Buckling of Skew Plates and Corner Condition for Simply Supported Edges

Abstract

The paper considers the elastic buckling of skew plates subjected to in‐plane loadings. The buckling analysis is performed using the Rayleigh‐Ritz method with the newly proposed pb‐2 Ritz functions, which consist of the product of a two‐dimensional polynomial function and a basic function. The basic function is formed from taking the product of the equations of the boundaries, with each equation raised to the power of 0,1, or 2 corresponding to free, simply supported, or clamped edges; thus satisfying the kinematic boundary conditions at the outset. With pb‐2 Ritz functions, the analyst avoids the difficulty of searching for the appropriate function for any arbitrarily shaped plates with various combinations of supporting‐edge conditions. Using this efficient and accurate pb‐2 Rayleigh‐Ritz method, buckling solutions are obtained and presented in the form of design charts for skew plates with different edge conditions, angles, and aspect ratios. In addition, the differing viewpoints on the kinematic condition for a corner formed by two simply supported edges are discussed.