Thermal Stresses and Free-Edge Effects in Laminated Beams: A Variational Approach Using Stress Functions

Abstract

A variational method involving stress functions is used to determine the interlaminar stresses and the free-edge effects in a laminated beam under a temperature loading. The stress function in each layer is approximated by a cubic polynomial function of the thickness coordinate. The equilibrium equations, the traction boundary conditions, and the continuity conditions of the interlaminar stresses are exactly satisfied in this analysis, while the compatibility equations and interfacial continuity of the tangential strains are enforced in an averaged sense by applying the principle of complementary virtual work. The method is highly efficient and accurate. A thermal stress analysis for a three-layer beam using only eight eigenfunctions yield results that are comparable in accuracy to finite-element solutions involving thousands of degrees of freedom.