Analytical integrations in 3D BEM for elliptic problems: Evaluation and implementation

International Journal for Numerical Methods in Engineering

Volumn 84, Issue 5, 2010, Pages 505-542

  Salvadori, A ^a  

^a UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Analytical integrations; Boundary elements; Finite part of Hadamard; Integral equations

Indexed keywords

ANALYTICAL INTEGRATION; ARBITRARY DEGREE; BOUNDARY ELEMENTS; CLOSED FORM; DISCRETIZATIONS; DOUBLE LAYERS; ELLIPTIC BOUNDARY VALUE PROBLEM; ELLIPTIC PROBLEM; FINITE PART; HADAMARD; HOMOGENEOUS MATERIALS; HYPERSINGULAR; LEBESGUE INTEGRAL; LINEAR PARTIAL DIFFERENTIAL EQUATIONS; LOCAL COORDINATE SYSTEM; NUMERICAL APPROXIMATIONS; SHAPE FUNCTIONS; SINGLE LAYER; SINGULAR INTEGRAL; YALE UNIVERSITY;

BOUNDARY ELEMENT METHOD; DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; NUMERICAL METHODS;

THREE DIMENSIONAL;

EID: 77955467120     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2906     Document Type: Article

References (44)

1. Partridge PW, Wrobel LC. An inverse geometry problem for the localisation of skin tumors by thermal analysis. Engineering Analysis with Boundary Elements 2007; 31:803-811.
2. Chandra A, Mukherjee S. Boundary Element Methods in Manufacturing. Oxford Engineering Science Series. Oxford University Press: Oxford, 1997.
3. Benallal A, Fudoli CA, Venturini WS. An implicit BEM formulation for gradient plasticity and localization phenomena. International Journal for Numerical Methods in Engineering 2001; 53(8):1853-1869.
4. Liu YJ, Chen XL. Continuum models of carbon nanotube-based composites using the BEM. Electronic Journal of Boundary Elements 2003; 1(2):316-335.
5. El-Awady JA, Bulent Biner S, Ghoniem NM. A self-consistent boundary element, parametric dislocation dynamics formulation of plastic flow in finite volumes. Journal of the Mechanics and Physics of Solids 2008; 56:2019-2035.
6. Linkov AM, Mogilevskaya SG. Finite-part integrals in problems of three-dimensional cracks. Notes Academy of Science USSR 1986; 50:841-850. In Russian; translated into English in Applied Mathematics and Mechanics.
7. Sirtori S, Maier G, Novati G, Miccoli S. A Galerkin symmetric boundary-element method in elasticity: formulation and implementation. International Journal for Numerical Methods in Engineering 1992; 35:255-282.
8. Hong KH, Chen JT. Derivations of integral equations of elasticity. Journal of Engineering Mechanics (ASCE) 1988; 114:1028-10446.
9. Bonnet M, Maier G, Polizzotto C. Symmetric Galerkin boundary element method. Applied Mechanical Review 1998; 51:669-704.
10. Rjasanow S, Steinbach O. The Fast Solution of Boundary Integral Equations. Springer: Berlin, 2007.
11. Aliabadi MH. The Boundary Element Method, Volume 2-Application to Solids and Structures. Wiley: New York, 2002.
12. Maier G, Miccoli S, Novati G, Perego U. Symmetric boundary element method in plasticity and gradient plasticity. Computational Mechanics 1995; 17:115-129.
13. Salvadori A. Hypersingular boundary integral equations and the approximation of the stress tensor. International Journal for Numerical Methods in Engineering 2007; 72:722-743.
14. Young A. A single domain BEM for 3d elastostatic crack analysis using continuous elements. International Journal for Numerical Methods in Engineering 1996; 39:1265-1293.
15. Mantič V. On computing boundary limiting values of boundary integrals with strongly singular and hypersingular kernels in 3d bem for elastostatics. Engineering Analysis with Boundary Elements 1994; 13:115-134.
16. Mantič V. A new formula for the c-matrix in the Somigliana identity. Journal of Elasticity 1993; 33:191-201.
17. Hartmann F. The somigliana identity on a piecewise smooth surface. Journal of Elasticity 1981; 11:403-423.
18. Guiggiani M. Hypersingular boundary integral equations have an additional free term. Computational Mechanics 1995; 16:245-248.
19. Mantič V, Paris F. Existence evaluation of the two free terms in the hypersingular boundary integral equation of potential theory. Engineering Analysis with Boundary Elements 1995; 16:253-260.
20. Vodička R, Mantič V, Paris F. On the removal of the non-uniqueness in the solution of elastostatic problems by symmetric Galerkin BEM. International Journal for Numerical Methods in Engineering 2006; 66:1884-1912.
21. Cruse TA. Boundary Element Analysis in Computational Fracture Mechanics. Kluwer: Dordrecht, The Netherlands, 1988.
22. Aliabadi MH, Rooke DP. Numerical Fracture Mechanics. Kluwer: Dordrecht, 1991.
23. Cruse TA, Rizzo FJ (eds). Computational Applications in Applied Mechanics. ASME: New York, 1975.
24. Ligget JA, Liu PLF. The Boundary Integral Equation Method for Porous Media Flow. Allen and Unwin: London, 1983.
25. Portela A, Aliabadi MH, Rooke DP. The dual boundary element method: effective implementations for crack problems. International Journal for Numerical Methods in Engineering 1992; 33:1269-1287.
26. Carini A, Salvadori A. Analytical integrations in 3D BEM: preliminaries. Computational Mechanics 2002; 28(3-4):177-185.
27. Hadamard J. Lectures on Cauchy's Problem in Linear Partial Differential Equations. Yale University Press: New Haven, CT, U.S.A., 1923.
28. Schwab C, Wendland WL. Kernel properties and representations of boundary integral operators. Mathematische Nachrichten 1992; 156:187-218.
29. Martin P, Rizzo F. Hypersingular integrals: how smooth must the density be? International Journal for Numerical Methods in Engineering 1996; 39:687-704.
30. Zemanian AH. Distribution Theory and Transform Analysis. Dover: New York, 1987.
31. Guiggiani M. Formulation and numerical treatment of boundary integral equations with hypersingular kernels. In Singular Integrals in Boundary Element Methods, Sladek V, Sladek J (eds). Advances in Boundary Elements Series. Computational Mechanics Publications: Southampton, Boston, 1998; 85-124.
32. Gray LJ. Evaluation of singular and hypersingular Galerkin boundary integrals: direct limits and symbolic computation. In Advances in Boundary Elements, Sladek V, Sladek J (eds). Computational Mechanics Publisher: Southampton, Boston, 1998.
33. Gray LJ, Glaeser J, Kaplan T. Direct evaluation of hypersingular Galerkin surface integrals. SIAM Journal on Scientific Computing 2004; 25:1534-1556.
34. Gray LJ, Salvadori A, Phan AV, Mantič V. Direct evaluation of hypersingular Galerkin surface integrals. ii. Electronic Journal of Boundary Elements 2006; 4(3):105-130.
35. Salvadori A. Analytical integrations in 2D BEM elasticity. International Journal for Numerical Methods in Engineering 2002; 53(7):1695-1719.
36. Salvadori A. Analytical integrations of hypersingular kernel in 3D BEM problems. Computer Methods in Applied Mechanics and Engineering 2001; 190:3957-3975.
37. Nintcheu Fata S. Explicit expressions for 3d boundary integrals in potential theory. International Journal for Numerical Methods in Engineering 2009; 78(1):32-47.
38. Carini A, Diligenti M, Salvadori A. Implementation of a symmetric boundary element method in transient heat conduction with semi-analytical integrations. International Journal for Numerical Methods in Engineering 1999; 46:1819-1843.
39. Chernov A. Hp quadratures for integral operators on simplices in arbitrary dimension: algorithmic aspects. Advances in Boundary Integral Equations and Related Topics-A Conference in Honor of G.C. Hsiao's 75th Birthday, University of Delaware Network, Delaware, U.S.A., 2009.
40. Salvadori A. A symmetric boundary integral formulation for cohesive interface problems. Computational Mechanics 2003; 32(4-6):381-391.
41. Temponi A, Salvadori A, Bosco E, Carini A, Alsalaet J. Analytical integrations in 3d BEM elastodynamics. In Advances in Boundary Element Techniques IX, Aliabadi MH, Abascal R (eds). EC Ltd.: U.K., 2008. ISBN: 978-0-9547783-5-4.
42. Salvadori A, Gray LJ. Analytical integrations and SIFs computation in 2D fracture mechanics. International Journal for Numerical Methods in Engineering 2007; 70:445-495.
43. Gray LJ, Paulino GH. Crack tip interpolation, revisited. SIAM Journal on Applied Mathematics 1998; 58:428-455.
44. Galvin P, Dominguez J. Analysis of ground motion due to moving surface loads induced by high-speed trains. Engineering Analysis with Boundary Elements 2007; 31:931-941.