntest and ynanalysis

represent the m-th dynamic response time or fre-

quency of behaviors under dynamic loadings. test and analysis rep-resent the normalized dynamic displacements of test and analysis.

The sensitivity matrix consists of two parts: the sensitivity matrices

of normalized response times of behaviors and DDAC with respect

to design variables, {P}:

[Q] = [[Q1] [Q2] [Qn]]T =

jy1

jP

j1

jP

jy2

jP j2

jP

...jyn

jP

jn

jP

(27)

Updating the stiffness modeling using static displacement tests

involves minimizing the error function:

Err= [e]T[we][e] + [p]T[wp][p] (28)

where e is the difference between experimental and analytical

static displacements (e=j{uj}/j{pk}p={ujexp}{u

jana}) is the differ-

ence between updated and originally estimated parameters (pk =

pku pka) and w and wp are the diagonal weighting matrices for theselected updating the static displacements and the updating param-

eters, respectively.

4. Design optimization process

The overall engineering design roadmap and virtual prototypes

for the durability of the automotive structure [1117] are shown

in Figs. 3 and 4. The EMBS (elastic multi body simulation) is fre-

quently applied in order to determine the time depended load of

a flexible structure and predict the feasibly transferred load to the

components. The computation procedure which is presented, intro-duces a modally based dynamic simulation for the maximum dura-

bility load. The numerical examples show that the applications range

from quasi-static behavior to vibration dominated problems, includ-

ing nonlinear effects. This paper presents the procedure of the model

correlation shown in Fig. 3.

The design process of mechanical structures can be based on the

optimization process [18,19] to find the feasible configurations that

fulfill certain quality requirements. At this point, engineers often find

that they require multiple interfaces to build the computer models

that will simulate a product's performance. In this paper, the design

roadmap based on process integration for nonlinear structural per-

formances is iteratively solved by the NewtonRaphson method and

sequential quadratic programming. The fully stressed design is used

for the parameter corrections in the iterations that are widely prac-ticed for variably dimensioning the design parameters at its limit

Fig. 4. Virtual prototype for the durability load.

Fig. 5. Design flow for the model correlation of front rail structure.

under a given load. When performed iteratively, it usually convergesrapidly and yields a reasonable structural design. Commercial sim-

ulation program and process integration software are used for the

optimization design of model correlation in the nonlinear structural

specifications of automotive structure. A sensitivity-based correla-

tion algorithm requires the computation of design variable variations

for each configuration based on the corresponding analysis data. The

correlation equation can be given by

[Q]T[Q]{P} = [Q]T{R} (29)

[Q1]

[Q2]...

[Qn]

T

[Q1]

[Q2]...

[Qn]

{P} =

[Q1]

[Q2]...

[Qn]

T

{R1}

{R2}...

{Rn}

(30)
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where [Q] and {R} are the overall structural sensitivity matrix and

response error vectors between test and analysis. {P} is the vectorof

design variable variations. {Rn} represents the corresponding error

vector of the n-th configuration response.

The changes to the model update can be represented by Eq. (31).

The design variables are simultaneously used in the static and dy-

namic response correlations.

{R(P)}i+1 = {R(P)}i + [Q]i{P} (31)

where Qi,j = jRi/jPj.

Y3

Y2

Y1

0 1 2 2 3 3 -p -p

k= Effective Plastic Strain-p

k= 3

k= 2

k= 1

H3

H2

H1

Y(or s)-

E

Hk=Yk+1 - Yk

k+ 1 - k-p

Fig. 6. Stressstrain curve definition for the durability analysis.

Fig. 7. Road running simulation and crack zone from the durability test. (a) Road simulation, (b) Sampling Load history in the forward direction at RH tire, (c) SamplingLoad history in the lateral direction at RH tire and (d) Sampling Load history in the vertical direction at RH tire.

The design process for mechanical systems can be viewed as an

optimization process to find parts that fulfill certain quality require-

ments toward their functionality, appearance and economy. It can

be described as an iterative search process that uses the following

steps:

(1) Define an initial design p(i=0).

(2) Analyze the nonlinear characteristics using a nonlinear solverroutine.

(3) Compare the results of the analysis with such requirements as

allowable plastic strain or residual deformation.

(4) If the requirements are not met, perform the optimization

routine in order to set p.(5) Correct p based on the fully stressed design with = 0.9,

(p)new = (p)old

actualallowable

(32)

(6) Change the design variables using p(i+1) = p(i) + p.(7) If the requirements are satisfied, complete the discrete design

with consideration of manufacturability. Otherwise, go to (2)

The formulation of an optimization problem in the model correlation

appears as

Objective : R(P) min

Constraints : Ci(P)0

Design space : PLPPU (33)

Objective Ri(P) can be approximated for each design P(i) using the

series expansion,

Ri =Ri(P(i)) +

nj=1

j(R)ijPj

Pj (34)

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Fig. 8. Front rail structure model. (a) Finite element model for the model correlation

and (b) Weld points.

The gradient j(R)i/jPj can be obtained directly from the results

of finite element analysis. If the gradient is known, the search direc-tion P can be obtained from the solution of an approximate opti-

mization problem. However, the optimization problem in the model

correlations should be formulated in the minimization of strains and

stress, subject to the welding locations, panel thickness and panel

configurations due to their variations in the manufacturing environ-

ments.

5. Simulations

In order to study the behavior of the vehicle system for the well-

correlated model, a dynamic nonlinear finite element simulation is

performed. This simulation allows for the evaluation of destructive

test events using a model made up of the body structure, interior

components such as the seat frames, instrument panel and steer-ing system, and a suspension system and tire. Such destructive test

events are not only costly with respect to time, but require expen-

sive and scarce prototype vehicle, simulations of these events are

seen as the only way to accurately predict the vehicle behavior prior

to prototype vehicle availability. The destructive test events which

are chosen for simulation are a curb impact and a severe pothole

event. To perform the simulation, VPG is implemented. This tech-

nique makes use of vehicle FEA models in conjunction with the curb

road surface model.

The automotive body structure has the influences of the junction

boundaries and gradual variation shapes among the body panels.

Their manufacturabilities have influences on the structural behavior

characteristics of active stress points. In other words, the origin of

localized stress concentrations and the high strains arise from thecoupling from the welded characteristics, design variations of body

Fig. 9. Stress contour of front rail structure. (a) Stress contour without the model

correlation, (b) Stress contour with the model correlation and (c) Crack location of

front rail structure.

panels and physical properties. As a sheet metal component is

formed through a stamping process, the material undergoes changes

from its initial conditions for thickness and residual stresses. Since

materials in finite element models are typically considered uniform,

there is a potential for the material to be drastically different from

the specified, nominal material thickness. The updated material

thickness, with local material thickness changes may then be used

in the durability simulation, yielding a more accurate prediction

of potential durability problems. Their differences from the manu-

factured products may allow many gradual variations of structural

rigidity and durability that can change the location and gradients of

localized stresses. Thus, a method for predicting the body deforma-

tion during the running operations creates a body model based onthe characteristics extracted by modal analysis of the results of a

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Fig. 10. Relationship between geometric dimensions and welding location variations.

Fig. 11. Constraint trend in the simulation times.

vibration testing of an actual vehicle. In this example, the durabil-

ity loads were decided from the road running simulations based

on the actual experiments and through the maximum durability

conditions, the crack locations are found in the laboratory test. The

simulation model is limited to the front rail structure, which has

145,013 elements and 129,192 nodes. Fig. 5 shows the overall design

flow for the model correlation using the optimization design on the

geometric dimensions concerning the localized reinforced-beads

and panel thickness.

In particular, the welding locations and material thickness may

be used for minimizing the deviations of the required structural

specifications between test and simulation.

The basic concepts of the model correlation using the optimiza-

tion design as follows:

Minimize |WTEST WSIM|

Subject ton

i=1

|TESTi SIMi |

|Gweld|Gallowable,

|shape|allowable,

|tpanel| tallowable (35)

where WTest and WSIM are the respective weights for the designing

panes, TESTi and

SIMi are the strain measured from the experiment

and simulations in the Von-Mises criteria,Gweld is the location vari-

Fig. 12. Stress contour in the BIW (body-in-white) structure.

ations at the point of actual welding points, shape is the geometricvariations of the reinforced bead on the panels and tpanel is the panel

thickness. The linear constraints except the elasto-plastic material

properties [19,20] are explained as follows. The variations of weld-

ing locations have the 5 mm radius variations of spot center on

reference of CAD data. The variations of geometric dimensions have

the width, height and longitudinal length with 2.0 mm on refer-

ence of the measured stamped bead shapes. And, the panel thick-

ness has the 10% variations on reference of the initial CAD data.

The nonlinear constraints are the variations of material properties

(tangent modulus) of the stressstrain curve shown in Fig. 6, which

is concerned with the strain-hardening. The plasticity modulus (H)

shown in Fig. 6 is related to the tangent modulus (ET) by

H= ET/1 ETE

(36)

where E is the elastic modulus and ET = dY/d is the slope of theuniaxial stressstrain curve in the plastic region.
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Fig. 7 shows the road running simulation which represents the

proving ground and load time history. These loads were semi-

analytical loads and they were used as design and verification loads

to drive the design details and engineering design. Fig. 8 shows the

finite element model of front rail and weld points for the model

correlation, in the fully trimmed CAE model. In this model, all body

sheet an welds ere meshed in detail and all trim items attached to

body FEA model.Fig. 9(a) shows the stress contour of the wheelhouse of front

rail structure without the model correlation and Fig. 9(b) shows

stress contour of the wheelhouse of front rail structure with the

model correlation under maximum pothole load. Fig. 10 shows the

estimation point between geometric dimensions and welding loca-

tion variations of the specific parameters in the 3-dimension space,

which shows the nonlinearities of durability performance from the

inter-acted design parameters. In this distribution contour, it is im-

portant that the body designer decides the feasible points and inter-

relates them with other structural specifications. Thus, in the model

correlations, the design parameter screening is also important.

Fig. 11 shows the constraint trends in the simulation times. The error

shows the summation of linear and nonlinear constraints. The most

impact factor is the strain constraints with 5060% of total error.Fig. 12 shows the stress contour shown in the BIW structure under

the running condition of maximum pothole load. For the correlation

and nonlinear static analysis, the commercial softwares are used

[21,22].

6. Conclusion

The integration of simulation with physical test will accelerate

the product-development process. The bi-directional flow of infor-

mation between these two functions is critical and important for

the new design successes. Therefore, engineers should compare test

data from previous models or components against simulation results

and calibrate them to increase confidence in their simulation predic-

tions for current designs. In this point, this paper presents a designmethodology to account for nonlinear structural rigidities by con-

sidering such issues as plastic strain and residual deformation. Such

geometric dimensions as panel structure, thickness and shape can

be corrected through the optimization based correlation design pro-

cess and can consider the environment uncertainties. The advantage

of the presented procedure increases such accuracies of durability

designs as the damage locations and fatigue life. This procedure is

considered as an important tool to realize the integrated computa-

tion of dynamics and durability in the virtual prototype parts such

as the control arm and knuckle in the chassis parts. The integration

process of CAE in the design, engineering and development process

is a critical success factor for successfully delivering a vehicle with

the product integrity.

References

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[21] SIEMENS Software, NX.NASTRAN V5.0.[22] ENGINESOUS Software, iSIGHT V6.0.
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