A meshless collocation method on nonlinear analysis of functionally graded hyperelastic plates using radial basis function
Shahram Hosseini, Gholamhossein Rahimi, Davoud Shahgholian‐Ghahfarokhi
Abstract
Abstract In the present work, the nonlinear static analysis of functionally graded hyperelastic thin plate is investigated. The neo‐Hookean strain energy function and right Cauchy‐Green tensor are utilized to formulate the potential energy function. Also, the first‐order shear deformation theory of the plate is used to form the strain‐displacement relations. The strong form of the governing equations is derived using Euler‐Lagrange relations, and these relations are discretized using the meshless collocation method (MCM). The thin‐plate spline (TPS) radial basis function (RBF) is utilized to discretize the nonlinear governing equations, and the arc‐length continuation algorithm is used to solve the nonlinear algebraic system of equations. Square and circular plates with clamped and simply supported boundary conditions and various power‐law indexes are investigated using the MCM. The results are compared to those of the finite element method (FEM). The results show that the MCM is an accurate and efficient method in comparison to FEM for circular and square functionally graded (FG) hyperelastic thin plates.