A relative quantity integral equation formulation for evaluation of boundary stress resultants in shear deformable plate bending problems

Abstract

This paper presents new boundary element formulation for the shear deformable plate bending problems based on considering the relative displacement quantities. This can be done by subtracting the rigid body integral equations from the traditional displacement integral equations. The result is a new set of regularized integral equations, which could be used without any special integration considerations to compute the boundary generalized displacements. Using suitable constitutive relationships, new integral equations for computing boundary stress resultants are formulated. The behaviour of such equations are studied at smooth boundary points. Unlike the traditional formulation which contains kernels of O(1/ r 2), the newly derived equations are of O(1/ r), therefore they can be used to compute boundary values with the traditional quadratic continuous boundary elements. The main advantage of the present formulation is that it can be used to compute values anywhere within the plate domain or on the boundary, which gives the boundary element formulation a practical essence.