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