Buckling Analysis Of Thin Plates With Or Without A Hole Under Arbitrary Boundary Conditions Using The Galerkin Method

Abstract

This thesis demonstrates how to find the critical buckling load value of thin plates with or without a hole under different boundary conditions using the Galerkin method. The use of symbolic software is essential due to the lengthy computations involved because of the complexity of the problems. Firstly, the lateral deflection of the plate is expressed in a series of polynomials each of which satisfies the given boundary conditions. Then by using the Galerkin method, the coefficients of these polynomials are found and with the help of symbolic algebra system, the matrices for the corresponding eigenvalue problem are built from which the buckling loads (eigenvalues) are determined. Since this analysis involves very complex calculations, it is almost impossible to carry out all the computations involved without the aid of symbolic software.