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Integral characteristics of elastic inclusions and cavities in the two-dimensional theory of elasticity

Published online by Cambridge University Press:  16 July 2009

A. B. Movchan
A. B. Movchan
Affiliation:
School of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
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Abstract

Integral characteristics, such as elastic polarization matrices of elastic inclusions and cavities, are described. The matrix of elastic polarization of a finite cavity is constructed in the case of the two-dimensional Lamé operator under the assumption that the geometry of the domain occupied by the cavity is defined by a conformal mapping from the unit disk. Examples and applications of these integral characteristics in the theory of cracks are considered.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 1 , March 1992 , pp. 21 - 30
Copyright
Copyright © Cambridge University Press 1992

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References

Kondratiev, V. A. 1987 Boundary value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16, 227–313.Google Scholar
Maz'ya, V. G., Nazarov, S. A. & Plamenevskii, B. A. 1984 The asymptotic expansions of eigenvalues of the boundary value problems for the Laplace operator in domains with small holes. lzvestija Akad. Nauk SSSR: Mat. 48 (2), 346–371.Google Scholar
Movchan, A. B. & Nazarov, S. A. 1985 The asymptotic behaviour of a stress-strain state near the three-dimensional sharp inclusion. Mekhanika Compozit. Materialov. 5, 792–800.Google Scholar
Movchan, A. B., Nazarov, S. A. & Polyakova, O. R. 1991 The quasistatic growth of a semi- infinite crack in a plane containing small defects. C. R. Acad. Sc. Paris.Google Scholar
Muskhelishvili, N. I. 1927 Sur I'intégration approchée de I'équation biharmonique. Comptes Rendus. 185, 1184.Google Scholar
Muskhelishvili, N. I. 1953 Some Basic Problems of Mathematical Theory of Elasticity. Groningen: Noordhoff.Google Scholar
Pazy, A. 1967 Asymptotic expansions of solutions of ordinary differential equations in Hilbert space. Arch. Rational Mech. & Analysis 24, 193–218.Google Scholar
Pólya, G. & Szegö, G. 1951 Isoperimetric inequalities in mathematical physics. Ann. Math. Studies, No. 27. Princeton, NJ: Princeton University Press.Google Scholar
Romalis, N. B. & Tamuzh, V. P. 1984 A macrocrack propagation in a body with microcracks. Mekhanika Kompoziinykh Materialou (USSR). 1, 42–51.Google Scholar
Romalis, N. B. & Tamuzh, V. P. 1985 Propagation of cracks in a porous material. Mekhanika Kompozitnykh Materialov (USSR). 1, 146–149.Google Scholar
Rubinstein, A. A. 1986 Macrocrack-microcrack interaction. J. Applied Mech. 53, 505–510.CrossRefGoogle Scholar
Sedov, L. I. 1972 A Course in Continuum Mechanics. Vol. 4: Elastic and Plastic Solids and the Formation of Cracks. Groningen: Wolter-Noordhoff.Google Scholar
Sherman, D. I. 1935 On a method of solution of the static plane problem of the theory of elasticity for multiply connected regions. Trudy Seismologiczesk. Inst. A.N.SSSR. 54.Google Scholar
Zorin, I. S., Movchan, A. B. & Nazarov, S. A. 1988 The use of the elastic polarization tensor in problems of the mechanics of cracks. Izvestija Akad. Nauk SSSR: Mekhanika TV. Tela. 6, 128–134.Google Scholar
Zorin, I. S., Babich, V. M., Ivanov, M. I., Movchan, A. B. & Nazarov, S. A. 1989 Integral characteristics in elasticity problems. Preprint LOMI. P-6–89. Leningrad.Google Scholar