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.

中文翻译：

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基于径向基函数的FSDT和无网格配置法的超弹性板非线性弯曲分析

本文通过新胡克应变能函数研究了超弹性板的非线性弯曲分析。一阶剪切变形板理论（FSDPT）用于场变量的公式化。此外，非线性拉格朗日应变通过右 Cauchy-Green 张量考虑。控制方程和非线性边界条件是使用欧拉-拉格朗日关系导出的。采用基于径向基函数的无网格配置方法对超弹性板的控制方程进行离散化。研究了方形和圆形板，以评估基于薄板样条（TPS）和多二次（MQ）和对数薄板样条（LTPS）径向基函数的无网格搭配方法的准确性。还，将无网格法的结果与有限元法的结果进行了比较。在某些情况下，由于没有网格划分，无网格方法比有限元方法更有效。线性和非线性自然边界条件直接施加在刚度矩阵上并相互比较。线性和非线性自然边界条件之间的最大差异为 1.43%。将基于TPS基函数的无网格配置法的von-Mises应力与有限元法进行了比较。线性和非线性自然边界条件之间的最大差异为 1.43%。将基于TPS基函数的无网格配置法的von-Mises应力与有限元法进行了比较。线性和非线性自然边界条件之间的最大差异为 1.43%。将基于TPS基函数的无网格配置法的von-Mises应力与有限元法进行了比较。