Analysis of Structural Systems Undergoing Gross Motion and Nonlinear Deformations

Abstract

Recent developments in flexible multibody dynamics provided new tools for the analysis of structural systems undergoing geometric and material nonlinear deformations. The restrictions that some of the most popular methods present for the analysis of multibody system with flexible components are discussed within the framework of a general methodology. The equations of motion for a flexible body undergoing large overall motion are obtained based on the principles of continuum mechanics and employing nonlinear finite elements. These equations are then simplified based on a lumped mass formulation and referring the nodal accelerations to the inertial reference frame. The resulting equations, which describe completely the coupling between the nonlinear gross motion and the deformation of the flexible components of the system, present a mass matrix that is diagonal and constant. These equations can be further simplified for cases where the level of deformations lies within the elastic range and the geometric nonlinearities are not important. Under these assumptions the modal superposition method can be used to reduce the number of nodal degrees of freedom of the flexible components. If the assumptions of material and geometric linearity are not met the number of nodal degrees of freedom can still be reduced using a static condensation technique. The equations obtained in this manner are implemented in a general purpose program and solved numerically. The study of a light space structure is presented in order to show the effects of the nonlinear geometric deformations in behavior of the system. The application of the methodology described here to crashworthiness and structural impact is illustrated with the study of the rollover of an off-road vehicle.