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<p>The contact problem under complex conditions has always been a research hotspot in the field of computational mechanics, with particular attention given to thermoelastic contact problems. In response to this, a penalty-based cell vertex finite volume method (P-CV-FVM) is proposed. This method establishes discrete control equations for thermal contact and thermoelastic contact problems of planar and axisymmetric structures. A discrete form of point-to-surface contact is employed on the contact interface, and constraint conditions are imposed using the penalty function method. Consequently, contact forces and heat flux densities are transmitted through the nodes. The method exhibits strong applicability to irregular shape problems, allowing for triangular and quadrilateral mixed elements in the computational domain. Furthermore, it is suitable for axisymmetric structures without requiring a one-to-one correspondence between contact surface meshes. The P-CV-FVM is utilized to solve axisymmetric elastic contact problems, frictional contact problems, thermoelastic contact problems, and axisymmetric thermoelastic contact problems. The results show that the accuracy of P-CV-FVM is equivalent to that of the finite element method (FEM) when calculating the thermoelastic contact problems, but the required computational memory is smaller and the calculation speed is faster. Therefore, P-CV-FVM can serve as a numerical algorithm for solving thermoelastic contact problems with fewer computational resources.</p>

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Research on Nonlinear Problems of Thermoelastic Contact Based on the Cell Vertex Finite Volume Method

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • Jingfeng Gong,
  • Hongyu Guo,
  • Lingkuan Xuan,
  • Chu Yan,
  • Sinian Xu,
  • Chenqi Li

摘要

The contact problem under complex conditions has always been a research hotspot in the field of computational mechanics, with particular attention given to thermoelastic contact problems. In response to this, a penalty-based cell vertex finite volume method (P-CV-FVM) is proposed. This method establishes discrete control equations for thermal contact and thermoelastic contact problems of planar and axisymmetric structures. A discrete form of point-to-surface contact is employed on the contact interface, and constraint conditions are imposed using the penalty function method. Consequently, contact forces and heat flux densities are transmitted through the nodes. The method exhibits strong applicability to irregular shape problems, allowing for triangular and quadrilateral mixed elements in the computational domain. Furthermore, it is suitable for axisymmetric structures without requiring a one-to-one correspondence between contact surface meshes. The P-CV-FVM is utilized to solve axisymmetric elastic contact problems, frictional contact problems, thermoelastic contact problems, and axisymmetric thermoelastic contact problems. The results show that the accuracy of P-CV-FVM is equivalent to that of the finite element method (FEM) when calculating the thermoelastic contact problems, but the required computational memory is smaller and the calculation speed is faster. Therefore, P-CV-FVM can serve as a numerical algorithm for solving thermoelastic contact problems with fewer computational resources.