Deflection of Clamped Plates by Two-Step Membrane Analogue

Abstract

The Classical Kirchhofif–Love Theory for the deflection of thin plates leads to fourth order Lagrange's differential equation,D△4w — q = 0 for which a general solution is not always possible. Exact solutions are known so far only for a few special cases and, therefore, numerical solutions have often been tried. The advantage of numerical solution is that it can be applied easily to any plate plan form which is in marked contrast to the analytical method where, for mathematical reasons, definite restrictions have to be imposed on the geometrical shape of the plate. Among the various numerical methods, relaxation is the easiest, but when applied to solving a biharmonic equation, the process becomes extremely difficult and laborious as convergence is very slow and the unit relaxation operator cumbersome to deal with.