Fundamental Solutions For The General Laminate Problem With The Stress Function Formalism

Abstract

The linear coupled stretching-bending problem for general laminates is here formulated with the midplane stress function and the lateral deflection as independent field variables. A mathematical similarity between the two problems is achieved by introducing a re-arranged mid-plane strain tensor as one of the dependent variables. As a step towards a genuine boundary element solution for this problem, its fundamental solutions are derived using a Fourier transform approach. First, the transforms of the solutions are obtained in terms of the transform space variables and their inverses are deduced using complex integral calculus. Through the use of these fundamental solutions, boundary integral equations of the linear coupled stretching-bending problem are formulated without the presence of any irreducible domain integrals. Issues regarding the numerical implementation of this formulation are raised and discussed.