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A node-to-segment (NTS) algorithm based on the penalty method is proposed for the enforcement of contact constraints within an edge-based smoothed finite element framework. The analysis is performed directly using explicit dynamic relaxation technique. In our study, strain field is reconstructed based on subdomains associated with each edge using smoothing gradient techniques. It is found that the proposed method is able to generate close-to-exact stiffness for the discretized model and provides solution with high accuracy. Besides, the proposed NTS algorithm can pass the contact patch test, which the traditional NTS algorithm may fail. This is mainly because the constant pressure field at the contact interfaces is accurately transmitted based on constant proportional penetration. Through the contact patch test and numerical examples, it is demonstrated that the proposed approach is an accurate and efficient tool for 2D frictionless contact problem.

Contact problem; NTS algorithm; Edge-based smoothed finite element method; Strain energy; Contact patch test