Geometrically nonlinear analysis of shear deformable FGM shallow pinned arches on nonlinear elastic foundation under mechanical and thermal loads

The present investigation deals with the large amplitude response of shallow thick circular arches subjected to thermal, mechanical, or thermomechanical loads. The structure is resting on a three-parameter elastic foundation containing the Winkler springs, the shear Pasternak layer, and hardening nonlinear springs. The arch is made of a through-the-thickness functionally graded material. Except for Poisson’s ratio, the other properties of the arch are assumed to be temperature and position dependent. Each property is estimated according to the rule of mixtures in terms of the volume fraction of the constituents. The case of uniform temperature rise and uniform radial lateral load is considered. The governing equations of the arch are obtained with the aid of the third-order shear deformation arch theory and the von Kármán type of geometrical nonlinearity. The developed coupled and nonlinear equilibrium equations are solved using the two-step perturbation technique for the case of simply supported arches. Closed-form expressions are developed for nonlinear bending equilibrium path of shallow arches under thermal and mechanical loads. Results are provided for different power law indices, geometrical parameters, and the foundation stiffness.