메뉴 건너뛰기




Volumn 17, Issue 1, 2005, Pages 19-69

Steady state oscillation problems in the theory of elasticity for chiral materials

Author keywords

Boundary value problems; Elastic chiral materials; Elasticity theory; Potential theory; Pseudodifferential equations; Radiation conditions; Steady state oscillations

Indexed keywords


EID: 33845900160     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181075310     Document Type: Article
Times cited : (23)

References (46)
  • 1
    • 15944424512 scopus 로고
    • Continuum theory of asymmetric elasticity
    • (in Russian); Soviet Physics Solid State 5 (1964), 1892 1899 (in English).
    • E.L. Aero and E.V. Kuvshinski, Continuum theory of asymmetric elasticity. Microrotation effect, Solid State Physics 5 (1963), 2591 2598 (in Russian); Soviet Physics Solid State 5 (1964), 1892 1899 (in English).
    • (1963) Microrotation effect, Solid State Physics , vol.5 , pp. 2591-2598
    • Aero, E.L.1    Kuvshinski, E.V.2
  • 2
    • 0011506661 scopus 로고
    • Continuum theory of asymmetric elasticity
    • (in Russian); Soviet Physics Solid State 6 (1965), 2141 2148 (in English).
    • E.L. Aero and E.V. Kuvshinski, Continuum theory of asymmetric elasticity. Equilibrium of an isotropic body, Solid State Physics 6 (1964), 2689 2699 (in Russian); Soviet Physics Solid State 6 (1965), 2141 2148 (in English).
    • (1964) Equilibrium of an isotropic body, Solid State Physics , vol.6 , pp. 2689-2699
    • Aero, E.L.1    Kuvshinski, E.V.2
  • 3
    • 0003584504 scopus 로고    scopus 로고
    • Inverse acoustic and electromagnetic scattering theory
    • 2nd ed., Springer-Verlag, Berlin
    • D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, 2nd ed., Springer-Verlag, Berlin, 1998.
    • (1998)
    • Colton, D.1    Kress, R.2
  • 4
    • 0000438610 scopus 로고
    • Boundary integral operators on Lipschitz domains: Elementary results,
    • M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal. 19 (1988), 613 626.
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 613-626
    • Costabel, M.1
  • 5
    • 84961469047 scopus 로고
    • Strong ellipticity of boundary integral operators
    • M. Costabel and W.L. Wendland, Strong ellipticity of boundary integral operators, J. Reine Angew. Math. 372 (1986), 34 63.
    • (1986) J. Reine Angew. Math. , vol.372 , pp. 34-63
    • Costabel, M.1    Wendland, W.L.2
  • 6
    • 0012957193 scopus 로고
    • Integral equations and numerical methods
    • in Mathematical analysis and numerical methods for science and technology, Springer Verlag, Berlin
    • R. Dautray and J.L. Lions, Integral equations and numerical methods, Vol. 4, in Mathematical analysis and numerical methods for science and technology, Springer Verlag, Berlin, 1990.
    • (1990) , vol.4
    • Dautray, R.1    Lions, J.L.2
  • 7
    • 0011340183 scopus 로고
    • On multidimensional singular integral operators, I, II
    • 199 214
    • R. Duduchava, On multidimensional singular integral operators, I, II, J. Operator Theory 11 (1984), 41 76, 199 214.
    • (1984) J. Operator Theory , vol.11 , pp. 41-76
    • Duduchava, R.1
  • 9
    • 0038243439 scopus 로고
    • Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts I, II
    • 259 276
    • R. Duduchava, D. Natroshvili and E. Shargorodsky, Basic boundary value problems of thermoelasticity for anisotropic bodies with cuts I, II, Georgian Math. J. 2 (1995), 123 140, 259 276.
    • (1995) Georgian Math. J. , vol.2 , pp. 123-140
    • Duduchava, R.1    Natroshvili, D.2    Shargorodsky, E.3
  • 10
    • 0028158526 scopus 로고
    • Plane-wave representation of an elastic chiral solid slab sandwiched between achiral solid half-spaces
    • M.J. Elphinstone and A. Lakhtakia, Plane-wave representation of an elastic chiral solid slab sandwiched between achiral solid half-spaces, J. Acoust. Soc. Amer. 95 (1994), 617 627.
    • (1994) J. Acoust. Soc. Amer. , vol.95 , pp. 617-627
    • Elphinstone, M.J.1    Lakhtakia, A.2
  • 11
    • 0003295381 scopus 로고
    • Boundary value problems for elliptic pseudodifferential equations
    • Providence, RI
    • G. Eskin, Boundary value problems for elliptic pseudodifferential equations, Transl. Math. Monographs, Amer. Math. Soc. 52, Providence, RI, 1981.
    • (1981) Transl. Math. Monographs, Amer. Math. Soc. 52
    • Eskin, G.1
  • 12
    • 0000390501 scopus 로고
    • Existence theorems in elasticity
    • Bd. 6/2, Springer Verlag, Heidelberg
    • G. Fichera, Existence theorems in elasticity, Handb. der Physik, Bd. 6/2, Springer Verlag, Heidelberg, 1973.
    • (1973) Handb. der Physik
    • Fichera, G.1
  • 13
    • 84973070968 scopus 로고
    • Pseudodifferential boundary problems in Lp spaces
    • G. Grubb, Pseudodifferential boundary problems in Lp spaces, Comm. Partial Differential Equations 15 (1990), 289 340.
    • (1990) Comm. Partial Differential Equations , vol.15 , pp. 289-340
    • Grubb, G.1
  • 14
    • 0001178462 scopus 로고
    • The analysis of linear partial differential operators
    • Springer-Verlag, Heidelberg
    • L. Ḧormander, The analysis of linear partial differential operators, pseudodifferential operators, vol. 3, Springer-Verlag, Heidelberg, 1985.
    • (1985) pseudodifferential operators , vol.3
    • Ḧormander, L.1
  • 15
    • 85070504770 scopus 로고    scopus 로고
    • Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies, I
    • L. Jentsch and D. Natroshvili, Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies, I, Mem. Differential Equations Math. Phys. 17 (1999), 7 126.
    • (1999) Mem. Differential Equations Math. Phys. , vol.17 , pp. 7-126
    • Jentsch, L.1    Natroshvili, D.2
  • 16
    • 85070504770 scopus 로고    scopus 로고
    • Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies, II
    • L. Jentsch and D. Natroshvili, Three-dimensional mathematical problems of thermoelasticity of anisotropic bodies, II, Mem. Differential Equations Math. Phys. 18 (1999), 1 50.
    • (1999) Mem. Differential Equations Math. Phys. , vol.18 , pp. 1-50
    • Jentsch, L.1    Natroshvili, D.2
  • 17
    • 0040682330 scopus 로고    scopus 로고
    • General transmission problems in the theory of elastic oscillations of anisotropic bodies (Basic interface problems)
    • L. Jentsch, D. Natroshvili and W.L. Wendland, General transmission problems in the theory of elastic oscillations of anisotropic bodies (Basic interface problems), J. Math. Anal. Appl. 220 (1998), 397 433.
    • (1998) J. Math. Anal. Appl. , vol.220 , pp. 397-433
    • Jentsch, L.1    Natroshvili, D.2    Wendland, W.L.3
  • 18
    • 0005644109 scopus 로고    scopus 로고
    • General transmission problems in the theory of elastic oscillations of anisotropic bodies (Mixed interface problems)
    • General transmission problems in the theory of elastic oscillations of anisotropic bodies (Mixed interface problems), J. Math. Anal. Appl. 235 (1999), 418 434.
    • (1999) J. Math. Anal. Appl. , vol.235 , pp. 418-434
    • Jentsch, L.1    Natroshvili, D.2
  • 19
    • 0003771856 scopus 로고
    • Three dimensional problems of the mathematical theory of elasticity and thermoelasticity
    • Nauka, Moscow, North Holland Ser. Appl. Math. Mech. 25, North Holland Publ. Co., Amsterdam, 1979 (in English).
    • V.D. Kupradze, T.G. Gegelia, M.O. Basheleishvili and T.V. Burchuladze, Three dimensional problems of the mathematical theory of elasticity and thermoelasticity, Nauka, Moscow, 1976; North Holland Ser. Appl. Math. Mech. 25, North Holland Publ. Co., Amsterdam, 1979 (in English).
    • (1976)
    • Kupradze, V.D.1    Gegelia, T.G.2    Basheleishvili, M.O.3    Burchuladze, T.V.4
  • 20
    • 0035400967 scopus 로고    scopus 로고
    • Elastic and viscoelastic behavior of chiral materials
    • R.S. Lakes, Elastic and viscoelastic behavior of chiral materials, Internat. J. Mech. Sci. 43 (2001), 1579 1589.
    • (2001) Internat. J. Mech. Sci. , vol.43 , pp. 1579-1589
    • Lakes, R.S.1
  • 21
    • 0020244906 scopus 로고
    • Noncentrosymmetry in micropolar elasticity
    • R.S. Lakes and R.L. Benedict, Noncentrosymmetry in micropolar elasticity, Inter. J. Engrg. Sci. 29 (1982), 1161 1167.
    • (1982) Inter. J. Engrg. Sci. , vol.29 , pp. 1161-1167
    • Lakes, R.S.1    Benedict, R.L.2
  • 22
    • 0005064324 scopus 로고
    • Elastic wave propagation in noncentrosymmetric isotropic media: dispersion and field equations
    • A. Lakhtakia, V.K. Varadan and V.V. Varadan, Elastic wave propagation in noncentrosymmetric isotropic media: dispersion and field equations, J. Appl. Phys. 64 (1988), 5246 5250.
    • (1988) J. Appl. Phys. , vol.64 , pp. 5246-5250
    • Lakhtakia, A.1    Varadan, V.K.2    Varadan, V.V.3
  • 23
    • 0025033414 scopus 로고
    • Reflection of elastic plane waves at a planar achiral-chiral interface
    • A. Lakhtakia, V.K. Varadan and V.V. Varadan, Reflection of elastic plane waves at a planar achiral-chiral interface, J. Acoust. Soc. Amer. 87 (1990), 2314 2318.
    • (1990) J. Acoust. Soc. Amer. , vol.87 , pp. 2314-2318
    • Lakhtakia, A.1    Varadan, V.K.2    Varadan, V.V.3
  • 24
    • 0026667279 scopus 로고
    • Elastic wave scattering by an isotropic noncentrosymmetric sphere
    • A. Lakhtakia, V.V. Varadan and V.K. Varadan, Elastic wave scattering by an isotropic noncentrosymmetric sphere, J. Acoust. Soc. Amer. 91 (1992), 680 684.
    • (1992) J. Acoust. Soc. Amer. , vol.91 , pp. 680-684
    • Lakhtakia, A.1    Varadan, V.V.2    Varadan, V.K.3
  • 25
    • 0003896053 scopus 로고
    • Problèmes aux limites non homogènes et applications
    • Dunod, Paris
    • J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris, 1968.
    • (1968) , vol.1
    • Lions, J.-L.1    Magenes, E.2
  • 26
    • 0003797412 scopus 로고    scopus 로고
    • Strongly elliptic systems and boundary integral equations
    • Cambridge Univ. Press, Cambridge
    • W. McLean, Strongly elliptic systems and boundary integral equations, Cambridge Univ. Press, Cambridge, 2000.
    • (2000)
    • McLean, W.1
  • 27
    • 0040366845 scopus 로고
    • Micro-structure in linear elasticity
    • R.D. Mindlin, Micro-structure in linear elasticity, Arch. Rational Mech. Anal. 16 (1964), 51 78.
    • (1964) Arch. Rational Mech. Anal. , vol.16 , pp. 51-78
    • Mindlin, R.D.1
  • 28
    • 0010756220 scopus 로고
    • Investigation of boundary value and initial boundary value problems of the mathematical theory of anisotropic elasticity and thermoelasticity by means of potential methods
    • (in Russian).
    • D. Natroshvili, Investigation of boundary value and initial boundary value problems of the mathematical theory of anisotropic elasticity and thermoelasticity by means of potential methods, Doct. Thesis, A. Razmadze Math. Inst. of the Georgian Academy of Sciences, Tbilisi, 1 325, 1984 (in Russian).
    • (1984) Doct. Thesis, A. Razmadze Math. Inst. of the Georgian Academy of Sciences Tbilisi , pp. 1-325
    • Natroshvili, D.1
  • 29
    • 0039553450 scopus 로고
    • Mixed interface problems for anisotropic elastic bodies
    • D. Natroshvili, Mixed interface problems for anisotropic elastic bodies, Georgian Math. J. 2 (1995), 631 652.
    • (1995) Georgian Math. J. , vol.2 , pp. 631-652
    • Natroshvili, D.1
  • 30
    • 0030784734 scopus 로고    scopus 로고
    • Boundary integral equation method in the steady state oscillation problems for anisotropic bodies
    • D. Natroshvili, Boundary integral equation method in the steady state oscillation problems for anisotropic bodies, Math. Meth. Appl. Sci. 20 (1997), 95 119.
    • (1997) Math. Meth. Appl. Sci. , vol.20 , pp. 95-119
    • Natroshvili, D.1
  • 32
    • 0011827841 scopus 로고
    • Problems of the linear theory of elastic mixtures
    • Tbilisi University, Tbilisi
    • D. Natroshvili, A. Djagmaidze and M. Svanadze, Problems of the linear theory of elastic mixtures, Tbilisi University, Tbilisi, 1986.
    • (1986)
    • Natroshvili, D.1    Stratis, I.G.2
  • 34
    • 84880636888 scopus 로고    scopus 로고
    • Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains
    • to appear.
    • D. Natroshvili and I.G. Stratis, Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains, Math. Meth. Appl. Sci., to appear.
    • Math. Meth. Appl. Sci.
    • Natroshvili, D.1    Stratis, I.G.2
  • 35
    • 0003890212 scopus 로고
    • Ḿethodes directes en th́eorie des ́equations ́elliptiques
    • Masson ́Editeur, Paris
    • J. Necas, Ḿethodes directes en th́eorie des ́equations ́elliptiques, Masson ́Editeur, Paris, 1967.
    • (1967)
    • Necas, J.1
  • 36
    • 0017737280 scopus 로고
    • Green function for a hemitropic micropolar continuum
    • J.P. Nowacki, Green function for a hemitropic micropolar continuum, Bull. Acad. Polon. Sci., Śer. Sci. Tech. 25 (1977), 235 241.
    • (1977) Bull. Acad. Polon. Sci., Śer. Sci. Tech. , vol.25 , pp. 235-241
    • Nowacki, J.P.1
  • 37
    • 0017634345 scopus 로고
    • Some dynamical problems of hemitropic micropolar continuum
    • J.P. Nowacki, Some dynamical problems of hemitropic micropolar continuum, Bull. Acad. Polon. Sci., Śer. Sci. Tech. 25 (1977), 207 216.
    • (1977) Bull. Acad. Polon. Sci., Śer. Sci. Tech. , vol.25 , pp. 207-216
    • Nowacki, J.P.1
  • 39
    • 0004124990 scopus 로고
    • Theory of asymmetric elasticity
    • Pergamon Press, Oxford; PWN-Polish Sci. Publ., Warsaw
    • W. Nowacki, Theory of asymmetric elasticity, Pergamon Press, Oxford; PWN-Polish Sci. Publ., Warsaw, 1986.
    • (1986)
    • Nowacki, W.1
  • 40
    • 0001752125 scopus 로고
    • Singular integrals and boundary value problems
    • R.T. Seeley, Singular integrals and boundary value problems, Amer. J. Math. 88 (1966), 781 809.
    • (1966) Amer. J. Math. , vol.88 , pp. 781-809
    • Seeley, R.T.1
  • 41
    • 0041104476 scopus 로고
    • Elliptic systems of singular integral operators, I
    • E. Shamir, Elliptic systems of singular integral operators, I, Trans. Amer. Math. Soc. 127 (1967), 107 124.
    • (1967) Trans. Amer. Math. Soc. , vol.127 , pp. 107-124
    • Shamir, E.1
  • 43
    • 0003475679 scopus 로고
    • Introduction to pseudodifferential and Fourier integral operators
    • Pseudodifferential operators, Plenum Press, New York
    • F. Treves, Introduction to pseudodifferential and Fourier integral operators, Vol. 1, Pseudodifferential operators, Plenum Press, New York, 1982.
    • (1982) , vol.1
    • Treves, F.1
  • 44
    • 18444406055 scopus 로고
    • Interpolation theory
    • function spaces, differential operators, North Holland, Amsterdam
    • H. Triebel, Interpolation theory, function spaces, differential operators, North Holland, Amsterdam, 1978.
    • (1978)
    • Triebel, H.1
  • 45
    • 0001665464 scopus 로고
    • On metaharmonic functions
    • (in Russian)
    • I.N. Vekua, On metaharmonic functions, Trudy Tbiliss. Mat. Inst. 12 (1943), 105 174 (in Russian).
    • (1943) Trudy Tbiliss. Mat. Inst. , vol.12 , pp. 105-174
    • Vekua, I.N.1
  • 46
    • 0005007828 scopus 로고
    • Initial stress and skin effects in a hemitropic Cosserat continuum
    • Y. Weitsman, Initial stress and skin effects in a hemitropic Cosserat continuum, J. Appl. Math. 349 (1967), 160 164.
    • (1967) J. Appl. Math. , vol.349 , pp. 160-164
    • Weitsman, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.