Plate bending boundary element formulation considering variable thickness

Abstract

In this article the plate bending boundary element method formulation, based on the Kirchhoff’s hypothesis, is extended to take into account possible variation in the plate thickness or stiffness. For this particular case, an appropriate form of the Betti’s reciprocal work theorem was taken to derive integral representations of displacements and internal forces, starting by assuming that the plate domain exhibits variable thickness or stiffness. Some alternative integral representations to treat this problem are discussed pointing out the basic differences among them. The domain integrals, remaining in all integral equations and required to take into account the stiffness variation, are properly handled leading to small and reduced number of internal unknowns and their corresponding integral representations. As usual for this problem, only deflection integral representations related to boundary collocations are taken to write the necessary algebraic relations, written for singular and nonsingular points.