×

zbMATH — the first resource for mathematics

The method of fundamental solutions for layered elastic materials. (English) Zbl 1008.74081
Summary: We investigate the application of the method of fundamental solutions to two-dimensional elasticity problems for isotropic and anisotropic single materials and bimaterials. A domain decomposition technique is employed in the bimaterial case where the interface continuity conditions are approximated in the same manner as boundary conditions. The method is tested on several test problems, and its relative merits and disadvantages are discussed.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74E30 Composite and mixture properties
74E10 Anisotropy in solid mechanics
Software:
HYBRJ; minpack
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Balakrishnan, K.; Ramachandran, P.A., A particular solution Trefftz method for non-linear Poisson problems in heat and mass transfer, J comput phys, 150, 239-267, (1999) · Zbl 0926.65121
[2] Berger, J.R.; Karageorghis, A., The method of fundamental solutions for heat conduction in layered materials, Int J numer methods engng, 45, 1681-1694, (1999) · Zbl 0972.80014
[3] Berger, J.R.; Tewary, V.K., Boundary integral equation formulation for interface cracks in anisotropic bimaterials, Comput mech, 20, 261-266, (1997) · Zbl 0898.73068
[4] Burgess, G.; Mahajerin, E., A comparison of the boundary element and superposition methods, Comput struct, 19, 697-705, (1984) · Zbl 0552.73075
[5] Fairweather, G.; Karageorghis, A., The method of fundamental solutions for elliptic boundary value problems, Adv comput math, 9, 69-95, (1998) · Zbl 0922.65074
[6] Golberg, M.A.; Chen, C.S., The method of fundamental solutions for potential, Helmholtz and diffusion problems, (), 105-176, (chap. 4) · Zbl 0945.65130
[7] Golberg, M.A.; Chen, C.S., Discrete projection methods for integral equations, (1996), Computational Mechanics Publications Southampton
[8] Kitagawa, T., On the numerical stability of the method of fundamental solution applied to the Dirichlet problem, Jpn J appl math, 5, 123-133, (1988) · Zbl 0644.65060
[9] Garbow BS, Hillstrom KE, More JJ. MINPACK Project, Argonne National Laboratory, 1980.
[10] Mahajerin, E., An extension of the superposition method for plane anisotropic elastic bodies, Comput struct, 21, 953-958, (1985) · Zbl 0587.73123
[11] Patterson, C.; Sheikh, M.A., On the use of fundamental solutions in Trefftz method for porential and elasticity problems, (), 43-54
[12] Poullikkas, A.; Karageorghis, A.; Georgiou, G., Methods of fundamental solutions for harmonic and biharmonic boundary value problems, Comput mech, 21, 416-423, (1998) · Zbl 0913.65104
[13] Raamachandran, J.; Rajamohan, C., Analysis of composite plates using charge simulation method, Eng. anal. bndry. elem., 18, 131-135, (1996)
[14] Redekop, D., Fundamental solutions for the collocation method in planar elastostatics, App. math. mod., 6, 390-393, (1982) · Zbl 0492.73095
[15] Redekop, D.; Cheung, R.S.W., Fundamental solutions for the collocation method in three-dimensional elastostatics, Comput struct, 26, 703-707, (1987) · Zbl 0612.73091
[16] Redekop, D.; Thompson, J.C., Use of fundamental solutions in the collocation method in axisymmetric elastostatics, Comput struct, 17, 485-490, (1983)
[17] Stroh, A.S., Dislocations and cracks in anisotropic elasticity, Philos mag, 3, 625-646, (1958) · Zbl 0080.23505
[18] Tewary, V.K.; Wagoner, R.H.; Hirth, J.P., Elastic Green’s function for a composite solid with a planar interface, J mater res, 4, 113-123, (1989)
[19] Ting, T.C.T., Anisotropic elasticity, (1996), Oxford Science Publications Oxford
[20] Zwiers, R.I.; Ting, T.C.T.; Spilker, R.L., On the logarithmic singularity of free-edge stress in laminated composites under uniform extension, J appl mec, 49, 561-569, (1982) · Zbl 0522.73056
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.