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Application of the method of multipole expansions in the 3D‐elasticity problem for a medium with ordered system of spherical pores
Author(s) -
Goldstein R.V.,
Shushpannikov P.S.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800197
Subject(s) - multipole expansion , isotropy , elasticity (physics) , bounded function , mathematics , mathematical analysis , void (composites) , hydrostatic pressure , materials science , physics , mechanics , composite material , quantum mechanics
A problem of determination of the stress‐strain state in an elastic isotropic 3D‐space containing an ordered system of spherical voids in a bounded region subjected to hydrostatic pressure is considered. A method based on expansion of unknown solution in terms of multipoles located at pores centers is proposed for solving the problem. Expansion coefficients (multipoles intensities) are found by using an alternation method which implies successive satisfying the boundary conditions for each void of the system. Considered examples of application of the proposed method for structures with various number of pores show that the method gives a good approximation to the solution of the problem.