Solving Boundary Value Problems in Plate Deflection Theory

Abstract

Analysing the deflection of plates or beams generally requires the solution of a two-point boundary value probzem associated with an ordinary differential equation. Such problems can be solved by finite difference methods, by shooting techniques, or by spline approximation. We develop and analyse these three types of methods. We also cite sufficient conditions under which unique solutions of these boundary value problems exist and the requirements for obtaining solutions of various orders. Finite difference methods are easy to im plement, cheaper, and more accurate than the shooting methods of the same order. Spline methods are com parable to finite difference methods.