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A multi-parametrical contact problem on compression an axisymmetric elastic–plastic body involving large strain and friction is considered. A set of parameters consists of 3 geometrical characteristics and 4 material constants. Based on several simplifying hypotheses, an inexact analytical solution is deduced. Comparative analysis with a FEM solution demonstrates high accuracy of the analytical one and this accuracy can be regulated by means of the geometric parameters. A-priory error estimation is proposed. The effect of stabilization parameter on the accuracy for a nodal integrated stabilized finite element is studied. The analytical solution obtained can be used as a benchmark for program codes in 3D contact mechanics—ANSYS, NASTRAN, DEFORM, ABACUS, Super Forge, etc.

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A Contact Problem with Large Elastic–plastic Strain, Friction, and Close to Exact Analytical Solution

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  • 发表日期：

    2025年

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  • Pavel G. Morrev,
  • Alexey A. Markin

摘要

A multi-parametrical contact problem on compression an axisymmetric elastic–plastic body involving large strain and friction is considered. A set of parameters consists of 3 geometrical characteristics and 4 material constants. Based on several simplifying hypotheses, an inexact analytical solution is deduced. Comparative analysis with a FEM solution demonstrates high accuracy of the analytical one and this accuracy can be regulated by means of the geometric parameters. A-priory error estimation is proposed. The effect of stabilization parameter on the accuracy for a nodal integrated stabilized finite element is studied. The analytical solution obtained can be used as a benchmark for program codes in 3D contact mechanics—ANSYS, NASTRAN, DEFORM, ABACUS, Super Forge, etc.