Distributed and discrete nonlinear deformations on multibody dynamics

Two different multibody dynamics formulations for the simulation of systems 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 equations of the flexible body while the finite element method is subsequently applied to obtain a numerical description for the equations of motion. The computational efficiency of the formulation is increased by using a lumped mass description of the flexible body mass matrix and referring the nodal accelerations to the inertial frame. In the resulting equations of motion the flexible body mass matrix is constant and diagonal while the full nonlinear deformations and the inertia coupling description are still preserved. In some cases the flexible components present zones of concentrated deformations resulting from local instabilities. The remaining structure of the system behaves either as rigid bodies or as linear elastic bodies. The second formulation presents a discrete model where all the nonlinear deformations are concentrated in the plastic hinges assuming the multibody components are as being either rigid or flexible with linear elastodynamics. The characteristics of the plastic hinges are obtained from numerical or experimental crush tests of specific structural components. The structural impact of a train carbody against a rigid wall and the performance of its end underframe in a collision situation is studied with the objective of assessing 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 methodologies to large size models are drawn.