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<p>In this study, the discontinuous contact problem of functionally graded (FG) layers resting on a rigid plane and loaded with two rigid blocks is investigated. Body forces are taken into account, and it is assumed that all surfaces are frictionless and the discontinuity is between the layers. Stress and displacement expressions related to functionally graded layers are obtained with the help of Fourier integral transforms and Navier equations. In case of discontinuous contact between layers, when the boundary conditions are applied to the stress and displacement expressions of FG layers, the problem is reduced from three singular integral equations to an equation system where the contact stresses and the slope of the separation between the layers are unknown. The numerical solution of the integral equations is done by Gauss–Chebyshev integration method. As a result of the analytical solution, the contact stresses occurring between the functionally graded layers, the start and end points of the separation, and the opening shapes between the layers are obtained. In addition, the problem is also solved numerically using the finite element method (FEM) and the numerical results are compared with the analytical solution through tables and graphs.</p>

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Analytical and fem solution of the discontinuous contact problem between functionally graded layers

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月31日

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  • Ayhan Üstün,
  • İsa Çömez,
  • Talat Şükrü Özşahin

摘要

In this study, the discontinuous contact problem of functionally graded (FG) layers resting on a rigid plane and loaded with two rigid blocks is investigated. Body forces are taken into account, and it is assumed that all surfaces are frictionless and the discontinuity is between the layers. Stress and displacement expressions related to functionally graded layers are obtained with the help of Fourier integral transforms and Navier equations. In case of discontinuous contact between layers, when the boundary conditions are applied to the stress and displacement expressions of FG layers, the problem is reduced from three singular integral equations to an equation system where the contact stresses and the slope of the separation between the layers are unknown. The numerical solution of the integral equations is done by Gauss–Chebyshev integration method. As a result of the analytical solution, the contact stresses occurring between the functionally graded layers, the start and end points of the separation, and the opening shapes between the layers are obtained. In addition, the problem is also solved numerically using the finite element method (FEM) and the numerical results are compared with the analytical solution through tables and graphs.