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In this article, the buckling of multilayer rectangular thick plate made of functionally graded, transversely isotropic and piezoelectric materials in both closed and open circuit conditions are investigated. Based on the shear and normal higher-order deformation theory, the governing equilibrium equations of plate are obtained using the principle of minimum total potential energy and Maxwell’s equation. Using an analytical approach, the governing stability equations of functionally graded rectangular plates with piezoelectric layers have been presented in terms of displacement components and electric potentials. In order to obtain the stability equations, the adjacent equilibrium criterion is used. The stability equations are then solved analytically, assuming simply support boundary condition along all edges. Finally after ensuring the validation of the results, the effects of different parameters such as different loading conditions, functionally graded power law index, thickness-to-length ratio and aspect ratio, on the critical buckling loads of plates are studied in details. Furthermore, the effect of piezoelectric thickness on the plate critical buckling loads has been studied. The results present better accuracy in comparison with the classic and third order shear theories.

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In this paper, the nonlocal buckling behavior of a biaxially loaded graphene sheet with piezoelectric layers based on an isotropic smart nanoplate model is studied. The equilibrium equations are derived with the von Karman-type geometrical nonlinearity by considering the small scale effect. The buckling of multilayer smart nanoplate made of graphene and piezoelectric materials in open circuit conditions is investigated. Based on the nonlocal elasticity and shear and normal deformation theories, the governing equilibrium equations are obtained using the principle of minimum total potential energy and Maxwell’s equation.
Using an analytical approach, the governing stability equations of smart nanoplate have been presented in terms of displacement components and electrical potential. In order to obtain the stability equations, the adjacent equilibrium criterion is used. The stability equations are then solved analytically, assuming simply supported boundary condition along all edges. To validate the results, the critical buckling load values have been compared with available resources. Finally, following validation of the results, numerical results for intelligent nanoplate are presented.
Also, the effects of different parameters such as nanoplate length, different nonlocal parameter, piezoelectric layers thickness, the graphene thickness to length ratio, the piezoelectric layer thickness to graphene thickness ratio and type of Piezoelectric material on the critical buckling loads of intelligent nanoplate are studied in detail. Furthermore, the effect of the mentioned parameters on the critical buckling loads have been presented in some figures.