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<p>Two nonlinear mathematical models of the equilibrium of heterogeneous plates are studied. Each of the two models describes a&#xa0;contact interaction with a&#xa0;corresponding obstacle. It is assumed that the plates contain a&#xa0;bulk rigid inclusion of the same shape, which is in contact with a&#xa0;non-deformable obstacle in the reference state. For the model of the first type, the obstacle has a&#xa0;square shape and restricts displacements of the plates on the front surface. Another type of obstacle is also specified on the front surface, but has a&#xa0;point character. In this case, a&#xa0;non-penetration condition is imposed at one specified point corresponding to the rigid inclusion. The convergence of solutions of a&#xa0;family of nonlinear problems is proved as the parameter that specifies the length of the square side corresponding to the contact surface tends to zero. It turns out that the limit function is the solution to the problem describing the point contact of the plate.</p>

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Point Contact Problem on a Front Surface for a Timoshenko Plate with a Rigid Inclusion

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Nyurgun P. Lazarev,
  • Alexander Zarovnaev

摘要

Two nonlinear mathematical models of the equilibrium of heterogeneous plates are studied. Each of the two models describes a contact interaction with a corresponding obstacle. It is assumed that the plates contain a bulk rigid inclusion of the same shape, which is in contact with a non-deformable obstacle in the reference state. For the model of the first type, the obstacle has a square shape and restricts displacements of the plates on the front surface. Another type of obstacle is also specified on the front surface, but has a point character. In this case, a non-penetration condition is imposed at one specified point corresponding to the rigid inclusion. The convergence of solutions of a family of nonlinear problems is proved as the parameter that specifies the length of the square side corresponding to the contact surface tends to zero. It turns out that the limit function is the solution to the problem describing the point contact of the plate.