Nonlinear Bending Analysis of Hyperelastic Plates Using FSDT and Meshless Collocation Method Based on Radial Basis Function

Abstract

This paper investigates the nonlinear bending analysis of a hyperelastic plate via neo-Hookean strain energy function. The first-order shear deformation plate theory (FSDPT) is used for the formulation of the field variables. Also, the nonlinear Lagrangian strains are considered via the right Cauchy–Green tensor. The governing equations and nonlinear boundary conditions are derived using Euler–Lagrange relations. The meshless collocation method based on radial basis function is used to discretize the governing equations of the hyperelastic plate. Square and circular plates are studied to evaluate the accuracy of the meshless collocation method based on thin-plate spline (TPS) and multiquadric (MQ) and logarithmic thin-plate spline (LTPS) radial basis function. Also, the results of the meshless method are compared to those of the finite element method. In some cases, the meshless method is more efficient than the finite element method due to no meshing. The linear and nonlinear natural boundary conditions are directly imposed on the stiffness matrix and are compared to each other. The maximum differences between linear and nonlinear natural boundary conditions are 1.43%. The von-Mises stress using meshless collocation method based on TPS basis function is compared to those of the finite element method.