An analytical solution for buckling of plates with circular cutout subjected to non-uniform in-plane loading

Abstract

This paper investigates the buckling of isotropic plates with circular cutout subjected to non-uniform in-plane loading. The buckling load is calculated in two steps. In the first step, the prebuckling stress distribution is computed. The existence of cutout causes the solution of stress distribution to be nontrivial. In this paper, a novel analytical method is presented for calculating the stress distribution. This method is based on expansion of the stress function in polar coordinates and using a boundary integral to satisfy the boundary conditions at plate edges. In the second step, the obtained stress distribution is used to calculate the buckling load from the Ritz method. In this method, The displacement field is defined according to the first order shear deformation theory and the characteristic beam functions are used for approximation. The effect of cutout size, plate’s aspect ratio, different uniaxial and biaxial loading profiles, i.e. constant, parabolic and cosine loading and different boundary conditions on the buckling load is studied.