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 language||English (US)|
|Title of host publication||49th US Rock Mechanics / Geomechanics Symposium 2015|
|Publisher||American Rock Mechanics Association (ARMA)|
|Number of pages||8|
|State||Published - 2015|
|Event||49th US Rock Mechanics / Geomechanics Symposium - San Francisco, United States|
Duration: Jun 29 2015 → Jul 1 2015
|Name||49th US Rock Mechanics / Geomechanics Symposium 2015|
|Other||49th US Rock Mechanics / Geomechanics Symposium|
|Period||6/29/15 → 7/1/15|
Bibliographical notePublisher Copyright:
Copyright 2015 ARMA, American Rock Mechanics Association.