Dynamic Positional Finite Element Method Applied to Nonlinear Geometric 3D Solids

Abstract

This paper presents the dynamic positional nonlinear geometric formulation for tridimensional problems. The positional formulation is an alternative approach for non linear problems, since it considers nodal positions as variables of the nonlinear system instead of displacements as usual in literature. In order to avoid locking, tetrahedral third-order isoparametric finite element (20 nodes) is implemented for both displacement and stress field. Regarding to dynamic forces, it is considered the consistent mass matrix and damping effects proportional to the body mass. The well-known Newmark algorithm for time integration is applied. Some simple numerical examples are presented in order to show the accuracy of the proposed formulation.