Postbuckling of Polar Orthotropic Circular Plates Retrospective

Abstract

The postbuckling analysis of cylindrically orthotropic circular plates is a theoretically challenging problem characterized by singularities due to ortho‐tropy and axisymmetry of deformations. In addition, geometric nonlinearities and strong coupling between the in‐plane and transverse displacements make an explicit treatment difficult. The subject matter has attracted considerable attention due to recent interest in circular delamination buckling, a critical failure mode in fibrous composite laminates. A comprehensive initial‐value formulation is presented where a transformation of problem variables is introduced to include cylindrical ortho‐tropy; the resulting nonlinear, ordinary differential equations are numerically integrated using the Runge‐Kutta‐Merson method where general boundary conditions can be easily accommodated. Optimal forms of material orthotropy and their implications in pre‐ and postbuckling are examined. It is shown that the buckling load, as well as postbuckling stiffness, can be improved by increasing the orthotropy ratio, i.e., the ratio of circumferential to radial elastic modulus.