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An exact analytical solution is obtained for a nonlinear problem of elasticity theory for a plane with a rigid elliptical inclusion. A concentrated force and a moment are applied at the center of inclusion. The elastic properties of the plane are modeled by John’s harmonic material. Nominal stresses and displacements are expressed in terms of two analytical functions of a complex variable, which are determined from the boundary conditions on the contour of inclusion. Calculations of nominal stresses on the contour joining the plane with inclusion are performed.

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Nonlinear Deformation of Plane with Rigid Elliptical Inclusion Loaded by Force and Moment

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  • 发表日期：

    2025年

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  • Yulia Malkova

摘要

An exact analytical solution is obtained for a nonlinear problem of elasticity theory for a plane with a rigid elliptical inclusion. A concentrated force and a moment are applied at the center of inclusion. The elastic properties of the plane are modeled by John’s harmonic material. Nominal stresses and displacements are expressed in terms of two analytical functions of a complex variable, which are determined from the boundary conditions on the contour of inclusion. Calculations of nominal stresses on the contour joining the plane with inclusion are performed.