Scholarlink

Abstract <p>A three-dimensional mixed boundary-value problem of an isotropic homogeneous elastic half-space is considered. The boundary surface conditions employed are prescribed three displacements in the interior of a disc and zero traction components in the exterior of the disc. By expanding the stresses and displacements as Fourier series and applying the Hankel transform the problem is reduced to a system of three integral equations with the Weber–Schafheitlin kernels. The singularities of the solutions in the axisymmetric and non-axisymmetric cases are analyzed. The Wiener–Hopf method is used to map the system of integral equations into an order-3 vector Riemann–Hilbert problem. For two particular cases, a modified Westmann model problem and the Ressner–Sagoci problem, closed-form solutions are derived.</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

Integral Equations of the General Three-Dimensional Contact Problem of a Circular Stamp and a Half-Space

  • 期刊论文

  • 发表日期：

    2025年8月1日

查看全文
  • Yu. A. Antipov,
  • S. M. Mkhitaryan

摘要

Abstract

A three-dimensional mixed boundary-value problem of an isotropic homogeneous elastic half-space is considered. The boundary surface conditions employed are prescribed three displacements in the interior of a disc and zero traction components in the exterior of the disc. By expanding the stresses and displacements as Fourier series and applying the Hankel transform the problem is reduced to a system of three integral equations with the Weber–Schafheitlin kernels. The singularities of the solutions in the axisymmetric and non-axisymmetric cases are analyzed. The Wiener–Hopf method is used to map the system of integral equations into an order-3 vector Riemann–Hilbert problem. For two particular cases, a modified Westmann model problem and the Ressner–Sagoci problem, closed-form solutions are derived.