Analysis of edge stresses in composite laminates under combined thermo-mechanical loading, using a complementary energy approach

Abstract

An approximate method is presented to investigate the interlaminar stresses near the free edges of composite laminate plates that are subjected to a combined thermo-mechanical loading. The method is based upon admissible function representations of stresses which account for the effects of both the global mismatches and the local mismatches in two of the elastic properties, the Poisson's ratio and the coefficient of mutual influence. For this purpose, new thermo-mechanical mismatch terms are defined to reflect an effective deformation under the combined thermo-mechanical loading. Closed form solutions of all the stress components are sought by minimizing the complementary energy with respect to the unknown functions, in the stress representations, of the width coordinate. These unknown functions are determined by solving five ordinary differential equations along with a set of free edge boundary conditions, which allow complex as well as real roots for their exponential decaying rates. The resulting solutions satisfy the stress equilibrium and all of the boundary conditions exactly, but compatibility is met in a weak form. Numerical examples are given for several typical laminates, and are compared with previous results obtained by finite element and other approximate methods. It is found that the present approximate method yields interlaminar stress results in an efficient, fast and yet reliable way. It is also concluded that unlike some previous approximate methods, the current method is numerically robust and stable.