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<p>When a heavily distorted four-node quadrilateral (Q4) element is used in the standard finite element method, a negative Jacobian will result and the computation will fail. In addition, in a contact patch test (CPT) using the standard node-to-segment (NTS), an imbalance of interface moment will also result, leading to inaccurate solutions. To overcome these defects, this article proposes a novel NTS contact scheme with a distributed area regularization involving real slave nodes (NTS-DAR) based on the cell-based smoothed finite element method (CS-FEM). The proposed scheme performs a precise linearization of the contact virtual work, which enhances the convergence properties for Newton–Raphson solution approaches. This also ensures the reliability of implicit finite element techniques. The solution error caused by asymmetry between contact surfaces is significantly reduced by considering the contribution of each corresponding contact pair. The inherent softening effect of CS-FEM effectively reduces the “over-stiff” stiffness matrix, enhancing the solution's stability. Several benchmark and numerical examples are presented to examine the performance of the proposed method. It is found that continuous and smooth transition in both displacement and stress across the contact surfaces is successfully achieved, leading to accurate, stable and reliable solutions for contact problems.</p>

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A cell-based smoothed finite element method with a distributed area regularization technique for 2D small displacement contact problems

  • 期刊论文

  • 发表日期：

    2025年5月6日

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  • Chao Sun,
  • G. R. Liu,
  • S. H. Huo,
  • G. Wang,
  • Jingui Zhao,
  • Zirui Li

摘要

When a heavily distorted four-node quadrilateral (Q4) element is used in the standard finite element method, a negative Jacobian will result and the computation will fail. In addition, in a contact patch test (CPT) using the standard node-to-segment (NTS), an imbalance of interface moment will also result, leading to inaccurate solutions. To overcome these defects, this article proposes a novel NTS contact scheme with a distributed area regularization involving real slave nodes (NTS-DAR) based on the cell-based smoothed finite element method (CS-FEM). The proposed scheme performs a precise linearization of the contact virtual work, which enhances the convergence properties for Newton–Raphson solution approaches. This also ensures the reliability of implicit finite element techniques. The solution error caused by asymmetry between contact surfaces is significantly reduced by considering the contribution of each corresponding contact pair. The inherent softening effect of CS-FEM effectively reduces the “over-stiff” stiffness matrix, enhancing the solution's stability. Several benchmark and numerical examples are presented to examine the performance of the proposed method. It is found that continuous and smooth transition in both displacement and stress across the contact surfaces is successfully achieved, leading to accurate, stable and reliable solutions for contact problems.