Energy Based Boundary Elements for Finite Element Analysis

Abstract

A derivation of finite elements starting from a boundary discretization is proposed. The description of the internal displacement and stress fields is based on the Green functions, used as shape functions instead of the usual polynonomial approximations. The internal fields are linked to the polynomial functions used to approximate the boundary variables by the relations derived from the Somigliana equation. This procedure aims at combining the accuracy of the boundary element discretization with the flexibility in coupling different elements which is typical of energy based models. Two different approaches have been followed to construct such finite elements. The first represents a straightforward way of deriving the element energy, using a numerical integration of the domain strain energy expressed in terms of the boundary variables. The second, which involves a more complex formulation, is based on the Galerkin method and the related double integration. These models have been coded as numerical procedures for the analysis of plane elasticity problems defined on polygonal domains. Some tests show their numerical performance.