Advanced Vehicle Body Concept Modeling Approach Using Reduced …€¦ · identify issues and to include possible countermeasures already in the initial CAD design of the new vehicle

Advanced Vehicle Body Concept Modeling Approach Using Reduced Models of Beams and Joints

G. Stigliano1, D. Mundo2, S. Donders1, T. Tamarozzi3 1LMS International - http://www.lmsintl.com Interleuvenlaan 68, B-3001 Leuven, Belgium e-mail: [email protected], [email protected]

2University of Calabria, Department of Mechanical Engineering - http://www.unical.it Ponte Pietro Bucci, 87036 Rende, Italy e-mail: [email protected]

3K.U.Leuven, Department of Mechanical Engineering, Division PMA - http://www.mech.kuleuven.be Celestijnenlaan 300 B, B-3001, Heverlee, Belgium e-mail: [email protected]

Abstract The paper presents a vehicle body concept modeling methodology based on reduced models of beams,

joints and panels. The aim of the approach is to enable accurate Noise, Vibration and Harshness (NVH)

simulations of the vehicle Body in White (BIW) already in the initial phases of the vehicle design process,

when the detailed geometry information has not yet become available. In the presented approach, concept

models of beams and joints are created, respectively, by means of a geometric analysis of beam-member

cross-sections and a static analysis of joints FE models that results in an efficient matrix formulation.

Concept panels are modeled by coarsening the original FE mesh. Improvements to the approach are

proposed through the introduction of a new connection element, so-called “RBE2.5”, which permits to

refine the modeling of shell-based beam and joint ends, leading to more accurate joint matrix formulation.

Furthermore, a new optimization process has been worked out, which allows taking into account the

discontinuities of the original beam-like structure sections.. The proposed approach has been validated by

using an industrial case study, for which the beam, joint and panel concept methodology has been used in

combination with a substructuring technique to create an efficient and accurate vehicle BIW model. More

specifically, simplified models of beams, joints and panels of the upper region of the vehicle BIW are

created, while the bottom part has been reduced by means of MacNeal‟s Method.

1 Introduction

The necessity to reduce the time-to-market in car manufacturing industry and the requirement of

improving various functional performances attribute (NVH, dynamics, safety, emission, energy

efficiency, …) lead many researches to develop predictive Computer-Aided Engineering (CAE) tools,

which can be used to predict and improve the vehicle design from the concept phase of vehicle

development onwards. Conventional software packages based on detailed geometry data of the vehicle

(CAD) and/or detailed boundary/ finite element modeling (BEM/FEM) are not directly applicable in the

early phases of the design process. Accordingly, new efficient tools are indispensable for the designers to

evaluate the functionality and the quality of the ideas, already in the early stages of conceptual design

when the available geometric data is limited. Due to this necessity, many concept modeling approaches

have been proposed with the aim to simplify and speed up the design process. A state-of-the-art overview

of concept CAE methods is given in Donders et al. [1]. Methods are classified into three categories:

methods concurrent with CAD, methods based on predecessor FE models and methods “from scratch”.

4179

The first category incorporates CAE tools, used also in the early design stage, that provide simulation

results as soon as component-level CAD models are available [2]. The second category includes Mesh

Morphing [3, 4] and Concept Modification Approaches [5, 6, 7], which are used to design a variant or

incremental improvement of an existing vehicle model. They make use of a predecessor FE model to

identify issues and to include possible countermeasures already in the initial CAD design of the new

vehicle. For example Donders et al. [1] have proposed the “Reduced Beam and Joint Modeling” approach

based on predecessor FE models. This approach allows analyzing and improving the fundamental NVH

behavior of a vehicle Body in White (BIW) in an efficient manner. The idea behind the approach is to

define a layout of beams and joints, and to subsequently create a reduced modal model at the beam center

nodes. This leads to an efficient and accurate model of the body, to which modified beam elements and

joint superelements can be added, thus enabling a concept modification of the body and an accurate

prediction of dynamic NVH performance. The commercial software program LMS Virtual.Lab [8]

includes a user-friendly implementation of the Reduced Beam and Joint Modeling approach. Design

engineers can define a beam and joint layout, calculate the body reduced modal model and perform

efficient design modification and optimization of the body beam-like sections and joint connections.

The last category of the concept modeling approaches builds-up stand-alone concept models “from

scratch”. This class of methods includes “topology design optimization” and “Functional Layout Design”

methods. In the first case the material is eliminated from an initial admissible design domain in order to

make the structure lighter without violating functional requirements [9, 10, 11]. By using the “Functional

Layout Design” approach, the designer is able to predict the performance of the model using a simplified

concept model, consisting of beams, joints and panels, which represent the functional layout of the

structure [12]. Recently, Mundo et al. [13] have proposed an alternative replacement methodology based

on the “Reduced Beam and Joint Modeling”. The idea behind this approach is that simplified concept

models of beams and joints are created, respectively, by means of a geometric analysis of beam-member

cross-sections and a static analysis of joints. In a next step, also panels can be added to complete the

vehicle body concept model. The small-sized concept model then takes the place of the detailed Body in

White (BIW) structure, so that it can be used to quickly adapt the local beam/joint definitions and

optimize the vehicle performance (in terms of global body modes) in an early design stage. A number of

challenges can be distinguished in the industrial application of this methodology. Firstly, the choice of the

beam-to-joint connection model is important for the accuracy of the concept predictions. When a

connection area consists of a number of loose panels (e.g. a ring-shaped shell beam, or a joint end

consisting of a number of connected panels), inaccuracy may arise in the connection of concept beams to

joints and in the joint superelement calculation. In this paper, this effect is studied into detail on a simple

representative case study. A sensitivity analysis in terms of displacements using different connection

models has been carried out. In particular the importance, of the choice of the beam-to-joint connection

model has been demonstrated and the joints based on rigid and interpolated multi point constraint

connections have been compared with a new joint based on hybrid connection method, using a newly

proposed element, the so-called “RBE2.5” element. The proposed connection element permits to reduce

by “Beam and Joint Modeling” only part of the BIW and to perform a local optimization of the beams-

like structure of the vehicle body. The extended body concept modeling approach (for beams, joints and

panels) has been applied in conjunction with a dynamic reduction technique on an industrial vehicle

model. Static and dynamic comparisons between the original and the simplified model have been

performed with the aim to validate the proposed concept modeling approach.

The outline of the paper is as follows. In section 2, the beam and joint concept modeling approach is

summarized. The same section presents an academic application and a sensitivity analysis with the aim to

show the influence of the beam-to-joint connection modeling on the concept model response. In section 3,

the new “RBE2.5” connection element is proposed, and a new method to identify the correction factors of

the concept beam-like structure is reported. Finally, in order to demonstrate the effectiveness of the

proposed improvements, an industrial application is reported in section 4. The paper is concluded in

section 5.

4180 PROCEEDINGS OF ISMA2010 INCLUDING USD2010

2 The beam and joint concept modeling approach: method positioning and drawbacks

2.1 Methodology status

Starting from the BIW model of a car, one can subdivide the full structure in substructures and, in further detail, into the panels, the beams and the joints that connect the several beams. Beam-like members, i.e. structures for which the dimension in the longitudinal direction is much larger than the characteristic dimension of the cross-sectional area, are the primary structural elements in a BIW. They strongly influence the natural frequencies of the vehicle body [1]. Using a predecessor model FE model (possibly aligned with new styling lines using a mesh morphing approach), one can define an equivalent “concept model” by appropriate steps. In the FE model of a vehicle, beam-like members are typically thin-walled structures, formed by shell elements. The detailed mesh of such components is simplified into beam elements by the LMS Virtual.Lab software [8] which computes equivalent beam properties at a set of beam cross-section locations that have been located by the user. The beam-like structure is then modelled by beam elements with equivalent beam properties, replacing the original shell structures. The joint simplification is realized by the use of superelements obtained by Guyan reduction. This is a method (also known as static condensation) to reduce the FE model of structures into a reduced description in terms of the stiffness and mass matrices condensed at the end nodes [14]. In “Reduced Beam and Joint Modelling” the static condensation is performed on the central nodes of the interpolation constraint elements (RBE3 Nastran element) positioned at the end sections of the joint (see Figure 1). These central nodes of the RBE3 elements are used to connect the joint to the end nodes of the beam-like structures. Typically the beam-like members of a vehicle have discontinuity properties due to holes, spot-welds and stiffeners. In order to take into account this problem, the nominal reduced beam elements properties (I11,nom, I22,nom, I12,nom, Jnom) need to be corrected through the use of correction factors (C11, C22, C12, CJ) found by a model updating. Once the correction factors of each reduced beam-like structure are established, the corrected beam properties can be identified as well:

nomICI ,111111 (1)

nomICI ,222222 (2)

nomICI ,121212 (3)

nomJ JCJ (4)

where Iik,nom represents the stiffness parameter computed through the geometric approach, Cik is the corresponding correction factors and Iik is the corrected stiffness parameters.

An overview of the procedure that is used to estimate the mass and stiffness properties of the simplified beam and joint models can be found in Mundo et al. [13]; furthermore in that paper, the above mentioned approach for the replacement of beam-like structures and joints in a vehicle model has been proposed.

(a) (b)

Figure 1: Concept beams converging into a detailed (a) and a concept (b) joint

VEHICLE CONCEPT MODELLING 4181

Recently, Mundo et al. [15] proposed a new improvement of the technique by adding also the important

contribution of the panels into the concept model. Even if the global modes of a vehicle structure are

dominated by the primary beam and joint structure, the panels give an important contribution to the body

stiffness as well [16].

Therefore, in this last paper, also two-dimensional panels have been included in the approach to build up

the concept model of the car. For this reason, a procedure for the creation of panel concept models has

been proposed. In particular a concept model of the panel, with shape and curvature closely representing

those of the original model, is created by using a very coarse mesh (as compared to the detailed original

panels), which is sufficiently accurate for the concept predictions of interest. In order to connect the

surrounding concept beams and joints to the panels a point-to-point connection is achieved by rigidly

connecting each boundary node of the panel to the closest beam centre node. Furthermore, in order to

validate the approach, an application to a vehicle‟s BIW has been carried out. In particular two static load

cases and dynamic comparisons have been used. Differences of +0.26% and +0.06% of the stiffness

between the simplified and the original models have been obtained for the torsion and bending static load

cases, respectively. The dynamic comparison between the two models has shown a maximum

eigenfrequency difference of 1.59% and a MAC value of 0.94. This accurate static and dynamic prediction

of the behaviour of the full vehicle has been obtained after a single global optimization of the concept

model to improve the static performance. By the model updating procedure, the stiffness correction factors

for each beam-like structure can be found and so that a replacement model can be established by which it

is possible to perform an easily fast concept optimization. This global model updating of the concept

model represent a drawback of the procedure. In fact the correction factors of all the beam-like structures

were found by a unique optimization process and problems of compensation between the corrections

factors of the different beams can be achieve. In order to avoid this problem a local beam-like structure

model updating has to be carried out. Once the correction factors of each beam-like structure have been

found and so an accurate local representation has been obtained, the beams can be assembled in order to

obtain the final vehicle model. In this case an accurate beam to joint connection is essential for the

building of the full model. The present paper shows the influence of the beam and joint model in the

concept model with the final goal to realize an accurate “local model” for which no global optimization

step is required. Furthermore, this paper looks into detail into the joints models. The validity of the

conventional joint to beam connection is discussed and an alternative technique is introduced and

assessed.

2.2 Academic application and sensitivity analysis

In order to evaluate and to compare the contribution of the beam-to-joint connection into the conceptual

model the simple model reported in Figure 2 has been used. The model can be seen as a simplification of

the beams and joints of the upper region of a vehicle BIW. The displacements obtained on this “original

model” have been compared with those obtained on two different models obtained by subdividing and

reducing the original model in several parts; in particular the original structure (see Figure 1) has been

split in 8 beam-like structures (bright parts) and 3 joints (dark parts) following the procedure described in

Donders et al. [1]. The parts have been connected at the beam center nodes (see Figure 3) by using two

kinds of connection elements: a rigid spider (RBE2 Nastran elements) or an interpolation spider (RBE3

Nastran elements). Once the beams and joints have been identified, a reduction has been performed. In

particular, by the program LMS Virtual.Lab [8], the beam-like structures have been reduced (see Figure 4)

by equivalent beam elements and the joints have been reduced into superelements (Nastran DMIG - Direct

Matrix Input Grid) by the Guyan condensation at the central node of the connection elements (RBE3 or

RBE2).


Figure 2: Original structure. Figure 3: Particular of the

Joint-to-Beam connection.

Figure 4: Reduced model.

The structures have been loaded by a force (F) in y-direction and have been clamped on the external

beam-like structures. For the original structure, the load and constrains have been applied at the central

node of the rigid elements (Nastran RBE2 element) situated at the ends of the beam-like structures,

whereas for the reduced structure the load and constraints have been applied at the end nodes of the beam

elements. In order to evaluate the mean displacements of the cross-sections of the beam-like structures,

the central nodes of a series of RBE3 elements positioned in the beam-like structures have been used (see

Figure 5). The displacements in the y-direction obtained for the reduced models (RBE3-connected and

RBE2-connected) are compared in Figure 6 with the displacement obtained on the original structure; on

the horizontal axis, the X-position of the RBE3 elements used for the comparison has been reported.

0.00

0.05

0.10

0.15

0.20

0.25

100 210 290 370 450 620 710 790 870 950

X

Dis

pla

cem

ents

[m

m]

Original model

Concept model - RBE3 connected

Concept model - RBE2 connected

Figure 5: Detailed view of the RBE3

elements that are used for

interpolating/comparing the cross-

sectional displacements.

Figure 6: Influence of the beam-to-joint connection: the

displacements obtained on the original structure are

compared with the displacements obtained on concept

model.

One can observe that the displacements are very sensitivity to the beam-to-joint connection model used.

The same trend has been observed also when the load is applied in x and z directions. Small displacements

variations, within 1%, can be observed if the structure is split but not reduced, which means that no

problems in reduction of the original structure occur. On the contrary, large variations of the response can

be obtained by changing the beam-to-shell connection (RBE3 or RBE2). The RBE2 connection makes the

cut structure stiffer than the original connection, whereas the RBE3 connection makes it more flexible.

This stiffening is due mainly to the rigid connection of the end section with the central node of the rigid

element (used for the Guyan reduction), whereas the RBE3 elements accurately describe the displacement

of the end section but not its rotation [17]. Furthermore, „end effects‟ at the cut shell beams (that are not

reduced, but to which the concept beams and joints must be connected) and at the ends of the original

shell joints (that are used as a basis for the Guyan reduction) can increase the error introduced by the

„flexible‟ RBE3 connection at that end. The end effect problem is inherent to the splitting process, in


which the original structure is divided in beam-like structures and joints. In this case, the stiffness of the

section decreases because the shell elements that belong to the end-section of the beam-like structures are

not connected any more to the shell elements that belong to the end-section of the joints. Towards obtain

good results on the cut model and therefore on the reduced model, the development of an appropriate

beam-to-joint model connection is of crucial importance.

3 Advanced solution

3.1 New beam to joint connection: the RBE2.5 element

As it has been shown in the previous sections, the RBE3 connection is not appropriate to describe the

rotation of the beams and joints end-section, as the introduced flexibility by the RBE3 element limits the

accuracy of the concept model. On the other hand, the use of rigid RBE2 connection increases the

stiffness of the structure. To avoid this stiffening effect and to better describe the section-rotation with

respect its central node, a new connection has been developed that combines the best of both worlds (no

end effects and no stiffening effect). The proposed new connection element takes the quality of the RBE2

in describing the rotation of the end section but, it doesn‟t suffer from end effect problems (as the RBE3

element). In analogy, this new element has been called “RBE2.5” connection. As shown in Figure 7, this

new connection element is composed of 1 RBE2 and 10 RBE3 elements. In particular the end section is

divided in 10 sectors wherein all the nodes belong to each sector are connected by RBE3 elements to a

central node. These central nodes are found by an average of the positions of the nodes that belong to

each sector. Starting from the central nodes of the 10 RBE3 elements, an RBE2 element is built (see

Figure 7). The number of 10 RBE3 elements has been selected as a good balance between ensuring

connectivity while limiting the number of additional elements. The construction of the proposed

connection-element can be completely automatized also for general cross sections.

The new connection model has been applied to the end-section of the joints of the structure in Figure 2,

and the response of the reduced model has been obtained by using these new elements. The displacement

results are shown in Figure 8 and compared with the conventional results. As can be observed, the

response of the reduced structure modeled by using the RBE2.5 in the end sections of the joints is closer

to that of the original structure. A very limited stiffening effect with respect the original structure is

introduced mainly by the beam-like structures, which are modeled by few beam-elements and not by

shell-elements anymore. However, it is clear that the proposed connection element is a good solution for

the beam-to-joint connection.

0.00

0.05

0.10

0.15

0.20

0.25

100 210 290 370 450 620 710 790 870 950

X

Dis

pla

cem

ents

[m

m]

Original modelConcept model - RBE3 connectedConcept model - RBE2 connectedConcept model - RBE2.5 connected

Figure 7: RBE2.5 connection element: the

RBE2 element (red element) is connected by

spring elements to the central nodes of 10

RBE3 elements (green elements).

Figure 8: Influence of the beam-to-joint connection.


3.2 Local beam optimization

In the FE model of a vehicle, beam-like members are typically thin-walled structures, formed by shell

elements. In order to take into account the discontinuities of the original beam-like structure sections (due

to holes, spot-welds, stiffeners), and the fact that the beam-like structure modeled by beam elements are

stiffer than the original shell structure, the reduced beam elements properties (I11, I22, I12, J) need to be

corrected in an updating calculation. In Mundo et al. [13] the correction factors have been found by a

global model updating. This provides a substantial improvement as compared to not making the

correction, but it has the disadvantage that compensation effects might be introduced: for instance, a

corrected parameter at one beam might actually be compensating an error in another beam or a joint. This

compensation limits the representativeness of the concept model w.r.t. the original structure.

The use of the proposed RBE2.5 connection element avoids the end-effect problems and as such it permits

to perform a more accurate local beam optimization. In order to find the correction factors, a single model

updating can be carried out on each of the individual reduced beam-like structures. In this case, the static

response of the concept beam-like structure is compared to the response of the original structure. In the

updating analysis setup, the two structures are considered as cantilever beams (see figure 8 and 9): a

normal, a bending and a torsion load are applied in a single load case for both the original and the concept

model, and the reduced beam parameters are updated in such way that the static performance of the

reduced structure represents well the static performance of the original structure.

In particular for the original beam-like structures a RBE2.5 element is added to each end-section. The

characteristics of the concept beam elements are updated by a Genetic Algorithm (GA) [18] in order to

minimize the following error function:

3

1jO

j

O

j

C

j

O

j

O

j

C

j

x

xx

(5)

where jx is the displacement of the end node in j direction, j is the rotation of the end-node in j direction, the subscripts “O” and “C” denote the displacement or rotation obtained on the original beam and on the concept beam respectively.

4 Industrial application

In order to validate the proposed approach, the static and dynamic responses of a vehicle body in white

(BIW) are considered. These responses are evaluated for both the original BIW model and the simplified

(or conceptual) model. Figure 11 shows the flow chart of the process to reduce an original BIW into a

representative body concept model. In order to illustrate the concept modeling methodology, the front-

upper region of the vehicle has been selected as target of the concept design. As shown in Figure 11,

group of 11 beam-like structures are replaced by equivalent simple beams and a local beam optimization

is carried out for each of them following the procedure described in the previous section. Four joints are

replaced by static super-elements (i.e., the equivalent mass and stiffness matrices of each joint). Finally,

the vehicle concept model is completed by 3 panels (the front windshield, the vehicle roof and the rear

windshield). These panels are modelled with a coarse mesh, connected to the surrounding concept beams

Figure 9: Concept beam like structure. Figure 10: Original beam-like structure.


by means of rigid connections. The remainder part of the BIW is not the focus area of the concept study.

Therefore, in order to obtain a small FE model (in terms of degree of freedom) without losing accuracy in

the static and dynamic response, a dynamic reduction of this remainder part is performed. In particular,

the remainder FE model has been reduced by using a method based on MacNeal‟s reduction on the

interface nodes [19]. With the aim of assessing the proposed beam-to-joint connection, to model the joint

end section and to connect the remainder to the beam elements different solutions have been tested: the

RBE3, the RBE2 or the RBE2.5 connection elements.

Figure 11: flow chart of the BIW reduction.

In the following sections the static and dynamic comparisons have been reported.

4.1 Static validation

In order to validate the static accuracy of the concept model, in line with the standards used by automotive

manufacturers, two indicators of the full-vehicle static behaviour are defined: the bending and torsion

static stiffness. These indicators are evaluated for both the original and the concept body model by using

the two load cases shown in Figure 12. In both cases, the vehicle body is clamped at the rear suspension

locations, while two vertical forces are applied at the front suspensions (points A and B in the same

figure). Based on the estimation of the vertical displacements (vA and vB) at the excitation points, the

bending and torsion stiffness of the vehicle body are determined as:

b

b

LFK

2 (6)

t

t

WFK

(7)

Original Model Concept model

Beam & Joint reduction

Panel reduction

Remainder reduction

Coarsening

Guyan

Equivalence


where F is the amplitude of the vertical forces, L is the wheelbase and W denotes the width of the car, while the deflection angles in the bending and torsion load case are respectively given by b and t :

L

vvarctan BA

b2

(8)

W

vvarctan BA

t (9)

(a) (b)

Figure 12: Static load-cases defined to estimate the BIW stiffness under (a) torsion and (b) bending.

By means of static FE analyses, performed on both the original model and the concept model, the stiffness

properties of the vehicle body are estimated in accordance with eqs. (6) and (7). The variations of the

bending and torsion stiffness of the concept model as compared to the original model are provided in

Table 1. In the same table, the computational time to perform the Finite Element Analysis (FEA) is

indicated as well. The results show that both the bending stiffness and the torsion stiffness of the original

vehicle model are accurately predicted by the concept model, given that the errors are very limited (0.4%

for bending and 2.0% for torsion) when the RBE2.5 connection model is used. As for the academic case

study, also for this vehicle body analysis case the RBE2 connections increase the concept model stiffness

whereas the RBE3 elements are not suitable to model the beam-to-joint connections.

Model Stiffness variation (%) FEA

computational

time [s] Torsion Bending

Original model - - ~ 6000s

Concept model

RBE3-connected -33.6% -22.8% ~ 5s

RBE2-connected 38.4% 0.8% ~ 5s

RBE2.5-connected 2.0% 0.4% ~ 5s

Table 1: Comparison of torsion and bending stiffness for the original and the concept FE model.

By comparing the computational time reported in Table 1, it can be seen that the analysis of the concept

model is 1000 times faster than the analysis original model, while maintaining the accuracy in the

predictions. This makes the concept model very suitable for efficient model updating, modification

analysis and vehicle body optimization studies. Furthermore, the concept model allows more design

freedom for „what-if‟ studies on the stiffness characteristics of beams and joints. That is, one can easily

modify the (cross-sectional area, inertia, stiffness, …) properties of concept beams and joints to identify

the most suitable modifications to improve the functional performance of the full vehicle body, which is

not directly possible on the complex-shaped cross sections of the original shell mesh.

F F

A B

Clamped

F F

A B

Clamped


4.2 Dynamic validation

In order to validate the proposed concept modeling methodology in dynamic terms, the frequencies and

mode shapes of the BIW are estimated by a FE modal analysis for the concept model (RBE2.5 connected)

and for the original model. The eigenfrequency values of the global modes in the low-frequency range of

0–40Hz are used as dynamic indicators to evaluate the correlation between the two models. In Table 2, the

natural frequencies of the first 7 global modes for the original and the concept FE model are reported. The

results show that the concept model is very accurate in terms of eigenfrequency prediction for the first 4

modes, which are the global modes of the body. A further comparison is also performed in terms of modal

shapes by using the Modal Assurance Criterion (MAC) [20]. A correlation index between two generic

modes V1 and V2 that belong to the modal matrix of the original and the concept model respectively is

evaluated as:

j

H

ij

H

i

j

H

i

jiVVVV

VVMAC

2211

2

21

, (10)

where superscript H denotes the conjugate transpose of a vector. For the analyzed vehicle body and its

concept model, the resulting MAC matrix has been evaluated by using all the nodes that are shared by the

original and the simplified model is reported in Figure 13. Observing the diagonal MAC values, listed also

in Table 2, it can be seen that the concept model accurately approximates the detailed model in terms of

the first 6 global mode shapes.

Original

model

Concept

model

Mode [Hz] Mode [Hz] % MAC

1 27.3 1 27.3 0.0% 0.95

2 27.4 2 27.5 0.4% 0.90

3 30.4 3 30.5 0.3% 0.97

4 31.8 4 32.0 0.6% 0.91

5 34.9 5 35.9 2.9% 0.82

6 36.8 6 36.9 0.3% 0.81

8 37.6 9 39.8 5.9% 0.72

Table 2: Dynamic comparison between the original

and the final concept FE model in terms of natural

frequencies and modal correlation factors.

Figure 13: MAC matrix between the original

and the conceptual model.

Also in the dynamic analysis case, the computational time for the dynamic analysis of the concept model

is about 1000 times shorter than the time to calculate the original model.

5 Conclusion

In this paper, new improvements to the “Beam and Joint Concept Modeling” methodology have been

presented and validated. In particular, the importance of the choice of the beam-to-joint connection has

been highlighted and a new connection element has been proposed: the so-called RBE2.5 element. Further

improvements on the identification of the beam correction factors for the beam-like structures have been


obtained by a local beam updating procedure that can be used for concept models that are modeled with

the RBE2.5 connection elements (thanks to the avoidance of „end effect‟ errors with this new connection

model). In order to validate the methodology an academic and an industrial cases study have been

analyzed. In the industrial case, the original mesh of eleven beam-like members, four joints and three

panels from the front-upper part of a vehicle body have been replaced by equivalent beam elements, joint

super-elements and concept panels respectively. Finally, a dynamic reduction of the remainder part has

been carried out in order to obtain a very efficient body concept FE model with few degrees of freedom

respect the original model, on which accurate static and dynamic analyses can be performed. Accordingly,

this body concept model is very suitable for a fast concept optimization, as individual beam properties can

be modified efficiently and accurately, and moreover in a more straightforward manner as compared to

modifying the complex-shaped cross-sections of the original beam-like structure. In order to compare the

original and the concept models in terms of full vehicle static stiffness and dynamic behavior, two static

load cases and a modal analysis case have been used. In both cases, a good correlation between the

simplified and the original models has been obtained, which proves that the proposed approach can be

used as a valid tool also in the initial phases of the vehicle design and development process. Future

research includes the definition and solution of the inverse problems of the methodology: starting from an

optimized body concept model (with an optimum layout, mass and stiffness properties) one should be able

to smoothly/automatically derive a new 3D geometry model that corresponds with the optimum layout.

Acknowledgements

We kindly acknowledge IWT Vlaanderen for their support of the project IWT-090408 “CHASING”.

Furthermore, we gratefully acknowledge the European Commission for their support of the Marie Curie

ITN “VECOM” FP7-213543, from which Giambattista Stigliano and Tommaso Tamarozzi hold an Initial

Training Grant (http://www.vecom.org/).

References

[1] S. Donders, Y. Takahashi, R. Hadjit, T. Van Langenhove, M. Brughmans, B. Van Genechten, and

W. Desmet, A reduced beam and joint concept modeling approach to optimize global vehicle body

dynamics, Finite Elements in Analysis and Design 45 (2009), no. 6-7, 439–455.

[2] C. Ledermann, C. Hanske, J. Wenzel, P. Ermanni, and R. Kelm, Associative parametric CAE

methods in the aircraft pre-design, Aerospace Science and Technology 9 (2005), no. 7, 641–651.

[3] H. Van der Auweraer, T. Van Langenhove, M. Brughmans, I. Bosmans, N. El Masri, and S. Donders,

Application of Mesh Morphing Technology in the Concept Phase of Vehicle Development, Int. J. of

Vehicle Design, Issue on Computer Aided Automotive Development 43 (2007), no. 1-4, 281–305.

[4] M. Alexa, State-of-the-art reviews: recent advances in mesh morphing, Computer Graphics Forum

21 (2002), no. 2, 173––197.

[5] L. Long, Design-oriented translators for automotive joints, Ph.D. thesis, Virginia Polytechnic

Institute and State University, Blacksburg, Virginia, September 1998.

[6] J. Piranda, S.J. Huang, S. Corn, C. Stawicki, and X. Bohineust, Improvement of dynamic models in

car industry, Proceedings of IMAC XV, (1997), pp. 85–91.

[7] G. Prater Jr., A. Shahhosseini, E. Juo, P. Mehta, and V. Furman, Finite Element Concept Models for

Vehicle Architecture Assessment and Optimization, SAE 2005 World Congress Proceedings

(Detroit, MI, USA), no. 2005-01-1400, (2005).

[8] LMSInternational, LMS Virtual.Lab Rev 8B, (Nov 2008).

[9] M. Bendsøe, N. Olhoff, and O. Sigmund, Topology optimization - theory, methods, and applications,

second ed., Springer Verlag, Berlin, Germany, (2004).


[10] L. Wang, P. Basua, and J. P. Leiva, Automobile body reinforcement by finite element optimization,

Finite Elements in Analysis and Design 40 (2004), no. 8, 879–893.

[11] S.-L. Lee, D.-C. Lee, J.-I. Lee, C.-S. Han, and K. Hedrick, Integrated process for structural-

topological configuration design of weight-reduced vehicle components, Finite Elements in Analysis

and Design 43 (2007), no. 8, 620–629.

[12] C. B. Chapman and M. Pinfold, The application of a knowledge based engineering approach to the

rapid design and analysis of an automotive structure, Advances in Engineering Software 32 (2001),

no. 12, 903–912.

[13] D. Mundo, R. Hadjit, S. Donders, M. Brughmans, P. Mas, and W. Desmet, Simplified modeling of

joints and beam-like structures for BIW optimization in a concept phase of the vehicle design

process, Finite Elements in Analysis and Design 45 (2009), no. 6-7, 456–462.

[14] R. Guyan, Reduction of stiffness and mass matrices, AIAA Journal 3 (1965), no. 2, 380–387.

[15] D. Mundo, S. Donders, R. Hadjit, G. Stigliano, P. Mas, and H. Van der Auweraer, Concept

modelling of automotive beams, joints and panels, Proc. World Scientific and Engineering Academy

and Society (WSEAS) International Conference on FD, FEM, FV and BEM (Bucharest, Romania,

April 20-22), (2010), pp. 634–107.

[16] S. Gabbiadini, B. Van Genechten, B. Pluymers, S. Donders, M. Brughmans, and W. Desmet, On the

use of a panel contribution analysis for the characterization of vehicle static and dynamic stiffness

properties, Proceedings of ICED (International Conference on Engineering Dynamics) (Carvoeiro,

Portugal, 16th-18th April 2007), (2007), pp. 634–107.

[17] MSC, Nastran 2004 reference manual, MSC, Santa Ana, CA, USA, 2004.

[18] D. Mundo, J. Y. Liu, and H. S. Yan, Optimal synthesis of cam-linkage mechanisms for precise path

generation, Journal of Mechanical Design, ASME Transactions 128 (2006), no. 6, 1253––1260.

[19] R. H. MacNeal, A hybrid method of component mode synthesis, Computers & Structures 1 (1971),

no. 4, 581 – 601.

[20] W. Heylen, S. Lammens, and P. Sas, Modal Analysis Theory and Testing, second ed., Katholieke

Universiteit Leuven, Department of Mechanical Engineering, (1997).


Documents

Advanced Vehicle Body Concept Modeling Approach Using Reduced …€¦ · identify issues and to include possible countermeasures already in the initial CAD design of the new vehicle