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Abstract <p>In the approximation of the Föppl–von Kármán model, which takes into account the presence of plastic deformations, the solution of the problem of elastoplastic bending of a thin plate was obtained, under the boundary conditions of the type of rigid, or generalized elastic embedment type. The model of ideal plasticity with the Tresca–St-Venant yield surface was used. The use of the standard Kirchhoff–Love hypotheses allowed to reduce the problem to a system of ordinary differential equations. The numerical solution of this system for the boundary conditions of the generalized elastic embedment was obtained. The solution for the boundary conditions of rigid clamping is obtained as a particular case.</p>

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On The Elastic-Plastic Deformation of a Circular Plate under Centrally Symmetric Normal Loading

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • K. B. Ustinov,
  • D. V. Gandilyan

摘要

Abstract

In the approximation of the Föppl–von Kármán model, which takes into account the presence of plastic deformations, the solution of the problem of elastoplastic bending of a thin plate was obtained, under the boundary conditions of the type of rigid, or generalized elastic embedment type. The model of ideal plasticity with the Tresca–St-Venant yield surface was used. The use of the standard Kirchhoff–Love hypotheses allowed to reduce the problem to a system of ordinary differential equations. The numerical solution of this system for the boundary conditions of the generalized elastic embedment was obtained. The solution for the boundary conditions of rigid clamping is obtained as a particular case.