Scholarlink

<p>Two new nonlinear mathematical models describing a&#xa0;contact of a&#xa0;non-homogeneous Kirchhoff-Love plate with an inclined non-deformable obstacle are proposed. Some issues of mathematical correctness are studied. It is assumed that the plate has a&#xa0;thin rigid inclusion on a&#xa0;part of the lateral boundary. Signorini-type conditions of possible contact with non-deformable inclined obstacles are imposed on a&#xa0;given part of the boundary of a&#xa0;midplane, and homogeneous Dirichlet conditions are specified on the other part of the boundary. The unique solvability of minimization problems is proved. Continuous dependence of the solution on the external forces in the energy norm is proved. Under an additional regularity assumption on the solution of the minimization problem, the corresponding equivalent differential formulation is derived for one of the considered problems. A&#xa0;limiting case for a&#xa0;family of problems with the different lengths of contact zones is investigated when the length parameter tends to zero. Further, the strong convergence of solutions in the energy norm is proved as the length of the contact zone tends to zero.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Equilibrium Problem for a Kirchhoff–Love Plate Contacting by a Thin Rigid Inclusion with an Inclined Obstacle

  • 期刊论文

  • 发表日期：

    2025年8月27日

查看全文
  • Nyurgun Lazarev,
  • Semen Verkhovtsev

摘要

Two new nonlinear mathematical models describing a contact of a non-homogeneous Kirchhoff-Love plate with an inclined non-deformable obstacle are proposed. Some issues of mathematical correctness are studied. It is assumed that the plate has a thin rigid inclusion on a part of the lateral boundary. Signorini-type conditions of possible contact with non-deformable inclined obstacles are imposed on a given part of the boundary of a midplane, and homogeneous Dirichlet conditions are specified on the other part of the boundary. The unique solvability of minimization problems is proved. Continuous dependence of the solution on the external forces in the energy norm is proved. Under an additional regularity assumption on the solution of the minimization problem, the corresponding equivalent differential formulation is derived for one of the considered problems. A limiting case for a family of problems with the different lengths of contact zones is investigated when the length parameter tends to zero. Further, the strong convergence of solutions in the energy norm is proved as the length of the contact zone tends to zero.