Stability Analysis of Elastic Plates Under Non-Uniform Stress Fields by the Boundary Element Method

Abstract

This paper presents a boundary element formulation to investigate the onset of instability of elastic plates with a wide variety of boundary conditions and arbitrary geometries. Stresses caused by external loads are calculated by the formulation of plane elasticity boundary element method. Then, these stresses are introduced as body forces in the classical formulation of plates. The domain integrals due to body forces are transformed into boundary integrals using the radial integration method. In this method, body forces are approximated by a sum of radial basis functions, called approximation functions, multiplied by coefficients to be determined. Functions used for approximations are known as thin plate splines. Various numerical examples are analyzed in which critical loads, buckling modes, and coefficients of buckling are calculated. The accuracy of the proposed formulation is assessed by comparison with results from literature.