Finite element formulations for large displacement and large strain analysis

TLDR: In this article, finite element incremental formulations for nonlinear static and dynamic analysis are reviewed and derived starting from continuum mechanics principles, including large displacements, large strains, material nonlinearities and nonconservative forces.

Abstract: Starting from continuum mechanics principles, finite element incremental formulations for nonlinear static and dynamic analysis are reviewed and derived. No new formulation is presented. The aim in the report is a consistent summary, comparison, and evaluation of the two formulations, which are used in the general purpose nonlinear static and dynamic analysis program NONSAP. The general formulations include large displacements, large strains, material nonlinearities and nonconservative forces. For specific solutions in the report, elastic and hyperelastic materials only are considered. The numerical solution of the continuum mechanics equations is achieved in NONSAP using isoparametric finite element discretization. The specific matrices which need to be calculated in the formulations are discussed. (Author)