Elastic buckling analysis of side-cracked thin plates by weak form quadrature elements

Abstract

A weak form quadrature element formulation is established for elastic buckling analysis of thin plates with side cracks. The entire problem domain is divided into a square subdomain around the crack tip and several quadrilateral subdomains elsewhere. The stress distribution of a cracked plate is determined in pre-buckling analysis. In either pre-buckling analysis or buckling analysis of a cracked plate, the potential energy of the inner square subdomain is computed using asymptotic displacement expansion around the crack tip, while the potential energy elsewhere is computed using quadrilateral weak form quadrature elements. A generalized eigenvalue problem is dealt with to determine the critical loads and buckling modes. The first ten non-dimensional buckling loads and critical buckling modes for several typical problems are given to validate the present formulation.