Explicit expressions for three-dimensional boundary integrals in linear elasticity

Journal Article · Sat Jan 01 04:00:00 EST 2011 · Journal of Computational and Applied Mathematics

DOI:https://doi.org/10.1016/j.cam.2011.04.017· OSTI ID:1023297

Nintcheu Fata, Sylvain ^[1]

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1. ORNL

On employing isoparametric, piecewise linear shape functions over a flat triangle, exact formulae are derived for all surface potentials involved in the numerical treatment of three-dimensional singular and hyper-singular boundary integral equations in linear elasticity. These formulae are valid for an arbitrary source point in space and are represented as analytical expressions along the edges of the integration triangle. They can be employed to solve integral equations defined on triangulated surfaces via a collocation method or may be utilized as analytical expressions for the inner integrals in a Galerkin technique. A numerical example involving a unit triangle and a source point located at various distances above it, as well as sample problems solved by a collocation boundary element method for the Lame equation are included to validate the proposed formulae.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: SC USDOE - Office of Science (SC)
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1023297
• Journal Information: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: 15 Vol. 235; ISSN 0377-0427
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
Analytic integration
BOUNDARY ELEMENT METHOD
ELASTICITY
INTEGRAL EQUATIONS
SHAPE
SURFACE POTENTIAL
boundary element method
elastostatics
singular integrals