Displacement-function modeling of thermo-mechanical behavior of fiber-reinforced composite structures

•An efficient analytical model for thermomechanical stress analysis of structural problems of FRC with mixed and changeable physical conditions.•A single scalar function defined in terms of displacement components is used to integrate the coupled thermal and mechanical problems.•Two orthogonal gradients of temperature field are taken care of by two versions of the model in two sequential steps to obtain the solution.•FRC plates and thick-beams under various nonuniform temperature fields with mixed-mode conditions are analyzed in details.•Soundness and superiority of the model over conventional approaches is verified through comparison with analytical and numerical solutions. A new modeling scheme has been developed for the analysis of thermo-mechanical stresses in structural problems of fiber-reinforced composite materials with mixed mode of physical conditions. In contrast with conventional approaches, the coupled thermal and mechanical problems of structural mechanics are integrated here using a single scalar function of space variables, which is defined in terms of the displacement components of plane elasticity. The displacement-function is governed by a single partial-differential equation of equilibrium that takes into account the two orthogonal gradients of the resulting non-uniform temperature field through two different versions of the formulation. The temperature-dependent elastic field is determined using a two-step solution scheme that utilizes the two versions of displacement-function formulations in two sequential steps. The scheme is developed in such a flexible fashion that even the solution of the corresponding isotropic problems can readily be obtained with thermal and/or mechanical loading as a limiting case of the formulation. The application of the proposed modeling scheme is demonstrated through the solution of a number of problems of structural mechanics, namely plates and beams subjected to thermal as well as thermo-mechanical loadings with both uniform and mixed mode of physical conditions. An attempt is also made to verify the soundness and accuracy of the resulting thermoelastic fields by comparing them with the corresponding analytical as well as computational solutions available in the literature. Moreover, the correspondence between the versions of the displacement-function formulation is also verified by solving identical problems using different versions or different combinations of the versions of the formulation.