Exact Solution for Nonlinear Stability of Piezoelectric FGM Timoshenko Beams Under Thermo-Electrical Loads

In this article an exact solution is presented for the nonlinear response of hybrid functionally graded material (FGM) Timoshenko beams subjected to simultaneous action of thermal and electrical loads. Properties of the FGM media are graded across the thickness based on a power law form. Employing the Timoshenko beam theory and mid-surface based formulation in conjunction with the von-Karman strain-displacement relations, the three non-linear equilibrium equations along with the associated boundary conditions are obtained. The resulting equations are then uncoupled in a reasonable manner. An exact closed-form solution is presented to trace the load-deflection path for the clamped and simply supported beams. It is shown that the behavior of these two types of boundary conditions are totally different since the response of FGM clamped beam is of the bifurcation-type while the load-deflection path of FGM simply supported beams is unique and stable. This feature is detectable through the temperature-deflection or force-temperature paths. Numerical results are presented to investigate the effects of various involved parameters.

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