Thermal postbuckling analysis of variable angle tow composite cylindrical panels

Abstract

The advanced Automated Fiber Placement (AFP) technologies allow the fiber trajectories to be curvilinearly steered over the panel platform, which brings out a novel type of cylindrical panel structure, termed as Variable Angle Tow (VAT) composite cylindrical panel. So far, the thermal postbuckling problem of VAT composite cylindrical panels under temperature loadings remain unexplored. The aim of this article is to cover this lack by developing a methodology based on a generalized Rayleigh–Ritz formulation in the framework of the principle of thermoelastic complementary energy. The proposed panel model is based on Donnell’s shallow shell theory and accounts for von Kármán’s geometrical nonlinearity. With the aid of the Lagrange multiplier method and the introduction of Airy’s stress function, a mixed variational formula that governs the nonlinear thermoelastic problem of VAT composite cylindrical panels is derived from the principle of thermoelastic potential energy. The Rayleigh-Ritz formulation combined with the mixed variational formula is then applied to derive the simultaneous nonlinear thermoelastic equations, and the Crisfield’s arc-length method, which can cope well with snap-through or snap-back problems, is employed to trace the equilibrium path that characterizes the thermal postbuckling features. Two different modeling strategies, namely, semi-inverse method and Lagrangian multiplier method, are adopted to formulate the nonlinear thermoelastic problem of VAT composite cylindrical panels undergoing temperature change. The application of Lagrangian multiplier method overcomes some limitations inherent in semi-inverse method in terms of constructing Rayleigh-Ritz formulation, and thus provides generality to model general in-plane boundary constraint. The accuracy and robustness of the proposed Rayleigh-Ritz model are validated against finite element solutions and previously published results. Effects of geometric imperfection, curvature radius, aspect ratio and fiber orientation angle on thermal postbuckling responses of VAT cylindrical plates are discussed by several examples. The study presented here may be helpful for the preliminary design of VAT curved panels in thermal environments.