A stress function based model for transient thermal stresses of composite laminates in various time-variant thermal environments

Abstract

We present a study of transient thermal stresses of composite laminate in this work by means of stress function based approach considering various time-variant thermal environments. Two-dimensional temperature distribution is considered for both linear and quadratic temperature distributions. For each type of distribution, we consider three different cases to examine the effect off thermal transfer point on the distribution of thermal stresses. The proposed methodology uses the principle of complementary virtual work to develop the governing equations and consider the thermomechanical coupling in its constitutive equation. The Lekhnitskii stress functions are adopted as stress fields and the mode shape functions of clamped beam are adopted as stress trial functions. By means of the Rayleigh–Ritz method, we obtain a standard eigenvalue problem and further solve the eigen problem to obtain the solutions. We find that different temperature distributions affect the inhomogeneous equations, but they don't affect the homogeneous equations in the present model. The results will demonstrate the distributions of transient thermal stresses in angle-ply and cross-ply laminates under linear and quadratic temperature distributions. The present methodology is computationally efficient and accurate in calculating the transient thermal stresses, and it can be used in thermal stress analysis of laminated structures.