Application of Rayleigh-Ritz formulation to thermomechanical buckling of variable angle tow composite plates with general in-plane boundary constraint

Abstract

Variable Angle Tow (VAT) composites always exhibit in-plane variable stiffness property, which provides the designer with an extended freedom in stiffness tailoring to achieve higher structural performance for lightweight composite structures. In this paper, a methodology based on a generalised Rayleigh-Ritz formulation is developed to study the thermomechanical buckling response of symmetrical VAT composite plates with general in-plane boundary constraint. It is assumed that the material is of temperature-independent and the panel is exposed to an arbitrary in-plane temperature change. In the framework of thermoelastic theory, the principle of thermoelastic complementary energy in conjunction with Airy’s stress function formulation, for the first time, is applied to solve the in-plane thermoelastic problem of the tow-steered plate. The non-uniform distribution of in-plane force resultant over the entire plane is determined by utilizing the Rayleigh-Ritz formulation enhanced by Lagrangian multiplier method. The merit of the proposed modelling strategy lies in that the application of Lagrangian multiplier method removes the restrictions inherent in conventional Rayleigh-Ritz formulation and thus provides generality to model general in-plane boundary constraint against thermal expansion or contraction. During the buckling analysis, the governing equation of thermomechanical buckling problem of the tow-steered plate under a combination of both temperature change and general in-plane boundary constraint is derived based on the third-order shear deformation theory of Reddy’s type. The accuracy and robustness of the proposed Rayleigh-Ritz model is validated against finite element solutions and previously published results. Effects of boundary condition, fibre orientation angle and temperature change on the in-plane thermoelastic and thermomechanical buckling behaviours of VAT composite plates are studied by numerical examples. Finally, the mechanism of applying tow-steered technology to improve the thermomechanical buckling resistance of composite plates is explored.