Nonlinear bending analysis of hyperelastic plates using FSDT and meshless collocation method

Nonlinear static analysis of hyperelastic square plates is investigated in this paper. The physical and geometrical nonlinearity for bending analysis is considered. The physical nonlinearity of silicon-rubber is described through Neo- Hookean strain energy function. The strong form of governing equations is derived using the right Cauchy-Green deformation tensor and first order shear deformation plate theory. The nonlinear governing equations are solved using a meshless collocation method based on multiquadric radial basis function (MQ -RBF). The shape parameter of MQ-RBF is obtained using leave-one-out-cross-validation method. A discretized nonlinear system of equations obtained from the meshless method is solved using the arc-length continuation algorithm. To prove the accuracy of the meshless MQ-RBF method, the results are compared to those of the Abaqus finite element method. The results are shown that the meshless collocation method is an efficient method for the nonlinear bending analysis of hyperelastic plates. Also, the run-time of the MCM is less than the other numerical methods due to there is no meshing and integration. Consequently, MCM is truly meshless and is more efficient than the other numerical method based on numerical integration.

کلیدواژه ها:

Hyperelastic Materials ، Neo-Hookean function ، Right Cauchy-Green tensor ، Meshless Collocation ، Radial Basis Functions