A Numerical Solution to the General Large Deflection Plate Equations

The three equilibrium equations governing the large deflections of thin plates are presented. A finite-difference overrelaxation technique is developed for the approximate solution of this system of nonlinear partial differential equations on a digital computer. To insure stability and speed up convergence of the numerical solution, nonlinear terms in the equations are treated as constants, which are evaluated periodically as the iteration proceeds. This method gives stable solutions for practically all ranges of the over-relaxation factor; therefore, the overrelaxation factor can be chosen to give convergence in the minimum number of iterations. Results obtained by using this technique on a simple plate bending problem and the corresponding results obtained by Levy and Wang are presented for comparison.