Finite element analysis of geometric and material nonlinear dynamic response

In the first part of the paper recently implemented continuum mechanics and resulting finite element formulations are surveyed which include all nonlinear effects due to large displacements, large strains and material nonlinearities. Recommendations for the use of the formulations are given. Next, specific problems encountered in the implementation of nonlinear hypo-elastic and elastic-plastic material models are surveyed and the important interaction between the implementation of a material model and the continuum mechanics formulation used is described. In the third part of the paper the time integration procedures that have been employed extensively are presented and specific emphasis is given to the use of equilibrium iteration in nonlinear static and dynamic analysis. Finally, to demonstrate the recommendations given a variety of problem solutions are presented. These include the static and dynamic, geometric and material nonlinear analysis of beams, pipes, arches and shells that are subjected to high intensity mechanical and thermal loading conditions. (Auth.)