Boundary element method analysis of bending of elastic plates of arbitrary shape with general boundary conditions

Abstract

This paper presents an accurate compatible scheme for the analysis of bending of elastic Kirchhoff plates of arbitrary shape with general boundary conditions. The analysis models straight and circular boundaries exactly. Hermitian interpolation is adopted and singular integrals are calculated accurately by using particular solutions. Three equations are obtained at each boundary node through the use of appropriate fundamental solutions. General, i.e. clamped, simply supported, free and mixed boundary conditions are modelled here. The treatment of these general boundary conditions has also been discussed in previous publications 14–18 by the first author of this paper and his co-workers. The paper presents the mathematical formulation for the above problem together with many numerical examples. It appears from these examples that this scheme is very accurate and efficient for the solution of this important class of problems.