Boundary element analysis of non-planar three-dimensional cracks using complex variables

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper reports new developments on the complex variables boundary element approach for solving three-dimensional problems of cracks in elastic media. These developments include implementation of higher order polynomial approximations and more efficient analytical techniques for evaluation of integrals. The approach employs planar triangular boundary elements and is based on the integral representations written in a local coordinate system of an element. In-plane components of the fields involved in the representations are separated and arranged in certain complex combinations. The Cauchy-Pompeiu formula is used to reduce the integrals over the element to those over its contour and evaluate the latter integrals analytically. The system of linear algebraic equations to find the unknown boundary displacement discontinuities is set up via collocation. Several illustrative numerical examples involving a single (penny-shaped) crack and multiple (semi-cylindrical) cracks are presented.

Original languageEnglish (US)
Title of host publication49th US Rock Mechanics / Geomechanics Symposium 2015
PublisherAmerican Rock Mechanics Association (ARMA)
Pages2548-2555
Number of pages8
ISBN (Electronic)9781510810518
StatePublished - Jan 1 2015
Event49th US Rock Mechanics / Geomechanics Symposium - San Francisco, United States
Duration: Jun 29 2015Jul 1 2015

Publication series

Name49th US Rock Mechanics / Geomechanics Symposium 2015
Volume4

Other

Other49th US Rock Mechanics / Geomechanics Symposium
CountryUnited States
CitySan Francisco
Period6/29/157/1/15

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