Bending Solution for Simply Supported Annular Plates Using the Indirect Trefftz Boundary Method

Abstract

This paper presents the bending analysis of annular plates by the indirect Trefftz boundary approach. The formulation for thin and thick plates is based on the Kirchhoff plate theory and the Reissner plate theory. The governing equations are therefore a fourth-order boundary value problem and a sixth-order boundary value problem, respectively. The Trefftz method employs the complete set of solutions satisfying the governing equation. The main benefit of the Trefftz boundary method is that it does not involve singular integrals because of the properties of its solution basis functions. It can therefore be classified into the regular boundary element method. The present method is simple and efficient in comparison with the other methods. In addition, the boundary conditions can be embedded in this method. Finally, several numerical examples are shown to illustrate the efficiency and simplicity of the current approach.