Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure

Abstract

Abstract. The present paper addresses the nonlinear response of a FG square plate with two smart layers asa sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relationbased on the Von-Karman assumption. All the mechanical and electrical properties except Poisson’s ratio canvary continuously along the thickness of the plate based on a power function. Electric potential was assumedas a quadratic function along the thickness direction and trigonometric function along the planar coordinate.By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect toamplitude of displacements and electrical potential. The effect of non homogenous index was investigated onthe responses of the system. Obtained results indicate that with increasing the non homogenous index, thedisplacements and electric potential tend to an asymptotic value. Displacements and electric potential can bepresented in terms of planar coordinate system. A linear analysis was employed and then the achieved resultsare compared with those results that are obtained using the nonlinear analysis. The effect of the geometricnonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis.Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can bepresented as novelty of this study. Keywords: plate; mechanical properties; electrical properties; nonlinear; functionally graded material;piezoelectric; sensor.