A Study of the Point Matching Method as Applied to Thermally and Transversely Loaded Plates and Other Boundary Value Problems

摘要

The purpose of the work undertaken was to develop further the point-matching technique for application to thermally and transversely loaded plates and associated boundary value problems; to develop computer programs, based upon the method, which are capable of universal usage to solve plate problems involving arbitrary shape and loading; to demonstrate the use of the computer programs on practical problems; and to investigate the mathematical convergence properties of the method. The equations of linear, thin, elastic plate theory, including thermal effects, are presented. Solutions to the governing differential equation require complementary and particular parts. Application of the point matching method to other boundary value problems solvable in terms of harmonic and biharmonic functions is described; e.g., torsion, conductive heat transfer, plane elasticity, slow motion of a viscous fluid, membrane deflection, and electromagnetics. A method of analyzing plates having both transverse and in-plate loads is presented. This method uses an iterative application of the point matching technique. (Author)