Semi-analytical Solution of Two-dimensional Elasticity Problems By Finite Difference–distributed Transfer Function Method

A semi-analytical solution method, called the Finite Difference–Distributed Transfer Function Method, is developed for static and dynamic problems of two-dimensional elastic bodies composed of multiple rectangular subregions. In the development, the original two-dimensional elasticity problem is first reduced into a one-dimensional boundary-value problem by finite difference; the exact solution of the reduced problem is then obtained by using the distributed transfer functions of the elastic continuum. The proposed technique, which combines the simplicity of finite difference and the closed form of analytical solutions, is capable of handling arbitrary boundary conditions, delivers highly accurate solutions for static and dynamic problems, and is computationally efficient. The proposed method is illustrated on a square region and an L-shaped region.