Investigating the use of reduction techniques in concept modeling for vehicle body design optimization

Transcription

1 Investigating the use of reduction techniues in concept modeling for vehicle body design optimization T. Tamarozzi 1, G. Stigliano 2, M. Gubitosa 2, S. Donders 2, W. Desmet 1 1 K.U.Leuven, Department Mechanical Engineering - Celestijnenlaan 300 B, B-3001, Heverlee, Belgium Tommaso.Tamarozzi@mech.kuleuven.be 2 LMS International - Interleuvenlaan 68, B-3001 Leuven, Belgium marco.gubitosa@lmsintl.com Abstract The use of Computer Aided Engineering (CAE) tools in the automotive industry is nowadays a confirmed approach to predict the various functional performance attributes (ride and handling, NVH, crashworthiness, etc.) and adapt the design based on the outcome of virtual simulations. In particular, reduction of the time to market has been one of the main thrusts in the automotive sector in the last years, pushing researchers to find more efficient methods to solve design problems. This paper proposes a systematic procedure to efficiently evaluate the influence of design changes on the vehicle performance. The approach is based on a detailed Multibody (MB) model of chassis and suspensions of a passenger car including its Body In White (BIW) as a flexible element. Several reduction techniues (Guyan, MacNeal, Beam and Joint concept modelling) have been adopted in order to accurately represent the BIW flexibility, thus allowing a fast investigation of its influence on different driving scenarios. 1 Introduction In the last decades the use of CAE techniues has greatly reduced the time reuired to design new products. FE and MB techniues which worked in parallel in the past are now being integrated together by using flexible multibody techniues [1-3]. Detailed FE models for NVH analysis usually consist of a very large number of degrees of freedom (DOFs) making the integration between the rigid MB simulations a challenging and time consuming task. The need for expensive physical prototypes is still present even though the number of iterations between simulation results and tests on new models are being constantly reduced due to the increasing reliability of virtual models. In the vehicle industry, design engineers do not have to deal with design of new models from scratch (e.g. the BIW of a vehicle). Often detailed information from a predecessor CAE model can be re-used, and one can incorporate carry-over as well as newly designed components to already achieve predictive CAE models in the concept design stage of vehicle development. This is necessary in order to steer and give more reliable design guidelines for the first CAD model of the new vehicles, to avoid the need of substantial modifications at a later stage in the design timeline, when the cost of such changes will be much higher. This paper aims to give an overview of the full modeling process of a passenger car in which some of the above mentioned techniues will be applied together. The methodology will cover the preparation of a detailed rigid multibody model and the integration of a flexible concept model of the BIW (Fig. 1). The latter is obtained using a series of different reduction techniues which are briefly described [4-7]. This approach allows for fast modifications in order to explore different design possibilities to reach defined targets. Finally examples of ride and handling maneuvers are performed to evaluate the influence of the 4191

2 4192 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 body flexibility on some standard ride and handling parameters allowing the assessment of the method for industrial applications. Fig. 1 From Full FE to Concept Model. 2 Brief overview of the state of the use of the adopted methodologies The creation of a reliable flexible multibody model (FMB) to be used in vehicle dynamics performance evaluation is a complex task. Many software packages allow to exploit design changes and influence of various parameters on specific targets. In classical approaches the handling characteristics of vehicles, are evaluated with the aid of MB models in order to predict their overall behavior using a series of rigid bodies that are connected through ideal joints and force elements like spring, dampers and bushings. In a second stage, the reaction forces at the connection points evaluated with these models can be used as input in classic FE codes to evaluate the NVH characteristics of the considered system, with reasonable reliability. The need for increasing accuracy and reducing computational time pointed towards coupling together systems which undergo global large displacements and also local deformations. A number of methods of interest are outlined in the remainder of this section. 2.1 Flexible Multibody Different approaches are available in commercial software packages to couple flexibility of elements with their large global motion. A good review of these methodologies can be found in [1-2]. Three main approaches are distinguished: Floating Frame: a global frame that follows the gross motion of the body describes the large displacements of the system while a linear FE model or a modal reduction expressed in this local frame describes the flexibility of the single components; Co-rotational Frame: Each finite element of the flexible body is described within a local frame which follows the net motion of the element; Inertial Frame: Flexible motion is described in a global inertial reference frame. The two last approaches are more recent and can be used also to describe systems that undergo large deformations. For many vehicle dynamics applications this is not necessary, which explains why the first methodology is often preferred. The euation of motion of a FMB system using the floating frame of reference can be described by the euation (1):

3 VEHICLE CONCEPT MODELLING 4193 T e c M ( ) K [ ] Q (, t) Q (,, t) ( R,, f, t) (, t) 0 (1) In euation (1), [M()] is the mass matrix of the full system and [K] is a block diagonal matrix composed by the zero matrix in the part related to the floating frame position and orientation and by the constant stiffness matrix of the flexible bodies; {} = {R,θ, f } is the vector of unknowns of the system where R and θ represent the position and orientation of the floating frames of reference related to each body and f is the position of each node of the flexible components (or the modal participation factors of the vibration modes in case that a modal based reduction techniue is adopted). Ф is the set of algebraic constraint euations relative to the ideal joints present in the model (Ф represents its Jacobian) and Q e is the vector of the generalized forces acting on the bodies. Many software packages give nowadays the possibility to integrate flexible components in their MB codes using modal based approaches. In that case a full FE model can be simplified using reduced mass and stiffness matrices that have been obtained by Component Mode Synthesis (CMS) techniues. 2.2 Component mode synthesis (CMS) Since FE models of complex systems are typically very large models with many of degrees of freedom, it is usually impractical to include a full FEM within a MB model within a floating frame of reference approach. A range of techniues can be used to greatly reduce the number of degrees of freedom keeping a reasonable accuracy for the displacements of the flexible bodies in the freuency range of interest. The first author to propose such a reduction was Guyan [8] who reduced with the aid of static vectors the mass and stiffness matrices of FE models. This simple approach guarantees the modeling of the exact static behavior and approximate results in the uasi static range up to low freuency dynamics. To include a correct representation of both the static and dynamic response of the system in the model many authors [6-7] have proposed to use different sets of dynamically responding vectors (namely normal modes of vibration obtained using different boundary conditions at the interface points) and a set of static vectors computed applying unit loads or unit displacements to the original systems in all the DOFs that would have been loaded during the simulation. The combined set of dynamic and static vectors is used for the reduction of the FE mass and stiffness matrix. In this way the solution is guaranteed to be exact at 0Hz and high accuracy is obtained when all the excited dynamic modes are included in the normal modes base. Often, as a rule of thumb, normal modes up to times the maximum freuency of the excitation spectrum are included in the normal modes base. The reduction procedure of the full FEM with the aid of the selected static and dynamic modal base is summarized by e. (2-3) M M x xi x xi T ee ei e T ee ei e s ie M M ii s e M K R x s R K K ie xe K K ii f f x s s T f f e i (2) (3) Here Φ s represents the static vectors set, ψ the normal modes set, the suffix e stand for external DOFs (where loads are applied), i stands for internal (not loaded) DOFs and for the dynamic modal participation factors. The decision of the type of normal and static modes is often a matter of experience and is mainly driven by the engineering judgment related to the boundary conditions of the flexible component under analysis. Normal modes can be computed by imposing different boundary conditions (BCs) at the location where the flexible body is connected to the rest of the structure. Generally, when the BCs are considered to

4 4194 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 constrain the component in a very rigid way, fixed interface normal modes are adopted. When the BCs are instead less stiff (e.g. connection with soft springs), free-free interface BCs are imposed. The selection of static modes brings the same static response of the original FE model provided that a statically complete set is adopted [7]. This means that a static mode should be included in the set for each interface DOF as well as for any DOF that is externally loaded. In complex structures like a car BIW, where the input and boundary locations are multiple and the true BCs are often unknown a priori the selection of the proper modal base is not trivial. Note here that by introducing static modes, one also introduces spurious eigenfreuencies at high freuency. These are not representative of any physical behavior. Thus when running a simulation, the engineer has to verify the way these modes are treated by the adopted software program. Solvers with numerical damping allow smoothening of the solution in the freuency domain above a certain freuency level [9]. Other common techniues are the application of modal damping to the static modes or modification of the modal mass matrix to shift these peaks at different freuencies. In this work different reduction techniues have been applied to a vehicle BIW application case, and finally the selection of free-free normal modes and static attachment modes was chosen. 2.3 Beams and Joint concept modeling One of the main drawbacks of CMS techniues is that, even though the proper dynamics of the reduced component is well captured, it is often difficult to uickly make modifications to the model in order to evaluate different design changes. As highlighted in the introduction (Fig. 1) the original FEM of the BIW of a passenger vehicle was reduced and combined with a detailed MB model describing driveline and suspensions. The aim is to explore the influence of the flexibility of the BIW on the ride and handling performance in view of uick troubleshooting related to different design modification. Adopting standard CMS techniues on the full body is uite impractical for sensitivity analysis since a new reduction should be performed for each modification to be applied to the original FEM. The reduction procedure is relatively time consuming for models comprising millions of DOFs. For this main reason the top part of the car BIW has been reduced following a concept modeling approach named Beam and Joints [11]. This methodology proposes the reduction of thin-walled beam-like structures into simple beam elements. In the considered BIW a group of beam-like structures that are originally modeled with shell elements is replaced by euivalent beams whose properties are computed by means of a local beam optimization procedure as described in [5;11]. After this reduction is performed all the beams are connected together by means of the original joints reduced with the Guyan techniue. The top part of the vehicle is then attached to the remainder part of the BIW which has been reduced by means of 25 free-free normal modes and static attachment modes at the connections with driveline, suspensions and sub-frame. The layout of the reduced model is shown in Fig. 2. This methodology has been validated and it has been shown that reliable results are obtained regarding the static response of the system both in bending and torsion. Moreover the modes up to the 8 th resonance freuency were found to have a high value of the Modal Assurance Criterion (MAC) when compared to the original FE model and a small error on the predicted natural freuencies (Table 1). Mode number 6 was instead not detected properly, probably due to the fact that it is a local mode of one of the roof beams and the concept model was not able to detect it in a correct way. Note that the concept model is mainly aimed to provide insights relating to the global flexible behavior of the BIW so that it is not strictly needed to produce accurate local information e.g. at a particular location on the beam-like structures. Table 1 also shows results related to percentage difference between the eigenfreuencies of the original model and of two variants of the flexible BIW in which the beams and remainder stiffness properties were modified. These models will be more accurately discussed in the next sections.

5 VEHICLE CONCEPT MODELLING 4195 Fig. 2: The reduced Concept modeling and MAC (0.3-1 scale) comparison of the connection nodes wrt to the original model REFERENCE MODEL MODES # ORIGINAL CONCEPT MODEL Error % MOD. BEAMS CONCEPT MODEL Difference % MOD. REMAINDER CONCEPT MODEL Difference % 1 1.3% 2.8% 9.2% 2 1.2% 8.4% 9.5% 3 0.1% 0.0% 14.9% 4 0.5% 0.9% 12.8% 5 0.0% 0.7% 14.0% 6 NOT DETECTED 7 0.3% 0.7% 14.1% 8 2.2% 2.5% 13.0% 9 0.3% 3.8% 13.8% Table 1 : % error and differences between eigenfre. of the original model and of the 3 variants of the flexible BIW 3 The Rigid MB model and the integration of the flexible BIW Starting from an industrial FE model of a full vehicle (provided by a car manufacturer), a detailed MB model has been prepared with the aid of the software LMS Virtual.Lab Motion [21]. The mass and inertia properties of all the rigid bodies have been evaluated and the location of all the connection points between the bodies has been extracted. The vehicle under analysis is a rear wheel drive (RWD) model mounting a multilink back suspension and a McPherson type front suspension. The bushings connecting the suspension links to the BIW and to the subframe have been mainly modeled with static non-linear stiffness and damping characteristics. Shock absorbers have been modeled with non-linear stiffness and damping properties; bump and rebound stops have been included as well. The steering system has been modeled by means of kinematic joints. The driveline masses and connections have also been included. The vehicle was driven by velocity drivers applied to the revolute joint between the wheel rims and the spindles. The exhaust pipe has been modeled as a rigid body, rigidly bracketed to the engine block. Two torsion bars (front and rear) have also been included by means of concentrated rotational springs. Windshields, doors and roof have not been included in this preliminary study even if it can be shown that they play a major role in the torsional stiffness characteristics of a BIW. The model with the conceptual BIW is shown in Fig (3). The total weight is about 1240 kg, 74 rigid bodies and one flexible are connected via 65 ideal joints (bracket, rotational, spherical, CV, etc.) and 75 force elements (spring, damper, tyre, bushings, etc.). Table 2 shows some of the details and settings of the MF tyre (i.e. Delft Tyre by TNO [22]) model adopted for the simulations.

6 4196 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 Tyre Characteristics Tyre operational settings Tyre Weigth [ kg] 9.3 Contact Type used Smooth road / 2d road Rim Radius [mm] 190 Dynamics Non Linear Relaxation / Rigid Ring Width [mm] 152 Slip Forces Combined slip Unload Radius [mm] 312 Table 2 : Tyre model characteristics Fig. 3 : The flexible multibody model under analysis After the preparation of the rigid MB model (addressed to as RIGID), three different flexible BIW models have been prepared. The first model (denoted as FLEX from here onwards) is the one described in section 2.3 which allowed for an accurate description of the global modes up to around 36 Hz. In the second model (BEAMS FLEX) the inertia properties of the beams (Ixx, Ixy, Iyy, Izz) were reduced with 50% without changing the section area to assess their influence on the global modes. It was found (table 1) that only a slight freuency shift of the global modes was induced after the 3 rd freuency while the first two global modes freuencies (torsion and bending) were reduced. This might indicate that the modes after the third are only slightly influenced by the beams stiffness while it seems that the remainder part of the vehicle played a higher role. To further investigate this assumption a fourth model was prepared (REMAINDER FLEX) keeping the original concept beams and reducing homogeneously the stiffness property of the steel components of the remainder from 210 GPa to 150 GPa. Table 1 shows that the remainder stiffness characteristics are highly influencing the global behavior of the BIW for this particular very stiff BIW model. For all the simulations, damping related to the spurious freuencies brought into the system by the use of the static modes in the reduction techniues had to be included. In the present case study a modal damping was applied to the modes above 36 Hz up to 40% of the critical damping for very high freuency modes. This decision also avoided a drastic reduction of the time step chosen by the software solver due to the reduction of high freuency content present in the system. The four different models were also euipped with virtual sensors (according to ISO 8855 [12]) capable of evaluating the most important ride and handling parameters as yaw, roll and pitch rate, body slip angle, vertical acceleration, reaction forces at the most important connection points, etc. 4 Simulation of different drive scenario The combination of the rigid MB model and of the simplified flexible BIW has been applied on an industrially relevant case to investigate the influence of the body flexibility on the vehicle handling and

7 VEHICLE CONCEPT MODELLING 4197 ride properties. It is known [13-16; 19] that the bending and especially the torsional stiffness of the body of the car are key characteristics of a vehicle. It can be understood that if a too compliant body would be used instead of one with proper stiffness characteristics, this could influence the behavior of the car not only from the comfort point of view but also due to its potential influence on macroscopic handling parameters as load transfer, roll motion etc. Publications related to simplified models, especially of long wheelbase vehicles, investigated the influence of body flexibility on the ride behavior [17]. A few works also investigated the influence of body flexibility on handling parameters [14; 16]. These investigations showed interesting results and provided a deeper understanding of some of the complex mechanisms modeled in the present case study. Another important aspect is the lack of a validated test methodology to compare simulation results and test procedures, due to the fact that usually an accurate measure of the forces arising at the connection points between the body of the vehicles and e.g. the suspension system is rarely available. Recently, some works [15; 19] have proposed test methodologies for predicting the flexibility influences on the handling behavior of vehicles, and some guidelines have been derived to correlate non-standard handling parameters with subjective rating given by test drivers. When the torsional stiffness of the BIW is high (few times more than the roll stiffness of the suspensiontorsion bar system), it was shown that the influence of the flexibility of the body is uite low [14]. This is the case in many scenarios, especially when high performance cars are being evaluated, however with the advent of lightweight materials used in the car industry to reduce the weight of the vehicles (which are more and more loaded by a number of actuators to complement with active safety features) this trend might change in the future. It is important for engineers to properly analyze the limit that cannot be exceeded in order to have proper ride and handling behavior. The next sections show some results obtained by simulating different driving scenarios. 4.1 Scenario 1: Double Lane Change Fig. 4 : ISO Double lane change test performed by the flexible MB model The first maneuver is a transient handling maneuver named Double Lane Change. This maneuver is performed according to the ISO Part 1 [18]. This test is usually performed for subjective evaluation of vehicle handling response in transient behavior. The steering input (Fig. 5) is not regulated by the norm so that the driver ability has a large impact on the test results [18]. This simulation was mainly performed as a starting point to allow comparing the driver subjective feelings and objective measured data and to initiate an investigation to improve correlations between parameters related to the body flexibility and the subjective rating of test drivers. A number of relevant handling parameters have been compared between the four different models showing a very small influence of the modeled flexibility. The Yaw and Roll rate were found to be almost identical. Fig. 6 and 7 show the lateral displacement of the vehicle and the differences between left and right reaction forces at the spring connection points between the back suspension and the BIW. Even in

8 4198 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 this case only small differences are reported and it can be seen that the different flexible models (FLEX, BEAM FLEX and REMAINDER FLEX) behave very similarly: differences up to maximum 100 N are found. It is interesting to notice that the load transfer is higher when flexible elements are involved. It was shown for simplified models [14] that, depending on the roll stiffness distribution between front and rear, this might in fact be the case. The results could be explained by the following observations: The vehicle BIW under analysis is uite stiff and representative of sporty sedan car. The concept flexible model used is not able to represent accurately local compliances at the connection points between the BIW, the suspensions and the driveline. The precise modeling of the local stiffness is important to accurately evaluate the reaction forces at the connection points. Further work including validation of the connection compliances through experimental data is foreseen. For the integration of the flexible body with the rigid MB model, an assumption has been made for the integration of the flexible body with the rigid MB model. More specifically, the flexible body is included adopting a modal reduction of the full concept BIW and lumping the rigid mass and inertia characteristics at the BIW center of gravity. Since the results are in good agreement with some other reported investigations [14; 16; 19], it is expected that this assumption does not adversely affect the uality of results. Still, the validity of the assumption will be checked as part of follow-up research. Fig. 5 : Steering input as function of time

9 VEHICLE CONCEPT MODELLING 4199 Fig. 6 : Double Lane Change BIW C.G. y displacement Fig. 7 : Double Lane Change Differences in the load transfer at the back suspension 4.2 Scenario 2: Sweep Steer This type of simulation is not related to an ISO maneuver. However, the maneuver is useful to provide insights relative to the vehicle dynamics in an objective manner. The vehicle is kept at a constant speed of 80 km/h and the steering input is linearly varied between 0.2 and 4 Hz (Fig. 8). Even if the steering input introduces a low freuency input into the vehicle system, compared to the first resonance peaks related to the deformation modes, it is possible that complex interactions between the flexible body deformation and the rigid MB model arise, also due to the high nonlinearity of the system. In this case it was found that at very low input freuencies ( Hz) the models are behaving almost identically; when the stimulus freuency is increased ( Hz) some differences started to arise. Around 3 Hz, one of the eigenfreuencies of the MB model is found, which has been checked via linearization procedures in several configurations. Fig. 8 highlights the fact that the yaw rate amplitude of the rigid model has slightly higher values compared to the one observed with the flexible body. This behavior can be explained by considering the possible interaction between the global modes of the vehicle and the flexible modes of the vehicle body. Similar trends were found by comparing torsion bar torue and roll rate. These results can be compared with the simplified model analyzed in [14]. In that case it was shown that the tendency of

10 4200 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 increasing the BIW stiffness (with as limit case the rigid body) tends to increase the damping of the yaw mode. As a result, one can notice higher amplitudes of the yaw rate response for the rigid case at freuencies that are slightly higher than the yaw resonance freuency. It is also interesting to underline that the rate of change in the sweep freuency also influences the vehicle response. Again the three flexible models behave very similarly between each other. Fig. 8 : Steering input and Yaw rate (with zoom) related to the BIW C.G. 4.3 Scenario 3: Ride over a Bump The simulation was performed with the car riding over a bump of 5 cm of height and 30 cm of length at a constant speed close to 80 km/h. In this way the freuency spectrum of the input is supposed to be broader, potentially exciting the BIW resonance freuencies. Fig. 9 shows the reaction force in the local axial direction of a radial bushing (one of the engine mounts). In this case the different models seem to behave differently, especially in the decaying phase. The flexible models seem to decay with a slightly lower freuency with respect to the rigid body. Moreover, the more flexible are the models (REMAINDER FLEX) the larger is the time delay in the response. This could be due to the fact that the flexible models tend to oscillate at a slightly lower freuency as compared to the rigid model and also to the local stiffness properties at the mount connections. The pitch rate was also analyzed and showed a similar trend. Fig. 9 Engine Mount reaction force The vertical acceleration response is one of the standard outputs which are used to evaluate maneuvers such as the ride over a bump. Two locations have been analyzed; the vertical acceleration at the center of gravity (C.G.) of the BIW and the local vertical acceleration at a position of a node placed on the right b-

11 VEHICLE CONCEPT MODELLING 4201 pillar with vertical position similar to the one of the BIW C.G.. Fig. 10 shows that some high freuency behavior is reported in both responses for the flexible models. The C.G. response is influenced by the redistribution of the loads around all the connection points of the BIW. The differences are clear but less evident as compared to the ones encountered at the node location. Similar behavior for the C.G. position has also been reported in [16]. The nodal responses are characterized by higher differences during the bump hit as well. Note again that the nodal response represents local phenomena which are highly influenced by the local behavior of the different concept models implemented and, as such, they do not represent a global characteristic of the vehicle. Fig. 10 : Vertical acceleration responses at the BIW C.G. and at a nodal position A freuency spectrum of the above mentioned vertical acceleration is presented in Fig. 11. Here it can be seen that the spectrum relative to the C.G. acceleration is similar between the different model up to about 24 Hz. Above this freuency we can see the influence of all the activated normal modes of the BIW; especially the spectrum relative to the more flexible model is the one that presents more differences. As expected even more variations are present in the spectrum of the nodal acceleration due to the local contribution of the flexible modes up to around 36 Hz. Fig. 11 : Freuency spectrum of the BIW C.G. and nodal vertical acceleration 5 Conclusions In this paper different reduction methodologies have been applied on a flexible BIW of a commercial vehicle. Integrations with a rigid MB model of a full vehicle have been performed with the aid of commercial software. The proposed approach and in particular the use of the concept flexible BIW in a MB context is suitable for fast stiffness modifications which could be useful at early design stage.

12 4202 PROCEEDINGS OF ISMA2010 INCLUDING USD2010 Optimization procedure can be run in a fast way to find optimal stiffness values for the desired vehicles dynamics characteristics allowing comparisons between different setups in a relatively short time. For this particular stiff model only slight influences of the modeled flexibility are found. Some transient maneuvers have been simulated; steady state analysis can be also addressed with the aid of a similar model. Generally, the presented results show a fair agreement with the scarce literature related to the topic. In later works the inclusion of the flexible BIW in the MB model will be refined as pointed out in section 4. In particular more design modifications could be explored and higher attention should be given to local stiffness characteristics of the connection points of the BIW to accurately model interface reaction forces, through validation with test data. Acknowledgements The authors gratefully acknowledge the European Commission for their support of the Marie Curie ITN VECOM FP , from which Tommaso Tamarozzi, Giambattista Stigliano and Marco Gubitosa hold an Initial Training Grant ( References [1] Shabana AA. Flexible Multibody Dynamics: Review of Past and Recent Developments. Multibody System Dynamics 1997; 1(2): [2] Wasfy TM, Noor AK. Computational strategies for flexible multibody systems. Applied Mechanics Reviews 2003; 56(6): [3] M. Geradin and A. Cardona. Flexible multibody dynamics: a finite element approach. John Wiley, [4] 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, vol. 45, no. 6-7, pp , [5] 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, vol. 45, no. 6-7, pp , [6] R. H. MacNeal, A hybrid method of component mode synthesis, Computers & Structures, vol. 1, no. 4, pp , [7] Jr R.R. Craig. A Review of Time-Domain and Freuency-Domain component-mode synthesis methods, Journal of Modal Analysis, 59:59-72, [8] R.J. Guyan. Reduction of stiffness and mass matrices. AIAA journal, 3(2):380, [9] O. Bruls, M. Arnold. Convergence of the generalized-alpha scheme for constrained mechanical systems. Multibody System Dynamics, 18: , [10] D. Mundo, S. Donders, R. Hadjit, G. Stigliano, P. Mas, and H. Van der Auweraer, Concept modeling of automotive beams, joints and panels, in Proc. World Scientific and Engineering Academy and Society (WSEAS) International Conference on FD, FEM, FV and BEM, (Bucharest, Romania, April 20-22), pp , [11] G. Stigliano, D. Mundo, S. Donders, T. Tamarozzi. Advanced Vehicle Body Concept Modeling Approach Using Reduced Models of Beams and Joints in Proc. of ISMA 2010 (in press).

13 VEHICLE CONCEPT MODELLING 4203 [12] ISO Road vehicles Vehicle dynamics and road-holding ability Vocabulary, First Edition, [13] L.L. Thompson, P.H. Soni, S. Raju, and E.H. Law. The Effects of Chassis Flexibility on Roll Stiffness of a Winston Cup Race Car. In SAE CONFERENCE PROCEEDINGS P, volume 1, pages Citeseer, [14] A. E.Sampo', Sorniotti and A. Crocombe. Chassis Torsional Stiffness: Analysis of the Infuence on Vehicle Dynamics, SAE International, [15] R. Hadjit, M. Kyuse, and K. Umehara. Analysis of the Contribution of Body Flexibility to the Handling and Ride Comfort Performance of Passenger Car, SAE International, [16] J.A.C. Ambrosio and J.P.C. Goncalves. Complex flexible multibody systems with application to vehicle dynamics. Multibody System Dynamics, 6(2): , [17] IM Ibrahim, DA Crolla, and DC Barton. Effect of frame flexibility on the ride vibration of trucks, Computers & Structures, 58(4): ,v1996. [18] ISO Passenger cars Test track for a severe lane change maneuver Part 1: Double lane change, First Edition, [19] W.F. Milliken, D.L. Milliken, and L.D. Metz. Race car vehicle dynamics. SAE International Warrendale, PA, [20] J.H.Park, J.S. Jo, T. Geluk, G. Conti, J. Van Herbruggen, Improving the vehicle dynamic performance by optimizing the body characteristics using body deformation analysis, Presented at Chassis.tech 1 st International Chassis Symposium, Munich. [21] [22] TNO Automotive: MF-Tyre/MF-Swift Help Manual, TNO Automotive, The Netherlands, 2009

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