Analytical solutions for buckling analysis of cracked plates under in-plane compressive loads: 2D refined modeling

Abstract

Two refined two-dimensional (2D) crack models are developed to deal with rectangular isotropic and orthotropic plate problems with all-over part-through surface cracks under in-plane compressive loads. In the refined models, the crack terms are directly incorporated into the governing equations of cracked plates. In particular, the effect of internal in-plane forces can be investigated by theoretical analysis. The critical buckling loads of thin plates with uni-directional or bi-directional part-through cracks under uni-axial or bi-axial compressive loads can be determined analytically. In this work, different material properties, including steel, tempered glass, glass-fibre-reinforced composite, and graphite-epoxy composite, are considered. The influence of crack depth ratio and plate aspect ratio on the critical buckling loads of these structures is also presented. The analytical results are compared with those results obtained by the line-spring model and three-dimensional finite element method to verify their correctness and accuracy. The proposed models are highly effective for the buckling analysis of plates with part-through cracks.