Nonlinear bending analysis of multi-layer hyperelastic silicon-rubber plates using meshless based on radial basis functions

In this paper, bending analysis of a hyperelastic multi-layer square plate with clamped, simply supported, and free boundary conditions are studied. The right Cauchy-Green tensor and neo-Hookean strain energy function utilized to define the plate's physical nonlinear behaviour. The nonlinear strains formulated using first-order shear deformation plate theory, and the Euler-Lagrange equations employed to derive the strong form of the governing equations. The meshless collocation method based on radial point interpolation method used to solve the nonlinear governing equations. The nonlinear boundary conditions imposed directly on the plate in meshless collocation method. The logarithm basis function utilized for defining shape functions, and the nonlinear system of equations solved using the arc-length algorithm. The results of the meshless method compared to those of ABAQUS finite element software. The results show that the meshless collocation method based on radial basis functions are efficient in nonlinear bending analysis of the multi-layer hyperelastic plate with various boundary conditions such that the less difference between meshless method and finite element method is 0.93% for clamped and the most difference is 8.72% with free boundary conditions.