(A) coupled formulation of finite and boundary element methods in two-dimensional elasticity

Abstract

A symmetric stiffness formulation based on a boundary element method is studied for the structural analysis of the shear wall with or without cutouts and a new plane stress element, which can have cutouts in its interior domain and can be easily linked to finite beam elements, is developed by coupled formulation of finite and boundary element methods. To satisfy the compatibility with finite beam elements and to avoid problems due to the eventual discontinuities of the traction vector, different interpolation schemes are adopted to approximate the boundary displacements and tractions. The symmetric coupling techniques of both finite and boundary element methods have been utilized in the development, whereas the best set of boundary integral equations are obtained by finding the optimum positions of collocation points through minimization of the error norm proposed in this paper. Also, for the symmetric stiffness matrix of the element to satisfy the conditions of equilibrium and rigid body motion, an additional moment-balance constraint proposed in this study as well as the equilibrium constraints proposed by Kelly and Mustoe et al. are used. The newly developed element has the same form as a finite element and its incorporation within the existing finite element analysis software is straightforward. Some examples are analyzed using the new element and, from these results, the element is found to be highly efficient.