## Abstract

A new method, based on point set theory and properties of orthogonal functions, is developed for determining exact solutions to three-dimensional crack and contact problems with complicated geometric configurations (e.g. a star-convex domain) in an infinite linear elastic medium. The governing equation is a two-dimensional Fredholm integral equation of the first kind. The central idea of this method is the chain extension of an exact solution from a regular subdomain to an irregular entire domain. Examples are given illustrating how this solution procedure can be used to obtain exact closed form solutions for a general Hertz contact problem and various crack problems in an inhomogeneous isotropic medium with an elastic modulus which is a power function of depth.

Original language | English |
---|---|

Pages (from-to) | 215-239 |

Number of pages | 25 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 42 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1994 |

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering