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The radial integration method for evaluation of domain integrals with boundary-only discretization. (English) Zbl 1130.74461
Summary: A simple and robust method, called the radial integration method, is presented for transforming domain integrals into equivalent boundary integrals. Any two- or three-dimensional domain integral can be evaluated in a unified way without the need to discretize the domain into internal cells. Domain integrals consisting of known functions can be directly and accurately transformed to the boundary, while for domain integrals including unknown variables, the transformation is accomplished by approximating these variables using radial basis functions. In the proposed method, weak singularities involved in the domain integrals are also explicitly transformed to the boundary integrals, so no singularities exist at internal points. Some analytical and numerical examples are presented to verify the validity of this method.

74S15 Boundary element methods applied to problems in solid mechanics
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[1] Aliabadi, M.H.; Martin, D., Boundary element hyper-singular formulation for elastoplastic contact problems, Int J numer methods engng, 48, 995-1014, (2000) · Zbl 0974.74072
[2] Banerjee, P.K.; Wilson, R.B.; Miller, N., Advanced elastic and inelastic three-dimensional analysis of gas turbine engine structures by BEM, Int J numer methods engng, 26, 393-411, (1988) · Zbl 0629.73073
[3] Becker, A.A., The boundary element method in engineering, (1992), McGraw-Hill London
[4] Brebbia, C.A., The boundary element method for engineers, (1978), Pentech Press London · Zbl 0414.65060
[5] Cheng, A.H.D.; Young, D.L.; Tsai, C.C., Solution of Poisson’s equation by iterative DRBEM using compactly supported, positive definite radial basis function, Engng anal boundary elements, 24, 549-557, (2000) · Zbl 0966.65089
[6] Cheng, A.H.D.; Chen, C.S.; Golberg, M.A.; Rashed, Y.F., BEM for theomoelasticity and elasticity with body force—a revisit, Engng anal boundary elements, 25, 377-387, (2001) · Zbl 1014.74075
[7] Cruse TA. Boundary integral equation method for three-dimensional elastic fracture mechanics. AFOSR-TR-75-0813, ADA 011660, Pratt and Whitney Aircraft, Connecticut, 1975.
[8] Danson, D.J., A boundary element formulation for problems in linear isotropic elasticity with body forces, (), 105-122 · Zbl 0527.73085
[9] Gao, X.W.; Davies, T.G., 3D multi-region BEM with corners and edges, Int J solids struct, 37, 1549-1560, (2000) · Zbl 0969.74072
[10] Gao, X.W.; Davies, T.G., An effective boundary element algorithm for 2D and 3D elastoplastic problems, Int J solids struct, 37, 4987-5008, (2000) · Zbl 0970.74077
[11] Gao, X.W.; Davies, T.G., Boundary element programming in mechanics, (2002), Cambridge University Press Cambridge
[12] Gao XW. Boundary only integral equations in boundary element analysis. Proceedings of the International Conference on Boundary Element Techniques, 16-18 July, 2001, Rutgers University, NJ, USA, p. 39-46.
[13] Golberg, M.A.; Chen, C.S.; Bowman, H., Some recent results and proposals for the use of radial basis functions in the BEM, Engng anal boundary elements, 23, 285-296, (1999) · Zbl 0948.65132
[14] Henry, D.P.; Pape, D.A.; Banerjee, P.K., New axisymmetric BEM formulation for body forces using particular integrals, ASCE J engng mech div, 113, 671-688, (1987)
[15] Jaswon, M., Integral equation methods in potential theory. I, Proc R soc ser A, 275, 23-32, (1963) · Zbl 0112.33103
[16] Kane, J.H., Boundary element analysis in engineering continuum mechanics, (1994), Prentice-Hall Englewood Cliffs, NJ
[17] Ma, H.; Kamiya, N.; Xu, S.Q., Complete polynomial expansion of domain variables at boundary for two-dimensional elasto-plastic problems, Engng anal boundary elements, 21, 271-275, (1998) · Zbl 0969.74606
[18] Mukherjee, S., Boundary element methods in creep and fracture, (1982), Applied Science Publishers London · Zbl 0534.73070
[19] Nardini, D.; Brebbia, C.A., A new approach for free vibration analysis using boundary elements, (), 312-326 · Zbl 0541.73104
[20] Neves, A.C.; Brebbia, C.A., The multiple reciprocity boundary element method in elasticity: a new approach for transforming domain integral to the boundary, Int J numer methods engng, 31, 709-727, (1991) · Zbl 0825.73800
[21] Nowak, A.J.; Brebbia, C.A., The multiple-reciprocity method. A new approach for transforming B.E.M. domain integrals to the boundary, Engng anal boundary elements, 6, 164-168, (1989)
[22] Ochiai, Y.; Kobayashi, T., Initial stress formulation for elastoplastic analysis by improved multiple-reciprocity boundary element method, Engng anal boundary elements, 23, 167-173, (1999) · Zbl 0940.74076
[23] Partridge, P.W.; Brebbia, C.A.; Wrobel, L.C., The dual reciprocity boundary element method, (1992), Computational Mechanics Publications Southampton · Zbl 0758.65071
[24] Partridge, P.W., Towards criteria for selecting approximation functions in the dual reciprocity method, Engng anal boundary elements, 24, 519-529, (2000) · Zbl 0968.65097
[25] Power, H.; Mingo, R., The DRM subdomain decomposition approach to solve the two-dimensional navier – stokes system of equations, Engng anal boundary elements, 24, 107-119, (2000) · Zbl 0981.76061
[26] Rizzo, F.J., An integral equation approach to boundary value problems of classical elastostatics, Q J appl math, 25, 83-95, (1967) · Zbl 0158.43406
[27] Rizzo, F.J.; Shippy, D.J., An advanced boundary integral equation method for three-dimensional thermoelasticity, Int J numer methods engng, 11, 1753-1768, (1977) · Zbl 0387.73007
[28] Takhteyev, V.; Brebbia, C.A., Analytical integrations in boundary elements, Engng anal boundary elements, 7, 95-100, (1990)
[29] Tan, C.L., Boundary integral equation stress analysis of a rotating disc with a corner crack, J strain anal, 18, 231-237, (1983)
[30] Wen, P.H.; Aliabadi, M.H.; Rooke, D.P., A new method for transformation of domain integrals to boundary integrals in boundary element method, Commun numer methods engng, 14, 1055-1065, (1998) · Zbl 0940.65140
[31] Zhu, S.; Zhang, Y., Improvement on dual reciprocity boundary element method for equations with convective terms, Commun numer methods engng, 10, 361-371, (1994) · Zbl 0807.65119
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