Abstract
In this study, the boundary element equations are obtained from the influence functions of a displacement discontinuity in an anisotropic elastic medium. For this purpose, Kelvin fundamental solutions for anisotropic media on infinite and semi-infinite planes are used to form dipoles from singular loads. Various combinations of these dipoles are used to obtain the influence functions of the displacement discontinuity. Boundary element equations are then derived analytically by the integration of these influence functions on a constant element which results in a linear system for unknown displacement discontinuities. The boundary integrals are calculated in closed form over constant elements. The obtained formulation is applied to a number of classical engineering problems.
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References
Beer G, Watson JO (1992) Introduction to Finite and Boundary Element Methods for Engineers, Jhon Wiley & Sons, West Suessex, England
Green AE, Zerna W (1968) Theoritical Elasticity, 2nd Edn, Clarendon Press, Oxford
Lekhnitskii SG (1963) Theory of Elasticity of An Anisotropic Elastic Body, Holden-day, San Franciso
Xiao B, Carter JP (1993) Boundary Element Analysis of Anisotropic Rock Masses. Eng Analy Boundary Elements 11:293–303
Carter JP, Xiao B (1994) A 2D Coupled FE and BE Scheme To Simulate The Elastic Behaviour of Join ted Rock. Int J For Num and Analytical Methods in Geomech 18:49–71
Crouch SL, Starfield AM (1983) Boundary Element Methods in Solid Mechanics. George Allen & Unwin, London
Crouch SL (1976) Analysis of Stresses and Displacements Around Underground Excavations. Geomechanics Report to The National Scince Foundation. Minneapolis: University of Minnesota
Chan HCM (1986) Automatic Two-Dimensional Multi-Fracture Propagation Modelling of Brittle Solids With Particular Application to Rock, Sc. D. Dissertation, Dept Civil Eng MIT
Schclar NA (1994) Anisotropic Analysis Using Boundary Elements. Computational Mechanics Publications: Southamton, Boston
Pan E, Chen C.S, Amedei B (1997) A BEM Formulation for Anisotropic Half-Plane Problems. Eng Anal Boundary Elements 20:185–195
Gray LJ, Paulino GH (1997) Symmetric Galerkin Boundary Integral Fracture Analysis For Plane Orthotropic Elasticity. Comput Mech 20:26–33
Sladek V, Sladek J (1998) Singular Integrals in Boundary Element Methods. Computational Mechanics Publications: Southamton, Boston
Kimençe B. (1997) Displacement Discontiniuty Method in Anisotropic Bodies, Phd Thesis, Department of Civil Engineering, Istanbul Technical University, Istanbul
Brady BHG, Bray JW (1978) The Boundary Element Method for Elastic Analysis of Tabular Orebody Extraction, Assuming Complete Plane Strain. Int J Rock Mech Min Sci Geomech Abstr 15:29–37
Brady BHG, Bray JW (1978) The Boundary Element Method for Determining Stresses and Displacements Around Long Openings in a Triaxial Stress Field. Int J Rock Mech Min Sci Geomech Abstr 15:21–28
Dumir PC, Mehta AK (1987) BE Solution for Elastic Orthotropic Half-Plane Problems. Comput Struct 26:431–438
Rizzo FJ, Shippy DJ (1970) A Method for Stress Determination in Plane Anisotropic Body. J Comp Mat 4:36–61
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Kimençe, B., Ergüven, M.E. Influence functions of the displacement discontinuity method for anisotropic bodies. Comput Mech 36, 484–494 (2005). https://doi.org/10.1007/s00466-005-0683-4
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DOI: https://doi.org/10.1007/s00466-005-0683-4