This paper is proposed for the error estimates of the element‐free Galerkin method for a quasistatic contact problem with the Tresca friction. The penalty method is used to impose the clamped boundary conditions. The duality algorithm is also given to deal with the non‐differentiable term in the quasistatic contact problem with the Tresca friction. The error estimates indicate that the convergence order is dependent on the nodal spacing, the time step, the largest degree of basis functions in the moving least‐squares approximation, and the penalty factor. Numerical examples demonstrate the effectiveness of the element‐free Galerkin method and verify the theoretical analysis.

中文翻译：

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弹性材料中Tresca摩擦的准静态接触问题的无元素Galerkin方法

本文针对Tresca摩擦的准静态接触问题的无元素Galerkin方法的误差估计提出。惩罚方法用于施加限制的边界条件。还给出了对偶算法来处理与Tresca摩擦的准静态接触问题中的不可微分项。误差估计表明收敛阶数取决于节点间距，时间步长，移动最小二乘近似中基函数的最大程度以及惩罚因子。数值例子证明了无元素Galerkin方法的有效性并验证了理论分析。