An Approximate Solution To Buckling Of Plates By The Galerkin Method

Abstract

This thesis presents a semi-analytical method to solve the governing differential equation of plates using the Galerkin method. Symbolic algebra software is extensively used to perform necessary calculations. In this thesis, the lateral deflection of a plate is expressed in a series of polynomials each of which satisfies the given homogeneous boundary conditions. The coefficients of these polynomials are found out by the Galerkin method. Symbolic algebra software works best while handling necessary algebra to generate admissible polynomials and build required matrices for solving for the coefficients.This thesis demonstrates the calculation of the lateral load for different plates under different homogeneous boundary conditions and initial condition. As this analysis involves very complicated computation, it is almost impossible to handle all the calculations without the help of symbolic algebra software.Numerical examples are presented and the results are compared with the known analytical solutions. It was shown that a reasonable level of convergence is achieved with the present method.