Complex variables BEM modeling of three-dimensional crack problems

D. V. Nikolskiy, S. G. Mogilevskaya

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

Abstract

The paper presents further developments of the boundary element technique for solving three-dimensional problems of piecewise homogeneous elastic media containing multiple cracks of arbitrary non-planar shapes (previous results were reported in [1, 2]). In the developed technique, the elastic fields are represented by integral identities. Triangular elements are used to discretize the boundaries and polynomial (linear and quadratic) approximations of the unknown variables are adopted. In-plane components of the fields and geometrical parameters are arranged in various complex-valued combinations to simplify the integration. No singular integrals are involved since the limit, as the field point approaches the boundary, is taken after the integration. Analytical integration over each element is reduced to that over the contour of the element via application of Cauchy- Pompeiu representation [3]. The collocation method is used to set up the system of linear algebraic equations to find the boundary unknowns. Geoengineering applications of the method are discussed.

Original languageEnglish (US)
Title of host publication48th US Rock Mechanics / Geomechanics Symposium 2014
EditorsRay Sterling, Emmanuel Detournay, Will Pettitt, Joseph F. Labuz, Lee Petersen
PublisherAmerican Rock Mechanics Association (ARMA)
Pages457-461
Number of pages5
ISBN (Electronic)9781634395236
StatePublished - Jan 1 2014
Event48th US Rock Mechanics / Geomechanics Symposium 2014: Rock Mechanics Across Length and Time Scales - Minneapolis, United States
Duration: Jun 1 2014Jun 4 2014

Publication series

Name48th US Rock Mechanics / Geomechanics Symposium 2014
Volume1

Other

Other48th US Rock Mechanics / Geomechanics Symposium 2014: Rock Mechanics Across Length and Time Scales
CountryUnited States
CityMinneapolis
Period6/1/146/4/14

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  • Cite this

    Nikolskiy, D. V., & Mogilevskaya, S. G. (2014). Complex variables BEM modeling of three-dimensional crack problems. In R. Sterling, E. Detournay, W. Pettitt, J. F. Labuz, & L. Petersen (Eds.), 48th US Rock Mechanics / Geomechanics Symposium 2014 (pp. 457-461). (48th US Rock Mechanics / Geomechanics Symposium 2014; Vol. 1). American Rock Mechanics Association (ARMA).