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Abstract <p>The paper considers deformation of isotropic rectangular samples within the generalized plane stress state. Approximate models of different orders for elongated samples are constructed by representing the displacement field as an expansion in first- and second-order polynomials with unknown coefficient functions. The Kantorovich method within the Lagrange variational principle allows one to reduce the problem to a system of ordinary differential equations with constant coefficients and to form the corresponding boundary conditions. The models are verified by the finite element method (FEM) implemented in FlexPDE, the suitability of the obtained models is investigated depending on the relative thickness parameter of the rectangle. The inverse problem of reconstructing Poisson’s ratio and Young’s modulus from information on the displacement field on the lateral face is solved.</p>

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On the Applied Theory of Rectangle Stretching

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Alexandr Vatulyan,
  • Victor Yurov,
  • Ivan Gusakov

摘要

Abstract

The paper considers deformation of isotropic rectangular samples within the generalized plane stress state. Approximate models of different orders for elongated samples are constructed by representing the displacement field as an expansion in first- and second-order polynomials with unknown coefficient functions. The Kantorovich method within the Lagrange variational principle allows one to reduce the problem to a system of ordinary differential equations with constant coefficients and to form the corresponding boundary conditions. The models are verified by the finite element method (FEM) implemented in FlexPDE, the suitability of the obtained models is investigated depending on the relative thickness parameter of the rectangle. The inverse problem of reconstructing Poisson’s ratio and Young’s modulus from information on the displacement field on the lateral face is solved.