Non-linear thermo-elastic and buckling analysis of FGM shallow arches

The paper presents a theoretical investigation on the non-linear thermo-elastic behaviour of pin-ended functionally graded material (FGM) circular shallow arches. Temperature dependency of constituents is taken into account and the arch is subjected to a uniform temperature field. Classical arches theory along with the non-linear shallow shell theory of Donnell are postulated as the basic assumptions. The virtual displacement principle and calculus of variation techniques are implemented to obtain the equilibrium equations. An analytical solution is presented to trace the primary equilibrium path of a pin-ended arch under in-plane thermal loading. Afterwards, closed form expressions are yielded to obtain the radial and axial displacement, stress, strain and bending moment of the arch as a function of temperature parameter. Adjacent equilibrium criterion is used to extract the stability equation associated to the non-linear primary equilibrium path. A closed form solution is presented to estimate the fundamental thermal bifurcation points of the arch. Illustrative results examine the role of the various involved parameters such as power law index, opening angle and length to thickness ratio. Numerical results reveal that, in most cases, critical buckling temperature difference of the FGM shallow arches are too high, even for thin class of arches.