×

zbMATH — the first resource for mathematics

Mixed interface problems for anisotropic elastic bodies. (English) Zbl 0845.35125
Summary: Three-dimensional mathematical problems of the elasticity theory of anisotropic piecewise homogeneous bodies are discussed. A mixed type boundary contact problem is considered where, on one part of the interface, rigid contact conditions are given (jumps of the displacement and the stress vectors are known), while on the remaining part screen or crack type boundary conditions are imposed. The investigation is carried out by means of the potential method and the theory of pseudodifferential equations on manifolds with boundary.

MSC:
35Q72 Other PDE from mechanics (MSC2000)
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
35A15 Variational methods applied to PDEs
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
PDF BibTeX Cite
Full Text: DOI EMIS EuDML
References:
[1] V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and T. V. Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. (Translated from Russian)North-Holland series in applied mathematics and mechanics, v. 25,North-Holland Publishing Company, Amsterdam-New York-Oxford 1979; Russian original:Nauka, Moscow, 1976.
[2] L. Jentsch, Zur Existenz von regulären Lösungen der Elastostatik stückweise homogener Körper mit neuen Kontaktbedingungen an den Trennflächen zwischen zwei homogenen Teilen.Abh. Sächs. Akad. d. Wiss. Leipzig, Math.-Natur. Kl. 53(1977), H. 2, 1–45. · Zbl 0398.73100
[3] V. D. Kupradze, Contact problems of elasticity theory. (Russian)Differentsial’nye Uravneniya 16(2)(1980), 293–310.
[4] T. V. Burchuladze and T. G. Gegelia, Development of the potential methods in elasticity theory (Russian)Metsniereba, Tbilisi, 1985. · Zbl 0594.73026
[5] J. Jentsch and D. Natroshvili, Non-classical interface problems for piecewise homogeneous anisotropic elastic bodies.Math. Methods Appl. Sci. 18(1995), 27–49. · Zbl 0813.73058
[6] G. Fichera, Existence theorems in elasticity,Handb. d. Physik, Bd. VI/2,Springer-Verlag, Heidelberg, 1973.
[7] T. V. Buchukuri and T. G. Gegelia, Uniqueness theorems in the elasticity theory for infinite domains. (Russian)Differentisial’nye Uravneniya 25(9)(1988), 1556–1565.
[8] V. A. Kondratiev and O. A. Oleinik, Boundary value problems for the system of elasticity theory in infinite domains. (Russian)Uspekhi Mat. Nauk 43(1988), No. 5, 55–98.
[9] I. Sneddon, Fourier transforms.New York-Toronto-London, 1951. · Zbl 0038.26801
[10] H. Triebel, Interpolation theory, function spaces, differential operators.VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.
[11] H. Triebel, Theory of function spaces. Leipzig Birkhauser Verlag, Basel-Boston-Stuttgart, 1983. · Zbl 1235.46002
[12] J. L. Lions and E. Madgenes, Problèmes aux limites non homogènes et applications. Vol. 1.Dunod, Paris, 1968.
[13] M. Costabel and E. P. Stephan, An improved boundary element Galerkin method for three-dimensional crack problems.Integral Equations Operator Theory 10(1987), 467–504. · Zbl 0632.73091
[14] R. V. Duduchava, D. G. Natroshvili, and E. M. Shargorodsky, Boundary value problems of the mathematical theory of cracks.Proc. I. Vekua Inst. Appl. Math. 39(1990), 68–84. · Zbl 1016.35501
[15] D. G. Natroshvili, Investigation of boundary value and initial boundary value problems of the mathematical theory of elasticity and thermoelasticity for homogeneous anisotropic media using the potential method. (Russian)Dissertation for the Doctor of Science Degree, Tbilisi, 1984.
[16] R. Duduchava, On multidimensional singular integral operators, I, II.J. Oper. Theory 11(1984), 41–76, 199–214. · Zbl 0537.45015
[17] E. Shargorodsky, Boundary value problems for elliptic pseudodifferential operators: the halfspace case. (Russian)Proc. A. Razmadze Math. Inst. 99(1994), 44–80.
[18] E. Shargorodsky, Boundary value problems for elliptic pseudodifferential operators on manifolds. (Russian).Proc. A. Razmadze Math. Inst. 105(1994), 108–132.
[19] G. I. Eskin, Boundary value problems for elliptic pseudodifferential equations.Translations of Math. Monographs AMS,V. 52, Providence, RI, 1981. · Zbl 0458.35002
[20] D. Natroshvili, O. Chkadua, and E. Shargorodsky, Mixed boundary value problems of anisotropic elasticity. (Russian)Proc. I. Vekua Inst. Appl. Math. 39(1990), 133–181.
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.