Boundary integral equations for bending of thin plates

Abstract

There are a number of different ways to approach the formulation of boundary integral equations for plate bending. While in some sense these are equivalent (if correctly done) the differences becomes quite significant when the resulting formulations are implemented in the numerical solution of specific boundary value problems. Most early proposals for the direct numerical solution of plate bending boundary integral equations were based on so-called indirect formulations and generally were designed for specific classes of problems. One of the earliest significant examples is due to Jaswon and Maiti¹ who propose a formulation for uniformly loaded clamped and simply supported plates based on the introduction of two source distribution densities on the plate boundary generating harmonic potentials which are then related to the plate displacement. A somewhat different formulation of the same type to treat uniformly loaded simply supported polygonal plates was proposed by Maiti and Chakrabarty². Hansen³ derived two different boundary integral formulations designed mainly for plates containing holes with free edges.