Elastic-plastic large deformation of flexible multibody systems in crash analysis.

Abstract

The problem of formulating and numerically solving the equations of motion of flexible multibody systems for application to structural impact is considered in this dissertation. As an alternative to experimental tests and to numerical procedures such as hybrid models and finite element methods, multibody dynamics contains the ingredients for efficient crash analysis of these problems provided that a proper description of the deformations of the system components is included. Based on the principles of continuum mechanics, updated and total Lagrangian formulations are used to derive the equations of motion for a flexible body. The finite element method is applied to these equations in order to obtain a numerical solution of the problem. It is shown that the use of convected coordinate systems not only simplifies the form of the flexible body equations of motion, but it also lowers the requirements for objectivity of the material law. A simpler form of the finite element equations of motion is obtained when a lumped mass formulation is used, and the nodal accelerations are expressed in a nonmoving reference frame. In this form, not only the geometric and material nonlinear behavior of the flexible body is accounted for, but also the inertial coupling between the gross motion and the distributed flexibility is preserved. A reduction on the number of coordinates describing the flexible body is achieved with the application of the Guyan condensation technique or the modal superposition method. For partially flexible bodies with a small deformable part, an efficient kinetostatic method is derived assuming that the deformable part is massless. The equations of motion of the complete multibody system are formulated in terms of joint coordinates. The necessary velocity transformations between the set of independent velocities and the dependent velocities are derived. Special emphasis is paid to the formulation of the constraint equations of kinematic joints involving flexible bodies. The dynamics of a truck rollover are studied in order to illustrate the efficiency of the developed methodology. Several simulations are performed using a general purpose multibody dynamics analysis code.