Keywords: simplified models, multibody dynamics, crashworthiness, optimization, genetic algorithms, non-linear deformation, remodeling.

In the first stages of the design process of crashworthy structures, when the detailed characteristics of the vehicles are still unknown or when these characteristics are to be optimized, simplified models can be very useful. Simplified models for structural crashworthiness problems, based on multibody system dynamics, proved to be useful and accurate enough in simulating train collisions and in the optimization of energy absorption devices [1]. These simplified models require reduced simulation times, which makes them appropriate to be associated with evolutionary algorithms such as the genetic algorithm used [2]. The development of simplified models for the study of crashworthiness is an actual topic of research [3,4,5]. Usually the simplified models are based on spring-mass models that are easy to develop but for each structure or vehicle the equations need to be written. With multibody dynamics formulations, as presented in the present work, the development of the equations is automatic once the location of the deforming components is identified.

In this work new simplified multibody dynamics based models and methodologies are presented. The proposed work is divided in two major subjects that are closely related: In one side a design tool combining a graphical interface, a genetic algorithm [6] and a simplified impact simulation model (based on multibody dynamics) is presented. This tool has been developed to analyse train crash scenarios, optimizing resulting accelerations, deformations or energies using as its design variables masses, velocities or the physical characteristics of the train's structures, and has been validated by comparing results obtained in the past with deterministic algorithms. The application of evolutionary algorithms to multibody dynamics systems and impact problems requires that several of the algorithm's parameters be conveniently chosen. This aspect is also discussed in this work. With these tools single-criteria and multi-criteria optimization problems can be defined and solved efficiently.

In addition a new technique based on plasticity models using plastic hinges from multibody dynamics is presented. The plastic hinges locations are detected from the flexible bodies stress calculation, and the system is then remodelled by automatically redefining the number of bodies and plastic hinges, and their location, in order to include the new plastic deformation zones detected. To compute precise simplified models the energy absorption devices' simplified characteristics are needed and can be obtained from detailed finite element models, using parameter identification techniques or analytical models are proposed in this work.

Several examples are presented, and the simulation results are compared with experimental ones obtained in the past. Examples of energy absorption devices characteristics optimization are also presented, showing its utility in the simulation and design of railway vehicles.

1

J.P. Dias, M.S. Pereira, "Optimal Design of Train Structures for Crashworthiness using a Multi-load Approach", I. J. of Crashworthiness, 7, 331-343, 2002.

2

J.P. Dias, R. Corrêa, F. Antunes, "Crashworthiness Optimization of Train Structures with Evolutionary Algorithms", Eurogen 2003, Barcelona, 2003.

3

C.H. Kim, A.R. Mijar, J.S. Arora, "Development Of Simplified Models For Design And Optimization Of Automotive Structures For Crashworthiness". Struct Multidisc Optim 22-4:307-321, 2001. doi:10.1007/PL00013285

4

K. Hamza, K. Saitou, "Design for Structural Crashworthiness using Equivalent Mechanism Approximations", Proceedings of the 2003 ASME Design Engineering Technical Conferences, Chicago, Illinois, September 2-6, DETC2003/DAC-48751, 2003. doi:10.1115/DETC2003/DAC-48751

5

C. Oyan, "Dynamic Simulation of Taipei EMU Train", Vehicle System Dynamics 30:143-167, 1998. doi:10.1080/00423119808969441

6

K. Deb, "Multi-Objective Optimization Using Evolutionary Algorithms", John Wiley and Sons, LTD, 2001.

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