This paper presents the node-based smoothed finite element method with linear strain functions (NS-FEM-L) for solving contact problems using triangular elements. The smoothed strains are formulated by a complete order of polynomial functions and normalized with reference to the central points of smoothing domains. They are one order higher than those adopted in the finite element method (FEM) and the standard smoothed finite element method with the same triangular mesh. When using linear functions to describe strains in smoothing domains, the solutions are more accurate and stable. The contact interfaces are discretized by contact point pairs using a modified Coulomb frictional contact model. The contact problems are solved via converting into linear complementarity problems (LCPs) which can be tackled by using the Lemke method. Numerical implementations are conducted to simulate the contact behavior, including the bonding–debonding, contacting–departing and sticking–slipping. The effects of various parameters related to friction and adhesion are intensively investigated. The comparison of numerical results produced by different methods demonstrates the validity and efficiency of the NS-FEM-L for contact problems.

本文介绍了使用线性应​​变函数 (NS-FEM-L) 的基于节点的平滑有限元方法，用于使用三角形单元解决接触问题。平滑应变由多项式函数的完整阶公式表示，并参考平滑域的中心点进行归一化。它们比有限元法 (FEM) 和具有相同三角形网格的标准平滑有限元法中采用的方法高一个数量级。当使用线性函数来描述平滑域中的应变时，解更加准确和稳定。接触界面通过使用改进的库仑摩擦接触模型的接触点对离散化。接触问题通过转换为线性互补问题（LCP）来解决，可以使用 Lemke 方法解决。进行了数值实现来模拟接触行为，包括粘合-剥离、接触-分离和粘着-滑动。深入研究了与摩擦和粘附相关的各种参数的影响。不同方法产生的数值结果的比较证明了 NS-FEM-L 对接触问题的有效性和效率。