FORMULATION OF AN EQUILIBRIUM TRIANGULAR SUPERELEMENT FREE OF SPURIOUS ZERO-ENERGY MODES

M. K. Sangare (Côte d’Ivoire), E. Danho (Côte d’Ivoire) and J. I. Nene (Côte d’Ivoire)

Received November 5, 2007

Abstract

This paper presents the formulation of a triangular superelement (assembly of 3 simple triangles) based on pure equilibrium method for 2D elastic problems with null body forces. Being strongly inspired by the equilibrium element developed by P. Beckers et al., this element has the effect of having a stress field which satisfies tractions continuity condition along subelements common edges. These interfaces tractions continuity lead to directly obtain a stiffness matrix of the superelement without any spurious kinematics mode. Two examples of numerical applications in which this equilibrium element is compared with standard displacement elements are also presented. The results obtained with these dual analyses confirm the energy bound’s theorem.

Keywords and phrases: finite element, equilibrium formulation, force method, dual method.