Geometrically nonlinear analysis of composite piezoelectric plates using meshfree RPIM with a new layerwise approach

In this article, nonlinear analysis of piezoelectric plates using Ferreira layerwise theory based on radial point interpolation method (RPIM) meshfree method is presented. This paper develops Ferreira layerwise method for geometrically nonlinear analysis of composite plates considering piezoelectric effects. Based on this layerwise method, the first-order shear deformation theory is used for layers. Nonlinear Von Karman-type strains are considered to predict the geometrically nonlinear behavior of the piezoelectric plates. By a combination of Ferreira layerwise method and meshfree RPIM and using electrical enthalpy, the matrix form of nonlinear equations is obtained. The Newton-Raphson iteration method is used to obtain the solution of governing nonlinear equations. Using this form of formulation and combining it with the meshfree method increase the linear displacements and stresses accuracy. Consequently, the accuracy of the nonlinear results will increase. Linear and nonlinear solutions are compared with some numerical and exact solutions in the literature. The presented results show that there is a good agreement between them and the exact solution. The results presented in this paper show that Ferreira layerwise model has a good ability to predict the nonlinear behavior of thick or thin piezoelectric composite plates.