Solution of Partial Differential Equations by Arbitrary Grid Finite Difference Technique

摘要

The models arising in structural analysis involve systems of fourth order partial differential equations (PDE's) which collectively are equivalent to an eighth order PDE. Finite difference techniques have been used for numerical analysis of the PDE's for a number of years, but have been hampered by fairly heavy restrictions on the types of discretization grids that could be used. Relaxation of these restrictions in the application of the equilibrium (direct) finite difference method is presented with results from application to the biharmonic plate problem under a variety of boundary conditions. Two methods for generating suitable grids are presented with sample results. Methods for iteratively redistributing the nodes of a grid based on a-posteriori error estimation in order to reduce that error are also presented. One-dimensional results for this process are given both for direct discretization and variational finite difference analysis. (Author)