An approximate analytic solution method for the biharmonic problem

Abstract

A method is presented for the solution of the biharmonic equation through the use of a combination of polynomial and eigenfunction solutions. Results are presented comparing the method with an exact solution. Excellent agreement is obtained for economical solution representations. Calculations, and comparison with established results, of the displacement of an elastic plate under a uniform applied load are presented. Further, results are presented of the calculation of zero Reynolds number flow in a driven cavity.