DISTRIBUTED AND DISCRETE NONLINEAR DEFORMATIONS ON MULTIBODY DYNAMICS

Two different multibody dynamics formulations for the simulation of sy stems experiencing material and geometric nonlinear deformations while undergoing gross motion are presented in this paper. In the first, an updated Lagrangean formulation is used to derive the equilibrium equa tions of the flexible body while the finite element method is subseque ntly applied to obtain a numerical description for the equations of mo tion. The computational efficiency of the formulation is increased by using a lumped mass description of the flexible body mass matrix and r eferring the nodal accelerations to the inertial frame. In the resulti ng equations of motion the flexible body mass matrix is constant and d iagonal while the full nonlinear deformations and the inertia coupling description are still preserved. In some cases the flexible component s present zones of concentrated deformations resulting from local inst abilities. The remaining structure of the system behaves either as rig id bodies or as linear elastic bodies. The second formulation presents a discrete model where all the nonlinear deformations are concentrate d in the plastic hinges assuming the multibody components are as being either rigid or flexible with linear elastodynamics. The characterist ics of the plastic hinges are obtained from numerical or experimental crush tests of specific structural components. The structural impact o f a train carbody against a rigid wall and the performance of its end underframe in a collision situation is studied with the objective of a ssessing the relative merits of the formulations presented herein. The results are compared with those obtained by experimental testing of a full scale train and conclusions on the application of these methodol ogies to large size models are drawn.