Non-linear thermoelectrical stability analysis of functionally graded piezoelectric material beams

In this article, non-linear stability analysis of monomorph functionally graded piezoelectric material beams is investigated based on the Ritz formulation of the finite elements method. Each thermo–electro–mechanical property of the beam is assumed to be graded across the thickness based on a power law form. Geometrically non-linear behaviour of the structures is included based on the von-Karman simplifications of the complete Green strain tensor. Timoshenko beam theory and trigonometric distribution of electrical potential assumptions are held to obtain the governing equations, describing the equilibrium state of the beam. Non-linear equilibrium equations are solved based on both Newton–Raphson and Picard iterative techniques. It is shown that response of a monomorph functionally graded piezoelectric material beam cannot be considered as a bifurcation-point behaviour. While in some types of boundary conditions, there are critical temperatures through the load–deflection path of the beam.