The Pólya-Szegö matrices in asymptotic models of dilute composites

European Journal of Applied Mathematics

Volumn 8, Issue 6, 1997, Pages 595-621

  Movchan, A B ^a   Serkov, S K ^a  

^a UNIVERSITY OF BATH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0642302515     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S095679259700315X     Document Type: Article

References (18)

1. PÓLYA, G. & SZEGÖ, G. (1951) Isoperimetric Inequalities in Mathematical Physics. Princeton University Press.
2. OLVER, P. J. (1988) Canonical elastic moduli. J. Elasticity, 19, 189-212.
3. MILTON, G. W. & MOVCHAN, A. B. (1995) A correspondence between plane elasticity and the two-dimensional real and complex dielectric equations in anisotropic media. Proc. Royal Soc. Lond. A, 450, 293-317.
4. TAYLOR, G. I. (1928) The energy of a body moving in an infinite fluid, with an application to airships. Proc. Royal Soc. Lond. A, 120, 13-21.
5. MOVCHAN, A. B. (1992) Integral characteristics of elastic inclusions and cavities in the two-dimensional theory of elasticity. Euro. J. Appl. Math. 3, 21-30.
6. MOVCHAN, A. B. & SERKOV, S. K. (1992) Elastic polarization matrices for polygonal domains. Mech. Solids, 26 (3), 63-68.
7. MOVCHAN, A. B. & MOVCHAN, N. V. (1995) Mathematical Modelling of Solids with Nonregular Boundaries. CRC Press.
8. ZORIN, I. S., MOVCHAN, A. B. & NAZAROV, S. A. (1988) The use of the elastic polarization tensor in problems of crack mechanics. USSR Izvestiya. Mechanics of Solids, 26 (6), 128-134 (in Russian).
9. MILNE-THOMSON, L. M. (1962) Antiplane Elastic System. Springer-Verlag.
10. MUSKHELISHVILI, N. I. (1953) Some Basic Problems of the Mathematical Theory of Elasticity. Noorhoff, Groningen.
11. HETHERINGTON, J. H. & THORPE, M. F. (1992) The conductivity of a sheet containing inclusions with sharp corners. Proc. Royal Soc. Lond. A, 438, 591-604.
12. JASIUK, I. (1995) Cavities vis-a-vis rigid inclusions: elastic moduli of materials with polygonal inclusions. Int. J. Solid Structures, 32, 407-422.
13. JASIUK, I., CHEN, J. & THORPE, M. F. (1994) Elastic moduli of two dimensional materials with polygonal and elliptical holes. Micromechanics of random media. Applied Mechanics Reviews, 47 (1), part 2, 18-28.
14. THORPE, M. F. & JASIUK, I. (1992) New results in the theory of elasticity for two-dimensional composites. Proc. Royal Soc. Lond. A, 438, 531-544.
15. BAKHVALOV, N. S. & PANASENKO, G. P. (1989) Homogenization: Averaging processes in periodic media. Kluwer.
16. OLEINIK, O. A., PANASENKO, G. P. & YOSIFIAN, G. A. (1983) Homogenization and asymptotic expansion for solution of the elasticity system with rapidly oscillating periodic coefficients. Applicable Analysis, 15, 15-32.
17. MOVCHAN, A. B. & SERKOV, S. K. (1996) The Pólya-Szegö tensors in mathematical modelling of composite media. 19th ICTAM-96, Kyoto, Japan.
18. BIGONI, D., MOVCHAN, A., ESPOSITO, L., SERKOV, S. & VALENTINI, M. (1996) Crack propagation in brittle, elastic solid with defects. Atti del XII Convegno Nazionale del Gruppo Italiano Frattura, Parma, pp. 59-67.