Chapter 5 - Meshless analysis for thin plate bending problems

Abstract

Chapter 5 focuses on numerical solutions of the thin plate bending under transverse loads by the extended method of fundamental solutions. Based on the characteristics of the governing equation of thin plate bending, the analog equation method is first used to convert the original fourth-order partial differential governing equation into an equivalent standard inhomogeneous biharmonic equation; then the related homogeneous and particular solutions of the equivalent equation are expressed in terms of the fundamental solution and radial basis function interpolation, respectively. The strong-form satisfaction of the original governing equation and the specific boundary conditions at interior and boundary collocations are used to determine all unknowns in the solving system. Such a solving framework benefits the reader to track the method and attempts to extend it further to more complex thin plate bending problems such as thin plates with variable thickness or heterogeneous material.