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Volumn 65, Issue 1, 2000, Pages 1-28

Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC MODULI; ERROR ANALYSIS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS); THEOREM PROVING;

EID: 0034251205     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/65.1.1     Document Type: Article
Times cited : (19)

References (59)
  • 1
    • 0032219230 scopus 로고    scopus 로고
    • Asymptotically exact joining conditions at the junction of plates with very different characteristics
    • ALDOSHINA, I. A. & NAZAROV, S. A. 1998 Asymptotically exact joining conditions at the junction of plates with very different characteristics. J. Appl. Math. Mech. 62, 253-261.
    • (1998) J. Appl. Math. Mech. , vol.62 , pp. 253-261
    • Aldoshina, I.A.1    Nazarov, S.A.2
  • 2
    • 0030528253 scopus 로고    scopus 로고
    • Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model
    • ARNOLD, D. N. & FALK, R. S. 1996 Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. SIAM J. Math. Anal. 27, 486-514.
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 486-514
    • Arnold, D.N.1    Falk, R.S.2
  • 3
    • 0026818248 scopus 로고
    • Hierarchic models for laminated composites
    • BABUŠKA, I. 1992 Hierarchic models for laminated composites. Int. J. Numer. Methods Eng. 33, 503-535.
    • (1992) Int. J. Numer. Methods Eng. , vol.33 , pp. 503-535
    • Babuška, I.1
  • 4
    • 0025791621 scopus 로고
    • Hierarchic modeling of plates
    • BABUŠKA, I. & LI, L. 1991 Hierarchic modeling of plates. Comput. Struct. 40, 419-430.
    • (1991) Comput. Struct. , vol.40 , pp. 419-430
    • Babuška, I.1    Li, L.2
  • 5
    • 0021306264 scopus 로고
    • Thin elastic and periodic plates
    • CAILLERIE, D. 1984 Thin elastic and periodic plates. Math. Methods Appl. Sci. 6, 159-191.
    • (1984) Math. Methods Appl. Sci. , vol.6 , pp. 159-191
    • Caillerie, D.1
  • 6
    • 0018322217 scopus 로고
    • A justification of the two-dimensional linear plate model
    • CIARLET, P. G. & DESTUYNDER, P. 1979 A justification of the two-dimensional linear plate model. J. Méc. 18, 315-344.
    • (1979) J. Méc. , vol.18 , pp. 315-344
    • Ciarlet, P.G.1    Destuynder, P.2
  • 7
    • 0019560197 scopus 로고
    • Two-dimensional approximations of three-dimensional eigen-value problems in plate theory
    • CIARLET, P. G. & KESAVAN, S. 1981 Two-dimensional approximations of three-dimensional eigen-value problems in plate theory. Comput. Methods Appl. Mech. Eng. 26, 145-172.
    • (1981) Comput. Methods Appl. Mech. Eng. , vol.26 , pp. 145-172
    • Ciarlet, P.G.1    Kesavan, S.2
  • 10
    • 0000952851 scopus 로고
    • Développement asymptotique d'ordre arbitrare pour une plaque élastique mince encastrée
    • DAUGE, M. & GRUAIS, I. 1995 Développement asymptotique d'ordre arbitrare pour une plaque élastique mince encastrée. C. R. Acad. Sci. Paris, Sér. 1 321, 375-380.
    • (1995) C. R. Acad. Sci. Paris, Sér. 1 , vol.321 , pp. 375-380
    • Dauge, M.1    Gruais, I.2
  • 11
    • 0000477019 scopus 로고
    • Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité
    • DESTUYNDER, P. 1981 Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité. RAIRO Anal. Numer. 15, 331-369.
    • (1981) RAIRO Anal. Numer. , vol.15 , pp. 331-369
    • Destuynder, P.1
  • 12
    • 0002000002 scopus 로고
    • Error estimation for the linear three-dimensional elastic plate model
    • Berlin: Walter de Gruyter
    • DETUYNDER, P. & GRUIAS, I. 1995 Error estimation for the linear three-dimensional elastic plate model. In Asymptotic Methods for Elastic Structures. Berlin: Walter de Gruyter, 75-88.
    • (1995) Asymptotic Methods for Elastic Structures , pp. 75-88
    • Detuynder, P.1    Gruias, I.2
  • 14
    • 36348954787 scopus 로고
    • Derivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity
    • Russian
    • GOL'DENVEIZER, A. L. 1962 Derivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity. Prikl. Mat. Mekh. 26, 668-686 (Russian).
    • (1962) Prikl. Mat. Mekh. , vol.26 , pp. 668-686
    • Gol'denveizer, A.L.1
  • 15
    • 0009125887 scopus 로고
    • English translation
    • English translation: 1963 J. Appl. Math. Mech. 26, 1000-1025.
    • (1963) J. Appl. Math. Mech. , vol.26 , pp. 1000-1025
  • 16
    • 0000523926 scopus 로고
    • To the construction of two-dimensional equations of the theory of elastic thin plates
    • Russian
    • GOL'DENVEIZER, A. L. & KOLOS, A. V. 1965 To the construction of two-dimensional equations of the theory of elastic thin plates. Prikl. Mat. Mekh. 29, 141-161 (Russian).
    • (1965) Prikl. Mat. Mekh. , vol.29 , pp. 141-161
    • Gol'denveizer, A.L.1    Kolos, A.V.2
  • 17
    • 0343441390 scopus 로고
    • English translation
    • English translation: 1965 J. Appl. Math. Mech. 29.
    • (1965) J. Appl. Math. Mech. , vol.29
  • 18
    • 0021398742 scopus 로고
    • Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory
    • GREGORY, R. D. & WAN, F. Y. M. 1984 Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory. J. Elast. 14, 27-64.
    • (1984) J. Elast. , vol.14 , pp. 27-64
    • Gregory, R.D.1    Wan, F.Y.M.2
  • 19
    • 84918741742 scopus 로고
    • Asymptotic expansion of a solution of the system of elasticity theory with periodic, rapidly oscillating coefficients
    • Russian
    • IOSIF'JAN, G. A., OLEINIK, O. A., & PANASENKO, G. P. 1982 Asymptotic expansion of a solution of the system of elasticity theory with periodic, rapidly oscillating coefficients. DAN SSSR 226, 18-22 (Russian).
    • (1982) DAN SSSR , vol.226 , pp. 18-22
    • Iosif'jan, G.A.1    Oleinik, O.A.2    Panasenko, G.P.3
  • 20
    • 0343877087 scopus 로고
    • English translation
    • English translation: 1982 Sov. Math. Dokl. 26, 290-294.
    • (1982) Sov. Math. Dokl. , vol.26 , pp. 290-294
  • 21
    • 0001809603 scopus 로고    scopus 로고
    • Boundary value problems for the system of elasticity theory in unbounded domains. Korn's inequalities
    • KONDRAT'EV, V. A. & OLEINIK, O. A. 1998 Boundary value problems for the system of elasticity theory in unbounded domains. Korn's inequalities. Russian Math. Survey 43, 65-119.
    • (1998) Russian Math. Survey , vol.43 , pp. 65-119
    • Kondrat'ev, V.A.1    Oleinik, O.A.2
  • 23
    • 0039068408 scopus 로고
    • English translation: New York: Springer-Verlag
    • English translation: 1985 Appl. Math. Sci. 49. New York: Springer-Verlag.
    • (1985) Appl. Math. Sci. , vol.49
  • 24
    • 0002296328 scopus 로고
    • Derivation of limiting equations for elliptic problems in thin domains using computers
    • Russian
    • LEORA, S. N., NAZAROV, S. A., & PROSKURA, A. V. 1986 Derivation of limiting equations for elliptic problems in thin domains using computers. Zh. Vychisl. Mat. i Mat. Fiz. 26, 1032-1048 (Russian).
    • (1986) Zh. Vychisl. Mat. i Mat. Fiz. , vol.26 , pp. 1032-1048
    • Leora, S.N.1    Nazarov, S.A.2    Proskura, A.V.3
  • 25
    • 52549092785 scopus 로고
    • English translation
    • English translation: 1986 USSR Comput. Math. Math. Phys. 26, 47-58.
    • (1986) USSR Comput. Math. Math. Phys. , vol.26 , pp. 47-58
  • 27
    • 0000902230 scopus 로고
    • Herleitung der plattentheorie aus der dreidimensionalen elastizitätstheorie
    • MORGENSTERN, D. 1959 Herleitung der Plattentheorie aus der dreidimensionalen Elastizitätstheorie. Arch. Ration. Mech. Anal. 4, 145-152.
    • (1959) Arch. Ration. Mech. Anal. , vol.4 , pp. 145-152
    • Morgenstern, D.1
  • 28
    • 0343877078 scopus 로고
    • The structure of solutions of elliptic boundary value problems in slender domains
    • Russian
    • NAZAROV, S. A. 1982 The structure of solutions of elliptic boundary value problems in slender domains. Vestnik Leningrad Univ. 7, 65-68 (Russian).
    • (1982) Vestnik Leningrad Univ. , vol.7 , pp. 65-68
    • Nazarov, S.A.1
  • 29
    • 0040929154 scopus 로고
    • English translation
    • English translation: 1983 Vestn. Leningr. Univ. Math. 15, 99-104.
    • (1983) Vestn. Leningr. Univ. Math. , vol.15 , pp. 99-104
  • 30
    • 0026160206 scopus 로고
    • On three-dimensional effects near the vertex of a crack in a thin plate
    • Russian
    • NAZAROV, S. A. 1991 On three-dimensional effects near the vertex of a crack in a thin plate. Prikl. Mat. Mekh. 55, 500-510 (Russian).
    • (1991) Prikl. Mat. Mekh. , vol.55 , pp. 500-510
    • Nazarov, S.A.1
  • 31
    • 0040421940 scopus 로고
    • English translation
    • English translation: 1991 J. Appl. Math. Mech. 55, 407-415.
    • (1991) J. Appl. Math. Mech. , vol.55 , pp. 407-415
  • 32
    • 0026376626 scopus 로고
    • The spatial structure of the stress field in the neighbourhood of the corner point of a thin plate
    • Russian
    • NAZAROV, S. A. 1991 The spatial structure of the stress field in the neighbourhood of the corner point of a thin plate. Prikl. Mat. Mekh. 55, 523-530 (Russian).
    • (1991) Prikl. Mat. Mekh. , vol.55 , pp. 523-530
    • Nazarov, S.A.1
  • 33
    • 0026376626 scopus 로고
    • English translation
    • English translation: 1991 J. Appl. Math. Mech. 55, 523-530.
    • (1991) J. Appl. Math. Mech. , vol.55 , pp. 523-530
  • 34
    • 0039262337 scopus 로고
    • Three-dimensional effects at plate crack tips
    • NAZAROV, S. A. 1992 Three-dimensional effects at plate crack tips. C. R. Acad. Sci. Paris, Sér: 2 314, 995-1000.
    • (1992) C. R. Acad. Sci. Paris, Sér: 2 , vol.314 , pp. 995-1000
    • Nazarov, S.A.1
  • 35
    • 0141434392 scopus 로고
    • The Korn inequalities which are asymptotically sharp for thin domains
    • Russian
    • NAZAROV, S. A. 1992 The Korn inequalities which are asymptotically sharp for thin domains. Vestnik St-Petersburg. Univ. 8, 19-24 (Russian).
    • (1992) Vestnik St-Petersburg. Univ. , vol.8 , pp. 19-24
    • Nazarov, S.A.1
  • 36
  • 37
    • 0343441369 scopus 로고
    • Asymptotics of the solution to a boundary value problem in a thin cylinder with nonsmooth lateral surface
    • Russian
    • NAZAROV, S. A. 1993 Asymptotics of the solution to a boundary value problem in a thin cylinder with nonsmooth lateral surface. Izv. Ross. Akad. Nauk. Ser. Mat. 57, 202-239 (Russian).
    • (1993) Izv. Ross. Akad. Nauk. Ser. Mat. , vol.57 , pp. 202-239
    • Nazarov, S.A.1
  • 38
    • 0012503713 scopus 로고
    • English translation
    • English translation: 1994 Math. Izvest. 42, 183-217.
    • (1994) Math. Izvest. , vol.42 , pp. 183-217
  • 39
    • 0002364556 scopus 로고
    • A general scheme for averaging selfadjoint elliptic systems in multidimensional domains, including thin domains
    • Russian
    • NAZAROV, S. A. 1995 A general scheme for averaging selfadjoint elliptic systems in multidimensional domains, including thin domains. Algebra Analiz 7, 1-92 (Russian).
    • (1995) Algebra Analiz , vol.7 , pp. 1-92
    • Nazarov, S.A.1
  • 40
    • 0040335157 scopus 로고    scopus 로고
    • English translation
    • English translation: 1996 St Petersburg Math. J. 7, 681-748.
    • (1996) St Petersburg Math. J. , vol.7 , pp. 681-748
  • 41
    • 0039560594 scopus 로고    scopus 로고
    • On the accuracy of asymptotic approximations for logitudinal deformation of a thin plate
    • NAZAROV, S. A. 1996 On the accuracy of asymptotic approximations for logitudinal deformation of a thin plate. RAIRO Model. Math. Anal. Numer. 30, 185-213.
    • (1996) RAIRO Model. Math. Anal. Numer. , vol.30 , pp. 185-213
    • Nazarov, S.A.1
  • 42
    • 0002126722 scopus 로고    scopus 로고
    • Nonselfadjoint elliptic problems with the polynomial property in domains having cylindric outlets to infinity
    • Russian
    • NAZAROV, S. A. 1997 Nonselfadjoint elliptic problems with the polynomial property in domains having cylindric outlets to infinity. Zap. Nauchn. Sem. St-Petersburg Otdel. Mat. Inst. Steklov 249, 212-231 (Russian).
    • (1997) Zap. Nauchn. Sem. St-Petersburg Otdel. Mat. Inst. Steklov , vol.249 , pp. 212-231
    • Nazarov, S.A.1
  • 43
    • 0002001426 scopus 로고    scopus 로고
    • Justification of the asymptotic theory of thin rods. Integral and pointwise estimates
    • St-Petersburg: St-Petersburg Univ, (Russian)
    • NAZAROV, S. A. 1997 Justification of the asymptotic theory of thin rods. Integral and pointwise estimates. Probl. Mater. Anal. 17. St-Petersburg: St-Petersburg Univ, 101-152 (Russian).
    • (1997) Probl. Mater. Anal. , vol.17 , pp. 101-152
    • Nazarov, S.A.1
  • 44
    • 0031079451 scopus 로고    scopus 로고
    • Korn's inequalities for junctions of spatial bodies and thin rods
    • NAZAROV, S. A. 1997 Korn's inequalities for junctions of spatial bodies and thin rods. Math. Methods Appl. Sci. 20, 219-243.
    • (1997) Math. Methods Appl. Sci. , vol.20 , pp. 219-243
    • Nazarov, S.A.1
  • 46
    • 0009976184 scopus 로고
    • On asymptotics of solutions to the problems of thin plates bending under non-smooth loadings
    • Leningrad: Leningrad University, (Russian)
    • NAZAROV, S. A. & SEMENOV, B. N. 1981 On asymptotics of solutions to the problems of thin plates bending under non-smooth loadings. Prikl. Mech. 5. Leningrad: Leningrad University, 135-145 (Russian).
    • (1981) Prikl. Mech. , vol.5 , pp. 135-145
    • Nazarov, S.A.1    Semenov, B.N.2
  • 48
    • 0000367910 scopus 로고
    • Averaging the 3-D elasticity problem in nonhomogeneous plates
    • Russian
    • PANASENKO, G. P. & REZTSOV, M. V. 1987 Averaging the 3-D elasticity problem in nonhomogeneous plates. USSR Dokl. 294, 1061-1065 (Russian).
    • (1987) USSR Dokl. , vol.294 , pp. 1061-1065
    • Panasenko, G.P.1    Reztsov, M.V.2
  • 49
    • 0343441370 scopus 로고
    • English translation
    • English translation: 1987 Sov. Math. Dokl. 35, 630-636.
    • (1987) Sov. Math. Dokl. , vol.35 , pp. 630-636
  • 50
    • 0022162744 scopus 로고
    • Reflections on the theory of elastic plates
    • REISSNER, E. 1986 Reflections on the theory of elastic plates. Appl. Mech. Rev. 38, 1453-1464.
    • (1986) Appl. Mech. Rev. , vol.38 , pp. 1453-1464
    • Reissner, E.1
  • 51
    • 0001006031 scopus 로고
    • Passage à la limite de l'élasticité tridimensionelle à la théorie asymptotique des coques minces
    • SÁNCHEZ-PALENCIA, E. 1990 Passage à la limite de l'élasticité tridimensionelle à la théorie asymptotique des coques minces. C. R. Acad. Sci. Paris, Sér. 2 311, 909-916.
    • (1990) C. R. Acad. Sci. Paris, Sér. 2 , vol.311 , pp. 909-916
    • Sánchez-Palencia, E.1
  • 52
    • 0030521479 scopus 로고    scopus 로고
    • A-posteriori modeling error estimation for hierarchical plate models
    • SCHWAB, C. 1996 A-posteriori modeling error estimation for hierarchical plate models. Numer. Math. 74, 221-259.
    • (1996) Numer. Math. , vol.74 , pp. 221-259
    • Schwab, C.1
  • 53
    • 0015740785 scopus 로고
    • On asymptotically exact equations of thin plates of complex structures
    • Russian
    • SHOIKHET, B. A. 1973 On asymptotically exact equations of thin plates of complex structures. Prikl. Math. Mekh. 37, 867-877 (Russian).
    • (1973) Prikl. Math. Mekh. , vol.37 , pp. 867-877
    • Shoikhet, B.A.1
  • 54
    • 85037799472 scopus 로고    scopus 로고
    • English translation
    • English translation: J. Appl. Math. Mech. 37, 867-877.
    • J. Appl. Math. Mech. , vol.37 , pp. 867-877
  • 55
    • 0001622825 scopus 로고
    • On an energy identity in physically nonlinear elasticity, and estimations of errors for equations of plates
    • Russian
    • SHOIKHET, B. A. 1976 On an energy identity in physically nonlinear elasticity, and estimations of errors for equations of plates. Prikl. Math. Mekh. 40, 317-326 (Russian).
    • (1976) Prikl. Math. Mekh. , vol.40 , pp. 317-326
    • Shoikhet, B.A.1
  • 56
    • 0017242045 scopus 로고
    • English translation
    • English translation: 1976 J. Appl. Math. Mech. 40, 291-301.
    • (1976) J. Appl. Math. Mech. , vol.40 , pp. 291-301
  • 57
    • 0343440912 scopus 로고
    • Operator representation of the Lame system and limiting boundary-value problems of the thin plates theory
    • Russian
    • ZORIN, I. S. 1987 Operator representation of the Lame system and limiting boundary-value problems of the thin plates theory. Vestn. Leningr. Univ. 22, 108 (Russian).
    • (1987) Vestn. Leningr. Univ. , vol.22 , pp. 108
    • Zorin, I.S.1
  • 58
    • 0009129712 scopus 로고
    • Edge effect in the bending of a thin three-dimensional plate
    • Russian
    • ZORIN, I. S. & NAZAROV, S. A. 1989 Edge effect in the bending of a thin three-dimensional plate. Prikl. Mat. Mekh. 53, 642-650 (Russian).
    • (1989) Prikl. Mat. Mekh. , vol.53 , pp. 642-650
    • Zorin, I.S.1    Nazarov, S.A.2
  • 59
    • 0009129712 scopus 로고
    • English translation
    • English translation: 1989 J. Appl. Math. Mech. 53, 500-507.
    • (1989) J. Appl. Math. Mech. , vol.53 , pp. 500-507


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