Geometrically Non-linear Finite Element Analysis of Plane Stress Structures Using MATLAB Programme

Abstract

In this research Total Lagrangian formulation for geometric nonlinear plane stress problems was developed. The formulation is based on Green strains and 2nd Piola-Kirchoff stresses. The formulation was applied on two- dimensional elasticity using 4-node plane finite element. The formulation was implemented as a finite element program using MATLAB (2010b). The program was developed for linear and nonlinear analysis of plane stress structure subjected to different types of loading. The solution of nonlinear equilibrium equation was obtained by incremental method with Newton-Raphson approach. The program was applied to obtain nodal displacements, direct stresses and shear stresses at integration points of element based on Green strains and 2nd Piola-Kirchoff stresses. The accuracy of results was demonstrated by using three numerical examples for linear analysis. The results were in very good agreement when compared with results from references and known exact solutions. It was, also observed from Graphs and Tables that the results show high accuracy with mesh refinement and increment applied load. For the nonlinear analysis, the resulting displacements show good agreement when compared with known results or published papers results.