Based on the reproducing kernel particle method (RKPM) and the radial basis function (RBF), the radial basis reproducing kernel particle method (RRKPM) is presented for solving geometrically nonlinear problems. The advantages of the presented method are that it can eliminate the negative effect of diverse kernel functions on the computational accuracy and has greater computational accuracy and better convergence than the RKPM. Using the weak form of Galerkin integration and the Total Lagrangian (T.L.) formulation, the correlation formulae of the RRKPM for geometrically nonlinear problem are obtained. Newton–Raphson (N-R) iterative method is utilized in the process of numerical solution. Moreover, penalty factor, the scaling parameter, the shaped parameter of the RBF and loading step number are discussed. To prove validity of the proposed method, several numerical examples are simulated and compared to finite element method (FEM) solutions.

中文翻译：

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基于径向基再现核粒子法的几何非线性问题的无网格分析

基于再现核粒子法（RKPM）和径向基函数（RBF），提出了径向基再现核粒子法（RRKPM）求解几何非线性问题。该方法的优点是可以消除不同核函数对计算精度的负面影响，比RKPM具有更高的计算精度和更好的收敛性。利用Galerkin积分的弱形式和总拉格朗日(TL)公式，得到了RRKPM对几何非线性问题的相关公式。Newton-Raphson (NR) 迭代法用于数值求解过程。此外，还讨论了惩罚因子、缩放参数、RBF的形状参数和加载步数。为了证明所提出方法的有效性，