Development of Geometrically Nonlinear Finite Element Program Using Plane Stress/Strain Elements based on Engineering and True Stress Measures

Abstract

In this research, a general-purpose finite element system (NUSAP) is developed for the analysis of plate structures (plane stress/strain problems) subjected to static loading. The program is linked to two processors: Pre-Processor, developed specially to supply the program with the necessary data through an inter-active menu and dialogue boxes, and Post-processor for presenting the out put results in formatted sense. This study focused on the linear and nonlinear analysis of plane stress/strain structures using 4-node (QPM4) and 8-node (QPM8) plane stress/strain elements. A geometric nonlinear formulation based on the total Lagaregian formulation and using Green's strain (GNGRS), geometric strains (Engineering strains) (GNEGS) and Logarithmic strains (GNLGS) was adopted. The formulations were implemented into the nonlinear finite element program (NUSAP). The solution of nonlinear equations was obtained by the Newton-Raphson method. The accuracy of the results of the formulation is demonstrated by using four numerical examples and the results are in agreement with other available published solutions. The non-linear stresses from the different strain formulations were obtained. A comparison was made between the obtained strains and published results The true stress associated with the logarithmic strain was thus obtained for loads that result in very large displacements.