Explicit expressions for three-dimensional boundary integrals in linear elasticity

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...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 235; no. 15; pp. 4480 - 4495
Main Author Nintcheu Fata, S.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 01.06.2011
Elsevier
Subjects
Analytic integration
Analytical integration
Boundaries
BOUNDARY ELEMENT METHOD
ELASTICITY
Elastostatics
Exact sciences and technology
Exact solutions
Galerkin methods
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
INTEGRAL EQUATIONS
Integrals
Mathematical analysis
Mathematics
Measure and integration
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
SHAPE
Singular integrals
SURFACE POTENTIAL
Triangles
45E99
Analytical integration
65R20
65N38
Singular integrals
Elastostatics
35J25
Boundary element method
Shape function
Integration
Three-dimensional calculations
Singular equation
Arbitrary space
Triangle
Surface
Numerical analysis
Linear equation
Linear elasticity
Applied mathematics
Integral equation
Galerkin method
Collocation method
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Summary: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 Lamé equation are included to validate the proposed formulae.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
DE-AC05-00OR22725
USDOE Office of Science (SC)
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.04.017