Finite element solutions of plane elasticity problems by using isoparametric quadrilateral elements

Abstract

In this study a finite element program is developed to solve plane stress problems. The finite element method used is based on minimization of the potential energy of the system by using the Rayleigh- Ritz procedure. The potential energy of the system is formulated by using an assumed displacement field. The finite element formulation developed in this study is based on isoparametric quadrilateral finite elements. Effect of the degree of finite element used is illustrated by using second order eight-noded (quadratic), and third order twelve-noded (cubic)quadrilaters elements. The element stiffness matrices and the force vectors are evaluated by using a Gaussian-quadrature numerial integration technique. A computer code is developed based on the finite element method. The computer program is applied to various elasticity problems and the reults are compared with analytical solutions.