MATLAB FEM Code - From Elasticity to Plasticity

Abstract

A MATLAB Finite Element code for plane strain analysis of footings on an Elasto-plastic material using the Mohr Coulomb failure criteria has been developed. The first step is to develop codes for mesh generation and Gaussian numerical integration. Next, the force matrix, the stiffness matrix and the self weight matrix are assembled. After that functions for non linear analysis such as the plastic potential derivatives are formed. Finally plots of the mesh, displacement shadings, stress shadings and stress-strain curves are developed. For the purpose of verification results from the code for biaxial test are compared with the theoretical solution. Additionally comparison is made between the code and prandtl s bearing capacity solutions for a footing problem. These results show that accuracy depends on two factors: - the type of the element and the number of elements used. The three node triangular element and the four node rectangular element give less accurate results when compared to higher order element types. And for a relatively accurate result the number of elements should be too high.