Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation

Mohammad Arefi , M.N.M. Allam

Abstract

This paper presents nonlinear analysis of an arbitrary functionally graded circular plate integrated with two functionally graded piezoelectric layers resting on the Winkler-Pasternak foundation. Geometric nonlinearity is considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson\'s ratio can vary continuously along the thickness of the plate based on a power function. Electric potential is assumed as a quadratic function along the thickness direction. After derivation of general nonlinear equations, as an instance, numerical results of a functionally graded material integrated with functionally graded piezoelectric material obeying two different functionalities is investigated. The effect of different parameters such as parameters of foundation, non homogenous index and boundary conditions can be investigated on the mechanical and electrical results of the system. A comprehensive comparison between linear and nonlinear responses of the system presents necessity of this study. Furthermore, the obtained results can be validated by using previous linear and nonlinear analyses after removing the effect of foundation.

Key Words

Winkler-Pasternak foundation; nonlinear responses; functionally graded material; piezoelectric; circular plate

Address

Mohammad Arefi — 1Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran
M.N.M. Allam — Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

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