## Abstract

An integral-equation formulation is used to study the stress analysis and related contact problems for an elastic quarter-plane. The quarter-plane under conditions of general loading may be separated into two loading situations: one with normal stress and the other with shear. The same pair of coupled integral equations governs each case, and a formal solution is obtained using the Mellin transform. Fundamental solutions are determined for a point normal and shear load. An integral equation for the related contact problem is developed which contains a generalized Cauchy kernel; its effect on the field singularity at the corner is investigated. The magnitude of the stress at the corner for the case of a rigid contact extending to the corner is found in closed form.

Original language | English |
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Pages (from-to) | 364-383 |

Number of pages | 20 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 42 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1989 |

### Bibliographical note

Funding Information:The work reported in this paper is under the auspices of the Center for Engineering Tribology jointly supported by the National Science Foundation under grant ISI-8425521 and the industrial consortium at Northwestern University. Support under NSF grant EAR-8707392 is also gratefully acknowledged.

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics