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

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 , 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.

Automated summary

A weak form quadrature element formulation is proposed for the analysis of elastic buckling in thin plates with side cracks. The problem domain is divided into a square subdomain near the crack tip and quadrilateral subdomains elsewhere. The stress distribution is determined in pre-buckling analysis, and the potential energy is computed using asymptotic displacement expansion and weak form quadrature elements. A generalized eigenvalue problem is solved to find the critical loads and buckling modes, and the formulation is validated with numerical examples.