Triangular and rectangular plane elasticity finite elements

Abstract

A triangular and a rectangular strain based elements are developed for the general plane elasticity problems. The triangular element has the two essential external degrees of freedom at each of the three corner nodes and at a mid-side node. It is based on assumed independent linear direct strains and constant shearing strain. The rectangular element has the same degrees of freedom at each of the four corner nodes as well as at the centroidal node. This element is based on linear variations of all the three components of strains. These elements are used in various forms, including statical condensation and satisfying equilibrium to obtain solutions to two dimensional elasticity problems where the contribution of the shearing stress on the deformation can be significant.