## Abstract

This analysis deals with the determination of the elastic stress and displacement fields in a quarter-space under arbitrarily applied surface loadings. The problem is formulated in terms of two coupled two-dimensional integral equations. The integral equations contain a logarithmic singularity with an unknown coefficient which varies along the edge of the quarter-space. A special solution for a half-space is developed which isolates the elastic field caused by this singularity and it is incorporated into the numerical-boundary-element solution of the integral equations. Once the equations are solved, the elastic field in the quarter-space can be found in a relatively simple fashion. The solution so developed may then be used to analyse contact problems for an elastic quarter-space. Contact is modelled with ellipsoidal distributions of pressure and traction to one or both faces. Numerical results are given for the internal elastic stress field and the von Mises yield parameter for a variety of contact loadings.

Original language | English |
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Pages (from-to) | 561-587 |

Number of pages | 27 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 43 |

Issue number | 4 |

DOIs | |

State | Published - Nov 1990 |

### Bibliographical note

Funding Information:Acknowledgements 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