Buckling and Post-Buckling Analysis of Cracked Plates by The Boundary Element Method

Abstract

This thesis presents boundary element formulations for buckling and nonlinear buckling analysis of plates. Dual boundary element formulations are also presented for linear and nonlinear buckling, and large deformation analysis of crack behaviour in plates. Reissner plate theory is adopted to represent shear deformable plate bending, and two dimensional plane stress is used to model the membrane behaviour of plate. By taking into account the nonlinear interaction between forces and rotations in the equilibrium equation, the nonlinear formulation is formed by coupling equations of shear deformable plate bending and two dimensional elasticity. The boundary element formulation for plate buckling is developed. Plate buckling equations are written as a standard eigenvalue problem. Buckling coefficients and buckling modes are obtained using this formulation. Initially, the boundary is discretised into quadratic isoparametric elements, and the domain is discretised using constants cells. Next, the dual reciprocity method is utilized to transform the domain integral into equivalent boundary integrals. Examples are presented for plate buckling problems with different geometry, loading and boundary conditions. The results obtained are shown to be in good agreement with analytical and finite element results. The Dual Boundary Element Method (DBEM) for buckling analysis of plate is also developed. The plate buckling equations are also presented as a standard eigenvalue problem, which would allow direct evaluation of critical load factor and buckling modes for cracked plates. Geometrically nonlinear boundary element formulation is developed to analyse large deformation and nonlinear buckling of plates. Different load incremental approaches and solution procedures are presented. Nonlinear terms are evaluated using a radial basis function. Large deformation analysis for Fracture Mechanics problems is also presented. Five stress intensity factors are calculated, i. e. three for plate bending and two for membrane. Crack Opening Displacement (COD) is used to compute the stress intensity factors. The nonlinear buckling of thin plate is also presented. Two models of imperfection are introduced in the formulation, i. e. a small uniform transverse loads and distributed transverse loads based on eigenvectors. A simple numerical algorithm is presented to analyse the problems. Finally, nonlinear buckling analysis of cracked plate is presented. Numerical examples of nonlinear buckling and large deformation problems are presented. The BEM results presented are shown to be in good agreements with analytical and other numerical results.