Geometrically Nonlinear analysis using Plane Stress / strain Elements based on Alternative Strain Measures

Abstract

The description of deformation and the measure of strain are essential parts of nonlinear continuum mechanics. In this paper, a new formulation for geometric nonlinear plane stress/strain based on Logarithmic strains (GNLGS) is presented. This is coupled with a formulation based on the well known Greens strains and coupled with modifying a formulation based on geometric strains (conventional strains). A geometric nonlinear total lagrangian formulation applied on two-dimensional elasticity using 4-node plane finite elements is used. The formulations were implemented into the finite element program (NUSAP), which is developed for the analysis of plane stress/strain problems subjected to static loading. The solution of nonlinear equations was obtained by the Newton-Raphson method. The program was applied to obtain displacements for the different strain measures. The accuracy of the results was demonstrated by using two numerical examples and the results are in good agreement with other available published solutions and those obtained using commercial finite element solvers such as ANSYS. It could be concluded that the geometrically nonlinear formulations converge to the correct solution with coarse meshes and are computationally efficient. In addition, the resulting displacements clearly showed the effect of the nonlinearity in the deflected shape. It is also observed that all results were approximately identical when applying a small value of load and when a large value of a load was applied there was a difference between the results of the three strain measures.