SEARCH

SEARCH BY CITATION

References

  • [1]
    R.L. Actis, Hierarchic Models for Laminated Plates. Doctoral Dissertation (Washington University, St. Louis, 1991).
  • [2]
    L.A. Agalovian, On the Consideration of the Transverse Shear in Analysis of Ortothropic Shells (in Russian), in: Plate and Shell Theory, (Nauka, Moscow, 1973), pp. 7–13.
  • [3]
    L.A. Agalovian, Asymptotic Theory of Anisotropic Plates and Shells (in Russian) (Nauka, Moscow, 1997).
  • [4]
    O.K. Aksentian, On stress concentration in thick plates, J. Appl. Math. Mech. 30(5), 11461155 (1966).
  • [5]
    O.K. Aksentian and T.N. Selezneva, Determination of frequencies of natural vibrations of circular plates, J. Appl. Math. Mech. 40(1), 96103 (1976).
  • [6]
    H. Altenbach, Theories for laminated and sandwich plates. A review, Mech. Compos. Mater. 34(3), 243252 (1972).
  • [7]
    A.A. Amosov, One variant of constructing a theory of shells of revolution (in Russian), Proc. Tashkent Politechn. Univ. 244, 2130 (1978).
  • [8]
    A.A. Amosov, Determination of the Stress-Strain State of Thick-Walled Shells of Revolution (in Russian), in: Experimental and Theoretical Investigation of Engineering Structures (Tashkent Polytechn. University, Tashkent, 1985), pp. 3–8.
  • [9]
    A.A. Amosov, Algorithms for the Computer Design of Thick-Walled Shells (in Russian), in: The Use of Digital Computer in the Planning and Design of Structures (Tashkent Polytechn. University, Tashkent, 1986), pp. 7–12.
  • [10]
    A.A. Amosov, An approximate three-dimensional theory of thick plates and shells, Structural Mechanics and Design of Buildings (in Russian) 5, 3742 (1987).
  • [11]
    A.A. Amosov, An Approximate Three-Dimensional Theory of Thick Elastic Shells and Plates (in Russian), Dissertation for Dr. Sci., A. R. Beruny, (Tashkent Polytechn. University, Tashkent, 1989).
  • [12]
    A.A. Amosov, A.A. Knyazev, and S.I. Zhavoronok, On solution of 2D-problem of stressed curvilinear trapezoid (in Russian), J. Compos. Mech. Design 5(1), 6072 (1999).
  • [13]
    A.A. Amosov, K.A. Leontiev, and S.I. Zhavoronok, On the solution of some problems of stress-strain state of thick anisotropic shells of revolution using three-dimensional problem statement (in Russian), J. Compos. Mech. Design 10(3), 301310 (2004).
  • [14]
    A.A. Amosov and S.I. Zhavoronok, Reduction of the plane problem of elasticity theory to a sequence of one-dimensional boundary-value problems (in Russian), J. Compos. Mech. Design 3(1), 5262 (1997).
  • [15]
    A.A. Amosov and S.I. Zhavoronok, An approximate high-order theory of thick anisotropic shells, Int. J. Comput. Civil Struct. Eng. 1, 2838 (2003).
  • [16]
    A.A. Amosov and S.I. Zhavoronok, On the three-dimensional stress state of thick shells (in Russian), Bull. NITs “Stroitelstvo” 1(1), 208216 (2009).
  • [17]
    N.I. Antropova and A.L. Goldenweiser, Errors of construction of the main stress state and of the simple edge effect in the shell theory, Mech. Solids 5, 142150 (1971).
  • [18]
    M. Avalishvili, On a Dimensional Reduction Method in the Theory of Elasticity, in: Rep. of Enlarged Sess. of the Sem. of I. Vekua Inst. Appl. Math. (Tbilisi State University, Georgia, 1999), pp. 16–19.
  • [19]
    M. Avalishvili and D. Gordeziani, Investigation of two-dimensional models of elastic prismatic shell, Georgian Math. J. 10(1), 1736 (2003).
  • [20]
    A.Y. Aynola and U.K. Nigul, Wave processes of deformation of elastic plates and shells (in Russian), Dokl. Acad. Sci. Est. SSR 14 (1965).
  • [21]
    I. Babuŝka, I. Lee, and C. Schwab, On the a-posteriori estimation of the modeling error for the heat conduction in a plate and its use for adaptive hierarchical modeling, Appl. Num. Math. 14, 521 (1994).
  • [22]
    I. Babuŝka and L. Li, Hierarchical modeling of plates, Comp. Struct. 40, 419430 (1991).
  • [23]
    I. Babuŝka and L. Li, The problem of plate modeling – theoretical and computational results, Comp. Meth. Appl. Mech. Eng. 100, 249273 (1992).
  • [24]
    I. Babuŝka, B.A. Szabò, and R. Actis, Hierarchic models for laminated composites, Int. J. Numer. Methods Eng. 33, 503536 (1992).
  • [25]
    S. Banach, Théorie des Opérations Linéaires (PWN, Warszawa, 1932).
  • [26]
    N.K. Bari, Biorthogonal Systems and Basises in Hilbert Spaces (in Russian), in: Mathematics. Memoires of Moscow State Univ. (Moscow State Univ., Moscow, 1951), pp. 69–107.
  • [27]
    N.A. Bazarenko, Construction of refined applied theories for a shell of arbitrary shape, J. Appl. Math. Mech. 44, 513519 (1980).
  • [28]
    N.A. Bazarenko and I.I. Vorovoch, Analysis of the three-dimensional states of stress and strain of circular cylindrical shells. Construction of refined applied theories, J. Appl. Math. Mech. 33, 479494 (1969).
  • [29]
    V.L. Berdichevskiy, Variational methods of constructing models of shells, J. Appl. Math. Mech. 36(5), 743758 (1972).
  • [30]
    V.L. Berdichevskiy, Variational Principles of Continuum Mechanics (in Russian) (Nauka, Moscow, 1983).
  • [31]
    N. Chinchaladze, G. Jaiani, B. Maistrenko, and P. Podio-Guidugli, Concentrated contact interactions in cuspidate prismatic shell-like bodies, Arch. Appl. Mech. 81(10), 14871505 (2011).
  • [32]
    N. Chinchiladze, R.P. Gilbert, G. Jaiani, S. Kharibegashvili, and D. Natroshvili, Existence and uniqueness theorems for cusped prismatic shells in the N'th hierarchical model, Math. Methods Appl. Sci. 31(11), 13451367 (2008).
  • [33]
    P. Cicala, Sulla teoria elastica della pareta sottile, Giorn. Genio Civile 97(4,6,9), 238256; 429–449; 714–723 (1959).
  • [34]
    P. Cicala, Sulla teoria elastica della pareta sottile cilindrica, Giorn. Genio Civile 98(12), 937945 (1960).
  • [35]
    P. Cicala, Controlled Approximation Theory for Thin Elastic Shells (Instituto di Scienza delle Construzioni, Politecnico di Torino, Torino, 1961).
  • [36]
    P. Cicala, Teoria lineare della pareta sottile e applicazioni, Atti Accad. Naz. Lincei, Ren. Cl. Sci. Fiz. Mat. e Natur. 29(5), 232238 (1961).
  • [37]
    J. Descloux, Méthode des Éléments Finis (Ecole Politech. Fed. de Lausanne, Lausanne, 1973).
  • [38]
    Y.I. Dimitrienko, Asymptotic theory of multilayer thin plates, Bull. Moscow State Techn. Univ. 3, 86100 (2012).
  • [39]
    O.V. Egorova, S.I. Zhavornok, and L.N. Rabinskiy, Middle thickness shell interaction with acoustical wave (in Russian), Vestn. Moskovskogo Aviatsionnogo Instituta Journal 17(2), 127135 (2010).
  • [40]
    P.S. Epstein, On the theory of vibrations in plates and shells, J. Math. and Phys. 21, 198209 (1942).
  • [41]
    K. Friedrichs, Kirchhoff's Boundary Conditions and the Edge Effect for Elastic Plates, in: Proc. Simp. Appl. Math. (McGraw-Hill, New York, 1950), pp. 117–124.
  • [42]
    A.K. Galin'sh, Analysis of Plates and Shells Using Refined Theories (in Russian), in: Investigations on Plate and Shell Theories (Nauka, Moscow, 1967), pp. 23–64.
  • [43]
    I.T. Gokhberg and M.G. Krein, Introduction into the Theory of Nonself-adjoint Linear Operators in Hilbert Spaces (in Russian) (Nauka, Moscow, 1965).
  • [44]
    A.L. Goldenweiser, Derivation of an approximate theory of shells by means of asymptotic integration of the equations of the theory of elasticity, J. Appl. Math. Mech. 27(4), 903924 (1963).
  • [45]
    A.L. Goldenweiser, Methods for justifying and refining the theory of shells, J. Appl. Math. Mech. 32(4), 704718 (1968).
  • [46]
    A.L. Goldenweiser, Theory of Elastic Thin Shells (in Russian) (Nauka, Moscow, 1976).
  • [47]
    A.L. Goldenweiser and Y.D. Kaplunov, Dynamic boundery layer in problems of vibration of shells, Mech. Solids 23(4), 146158 (1998).
  • [48]
    A.L. Goldenweiser, Y.D. Kaplunov, and E.V. Nolde, Asymptotic analysis and improvement of plate and shell theories of Timoshenko-Reissner type, Mech. Solids 6, 124138 (1990).
  • [49]
    D. Gordeziani, On the solvability of some boundary value problems for a variant of the theory of thin shells (in Russian), Dokl. Phys. 215(6), 12891292 (1974).
  • [50]
    D. Gordeziani, To the exactness of one variant of the theory of thin shells (in Russian), Dokl. Phys. 216(4), 751754 (1974).
  • [51]
    D. Gordeziani and M. Avalishvili, Investigation of dynamical two-dimensional model of prismatic shell, Bull. Georgian Acad. Sci. 166, 1619 (2002).
  • [52]
    D. Gordeziani and M. Avalishvili, Investigation of hierarchic model of prismatic shell, Bull. Georgian Acad. Sci. 165, 485488 (2002).
  • [53]
    D. Gordeziani, M. Avalishvili, and G. Avalishvili, On the Investigation of a Dimensional Reduction Method for Elliptic Problems, in: Rep. Sem. I. Vekua Inst. Appl. Math. (Tbilisi State University, Georgia, 2003), pp. 15–25.
  • [54]
    D. Gordeziani, M. Avalishvili, and G. Avalishvili, Dynamcal hierarchical models for elastic shells, Appl. Math. Inform. Mech. 10(1), 1938 (2005).
  • [55]
    D. Gordeziani, M. Avalishvili, and G. Avalishvili, Hierarchical models for elastic shells in curvilinear coordinates, Comput. Math. Appl. 51, 17891808 (2006).
  • [56]
    A.G. Gorschkow, A.L. Medvedskiy, L.N. Rabinskiy, and D.V. Tarlakovskiy, Wave Processes in Continuous Media (in Russian) (Physmatlit, Moscow, 2000).
  • [57]
    A.G. Gorschkow, L.N. Rabinskiy, and D.V. Tarlakovskiy, Fundamentals of Tensor Analysis and Continuum Mechanics (in Russian) (Physmatlit, Moscow, 2000).
  • [58]
    A.E. Green, Boundary layer equations in the linear theory of thin elastic shells, Proc. R. Soc. Lond. A 269, 481491 (1962).
  • [59]
    A.E. Green, On the linear theory of thin elastic shells, Proc. R. Soc. Lond. A 266, 143160 (1962).
  • [60]
    E.I. Grigoliuk and E.A. Kogan, State of the art of the theory of multilayered shells, Int. Appl. Mech. 8(6), 583595 (1972).
  • [61]
    E.I. Grigolyuk and G.M. Kulikov, General direction of development of the theory of multilayered shells, Mech. Compos. Mater. 24(2), 231241 (1988).
  • [62]
    V.T. Grinchenko and V.V. Meleshko, Harmonic Oscillations and Waves in Elastic Bodies (in Russian) (Naukova Dumka, Kiev, 1981).
  • [63]
    V.I. Guliaev, B.A. Bazhenov, and P.P. Lizunov, Nonclassical Shell Theory and Applications in Engineering (in Russian) (Vishcha Shkola, Lvov, 1978).
  • [64]
    G.J. Hutchins and A.I. Soler, Approximate elasticity solution for moderately thick shells of revolution, J. Appl. Mech. 40(4), 955960 (1973).
  • [65]
    G. Jaiani, A cusped prismatic shell-like body under the action of concentrated moments, Z. Angew. Math. Phys. 59, 518536 (2008).
  • [66]
    G. Jaiani, Cusped Shell-like Structures (Springer, Heidelberg, Dordrecht, London, New York, 2011).
  • [67]
    G. Jaiani, S. Kharibegashvili, D. Natroshvili, and W.L. Wendland, Two-dimensional hierarchical modals for prismatic shells with thickness vanishing at the boundary, J. Elast. 77, 95122 (2004).
  • [68]
    G.V. Jaiani, Elastic bodies with non-smooth boundaries – cusped plates and shells, Z. Angew. Math. Mech. 76, 117120 (1996).
    Direct Link:
  • [69]
    G.V. Jaiani, On a mathematical model of bars with variable rectangular cross-sections, Z. Angew. Math. Mech. 81(3), 147173 (2001).
  • [70]
    V.K. Kabulov, Algorithmization in the Elasticity Theory (in Russian) (Acad. Sci. Uzb. SSR, Tashkent, 1966).
  • [71]
    V.P. Kagan, Fundamentals of the Theory of Surfaces (in Russian) (GITTL, Moscow, 1947).
  • [72]
    O.Y. Kalekin, Approximate theory of shells of moderate thickness, Int. Appl. Mech. 1(12), 2937 (1965).
  • [73]
    O.Y. Kalekin, Calculation of cylindrical shells of moderate thickness (in Russian), Dynamika i Prochnost Mashin 2, 8288 (1965).
  • [74]
    Y.D. Kaplunov, Integration of the equations of dynamic boundary layer, Mech. Solids 15(1), 148155 (1990).
  • [75]
    Y.D. Kaplunov, On the quasifront in two-dimensional shell theories, C. R. Acad. Sci. Paris, Ser. II 313(7), 731736 (1991).
  • [76]
    Y.D. Kaplunov, Vibrations of shells of revolution in response to high-frequency edge excitation, Mech. Solids 16(1), 147152 (1991).
  • [77]
    Y.D. Kaplunov, I.V. Kirillova, and L.Y. Kossovich, Asymptotic integration of the dynamic equations of the theory of elasticity for the case of thin shells, J. Appl. Math. Mech. 57(1), 95103 (1993).
  • [78]
    Y.D. Kaplunov, L.Y. Kossovich, and E.V. Nol'de, Dynamics of Thin-Walled Elastic Bodies (Academic Press, London, 1998).
  • [79]
    Y.D. Kaplunov, L.Y. Kossovich, and M.V. Wilde, The localized vibrations of a semi-infinite cylindrical shell, J. Acoust. Soc. Amer. 107(3), 13831393 (2000).
  • [80]
    Y.D. Kaplunov and E.V. Nol'de, A quasifront in the problem of the action of an instantaneous point impulse at the edge of a conical shell, J. Appl. Math. Mech. 59(5), 773780 (1995).
  • [81]
    Y.D. Kaplunov and D.A. Prikazchikov, A general representation of a boundary bending wave in elastic plate (in Russian), Vestn. Moscow State Techn. Univ. Natur. Sci. Special Issue, 164170 (2011).
  • [82]
    E.H. Kennard, The new approach to shell theory: circular cylinders, J. Appl. Mech. 20(1), 3340 (1953).
  • [83]
    E.H. Kennard, Cylindrical shells: energy, equilibrium, addenta and erratum, J. Appl. Mech. 22(1), 111116 (1955).
  • [84]
    E.H. Kennard, Approximate energy and equilibrium equations for cylindrical shells, J. Appl. Mech. 23(4), 645646 (1956).
  • [85]
    E.H. Kennard, A fresh test of the Epstein equations for cylinders, J. Appl. Mech. 25(4), 553555 (1958).
  • [86]
    I.Y. Khoma, Some problems of the theory of anisotropic shells of varying thickness, Int. Appl. Mech. 10(3), 243249 (1974).
  • [87]
    I.Y. Khoma, Dynamic equations of thick anisotropic shells, Int. Appl. Mech. 13(4), 331336 (1977).
  • [88]
    I.Y. Khoma, Solvability of boundary-value problem in a generalized theory of anisotropic shells, Int. Appl. Mech. 18(8), 741748 (1982).
  • [89]
    I.Y. Khoma, General Anisotropic Shell Theory (in Russian) (Naukova Dumka, Kiev, 1986).
  • [90]
    R. Kienzler, On consistent plate theories, Arch. Appl. Mech 72, 229247 (2002).
  • [91]
    R. Kienzler, H. Altenbach, and I. Ott (eds.), Theories of Plates and Shells: Critical Review and New Applications (Springer-Verlag, Berlin, 2004).
  • [92]
    N.A. Kil'chevskiy, Generalisation of the modern shell theory, J. Appl. Math. Mech. 2, 427438 (1939).
  • [93]
    N.A. Kil'chevskiy, Fundamentals of the Analytical Mechanics of Shells (in Russian) (AN UkrSSR, Kiev, 1963).
  • [94]
    N.A. Kil'chevskiy, G.A. Izdebskaya, and L.M. Kiselevskaya, Lectures on the Analytical Mechanics of Shells (in Russian) (Vishcha Shkola, Kiev, 1974).
  • [95]
    N.A. Kil'chevskiy, G.A. Kil'chinskaya, and N.E. Tkachenko, Fundamentals of the Analytical Mechanics of Continuous Systems (in Russian) (Naukova Dumka, Kiev, 1979).
  • [96]
    I.V. Kirillova, Dynamic boundary layer at elastic wave propagation in thin shells of revolution, Z. Angew. Math. Mech. 76(5, suppl.), 249250 (1996).
  • [97]
    I.V. Kirillova, On the Asymptotic Derivation of the Types of Approximation of Dynamic Equations of Elasticity Theory for Thin Shells (in Russian), PhD thesis (Saratov University, Saratov, 1998).
  • [98]
    I.V. Kirillova, Applicability regions of wave front boundary layers in shells of revolution of zero Gaussian curvature, Mech. Solids 29(6), 95101 (2003).
  • [99]
    I.V. Kirillova, Hyperbolic boundary layers in compound cylindrical shells, Mech. Solids 14(3), 409420 (2009).
  • [100]
    V.A. Kolos, On a refinement of the classical theory of bending of circular plates, J. Appl. Math. Mech. 28(3), 718726 (1964).
  • [101]
    L.Y. Kossovich and Y.D. Kaplunov, Asymptotic analysis of non-steady elastic waves in thin shells of revolution with shock loads at the edges (in Russian), Vestn. Saratov State Univ. New Ser.: Math., Mech., Inform. 1(2), 115120 (2001).
  • [102]
    F. Krauss, Über die Grundgleichungen der Elastizitätstheorie schwachdeformierter Schalen, Math. Ann. 101, 6192 (1929).
  • [103]
    G.M. Kulikov and S.V. Plotnikova, On the use of sampling surfaces method for solution of 3D elasticity problems for thick shells, Z. Angew. Math. Mech. 92(11–12), 910920 (2012).
  • [104]
    H. Lamb, On waves in an elastic plate, Proc. R. Soc. Lond. A. 93, 114128 (1917).
  • [105]
    L. Librescu, On the Thermoelastic Problem of Shells, Treated by Eliminating the Love-Kirchhoff Hypothesis (North Holland Publ. Co., Amsterdam, 1964), pp. 337–349.
  • [106]
    L. Librescu, On the theory of anisotropic elastic shells and plates, Int. J. Solids Struct. 3(1), 5368 (1967).
  • [107]
    A.I. Lurie, On the thick plates theory, J. Appl. Math. Mech. 6(2–3), 151169 (1942).
  • [108]
    A.I. Lurie, Three-Dimensional Problems of Elasticity Theory (in Russian) (Gostekhizdat, Moscow, 1955).
  • [109]
    S.A. Lurie, A generalized homogeneous-solution method in problems of plate and shell theory with a resolvent operator of order 2N (in Russian), J. Compos. Mech. Design 2(4), 4959 (1996).
  • [110]
    S.A. Lurie, A method of solving boundary-value problems of mathematical physics for equations of order 2N with constant coefficients. N-fold completeness of the generalized eigenfunctions (in Russian), J. Compos. Mech. Design 2(4), 93107 (1996).
  • [111]
    T. Meunargia, On Two-Dimensional Equations of the Linear Theory of Non-Shallow Shells, in: Proc. of I. Vekua Inst. of Appl. Math. (Tbilisi State University , Georgia, 1990), pp. 5–43.
  • [112]
    T. Meunargia, On nonlinear and nonshallow shells, Bull. TICMI 2, 4649 (1998).
  • [113]
    T. Meunargia, On conctruction of aproximate solutions of equations of nonlinear and nonshallow shells, J. Math. Sci. 157(1), 98118 (2009).
  • [114]
    S.G. Michlin, Variational Methods of Mathematical Physics (in Russian) (Nauka, Moscow, 1970).
  • [115]
    G.I. Mikhasev, Travelling wave packets in an infinite thin cylndrical shell under internal pressure, J. Sound Vib. 209(4), 543559 (1998).
  • [116]
    G.I. Mikhasev, Localized families of bending waves in a thin medium-length cylindrical shell under pressure, J. Sound Vib. 253(4), 833857 (2002).
  • [117]
    G.I. Mikhasev and P.E. Tovstik, Localized Vibrations and Waves in Thin Shells. Asymptotic Methods (Physmatlit, Moscow, 2009).
  • [118]
    K.M. Mushtari and I.G. Teregulov, On the theory of medium-thickness shells, Dokl. Phys. 128(6), 11441148 (1959).
  • [119]
    P.M. Naghdi, A survey of recent progress in the theory of elastic shells, Appl. Mech. Reviews 9, 365368 (1956).
  • [120]
    P.M. Naghdi, A new derivation of the general equations of elastic shells, Int. J. Eng. Sci. 1, 509522 (1963).
  • [121]
    Y.N. Nemish and I.Y. Khoma, Stress-strain state of thick plates and shells. Three-dimensional theory (survey), Int. Appl. Mech. 27(11), 10351055 (1991).
  • [122]
    Y.N. Nemish and I.Y. Khoma, Stress-strain state of non-thin plates and shells. Generalized theory (survey), Int. Appl. Mech. 29(11), 873902 (1993).
  • [123]
    U.K. Nigul, The hypothesis-free linear dynamic equations for elastic circular cylindrical shell (in Russian), Proc. Tallinn Politekhn. 176, 168 (1960).
  • [124]
    U.K. Nigul, Asymptotic theory of statics and dynamics of elastic circular cylindrical shells, J. Appl. Math. Mech. 26(5), 13931403 (1962).
  • [125]
    U.K. Nigul, Regions of effective application of the methods of three-dimensional and two-dimensional analysis of transient waves in shells and plates, Int. J. Solids Struct. 5(6), 607627 (1969).
  • [126]
    M.U. Nikabadze, A new kinematic hypothesis and new equations of motion and equilibrium in the theory of shells and planar curvilinear rods, Moscow Univ. Math. Bull.(6), 54–61 (1991).
  • [127]
    M.U. Nikabadze, On the christoffel symbols and the second tensor of the surface for the new parametrization of the shell space, Moscow Univ. Math. Bull.(3), 41–45 (2000).
  • [128]
    M.U. Nikabadze, On unit tensors of second and fourth rank for the new parametrization of the shell space, Moscow Univ. Math. Bull.(6), 25–28 (2000).
  • [129]
    M.U. Nikabadze, Several geometric relations of the theory of shells with two reference surfaces, Mech. Solids 35(1), 4145 (2000).
  • [130]
    M.U. Nikabadze, Location gradients in the theory of shells with two basic surfaces, Mech. Solids 36(4), 6469 (2001).
  • [131]
    M.U. Nikabadze, To a version of the theory of multilayer structures, Mech. Solids 36(1), 119129 (2001).
  • [132]
    M.U. Nikabadze, A version of the system of equations of the theory of thin solids, Moscow Univ. Math. Bull.(1), 30–35 (2006).
  • [133]
    M.U. Nikabadze, Some numbers concerning a version of the theory of thin solids based on expansions in a system of Chebyshev polynomials of the second kind, Mech. Solids 42(3), 391421 (2007).
  • [134]
    M.U. Nikabadze and A.R. Ulukhanyan, Statements of problems for a thin deformable three-dimensional body, Moscow Univ. Math. Bull.(6), 43–49 (2005).
  • [135]
    V.V. Novozhilov, The Theory of Thin Shells (Nordhof Ltd., Groningen, 1959).
  • [136]
    I.P. Obraztsov, S.A. Lurie, and P.A. Belov, Generalized expansions in applied problems of elasticity theory, with applications to problems in the mechanics of composite structures (in Russian), J. Compos. Mech. Design 3(3), 6279 (1997).
  • [137]
    V.V. Poniatovskiy, On the theory of bending of medium-thickness plates, J. Appl. Math. Mech. 26(2), 335341 (1962).
  • [138]
    V.V. Poniatovskiy, On the theory of bending of anisotropic plates, J. Appl. Math. Mech. 28(6), 10331039 (1964).
  • [139]
    V.K. Prokopov, Application of the symbolic method to the derivation of the equations of the theory of plates, J. Appl. Math. Mech. 29(5), 10641083 (1965).
  • [140]
    J. Rayleigh, On the free vibration of an infinite plate of homogeneous isotropic elastic matter, Proc. Lond. Math. Soc. 17, 411 (1885/1886).
  • [141]
    E. Reissner, On asymptotic expansions for circular cylindrical shells, J. Appl. Mech. 31, 245252 (1964).
  • [142]
    E.L. Riess, Symmetric bending of thick circular plates, J. Soc. Ind. Appl. Math. 10, 596609 (1962).
  • [143]
    C. Schwab, Dimensional Reduction for Elliptic Boundary-Value Problems, Ph.D. thesis. MD 20742 USA, Univ. of Maryland College Park, 1989.
  • [144]
    C. Schwab, Boundary layer resolution in hierarchical models of laminated composites, R.A.I.R.O Anal. Numer. Sér. Rouge 28, 517537 (1994).
  • [145]
    C. Schwab, A-posteriori modeling error estimation for hierarchic plate models, Numer. Math. 74, 221259 (1996).
  • [146]
    C. Schwab and M. Suri, The p and hp Versions of the Finite Element Method for Problems with Boundary Layers, Math. Research Rep. 95-01 (Dept. of Mathematics, UMBC, February 1995).
  • [147]
    C. Schwab and S. Wright, Boundary layer approximation in hierarchical beam and plate models, J. Elast. 38, 140 (1995).
  • [148]
    I.T. Selezov, Investigation of wave processes in cylindrical shells in basis of the generalized theory (in Ukrainian), Prikl. Mekh. 9(5), 480486 (1963).
  • [149]
    A.I. Soler, Higher order effects in thick rectangular elastic beams, Int. J. Solids Struct. 4, 723739 (1968).
  • [150]
    A.I. Soler, Higher-order theories for structural analysis using Legendre polynomial expansions, J. Appl. Mech. 36(4), 757762 (1969).
  • [151]
    P.E. Tovstik, On the asymptotic nature of approximate models of beams, plates, and shells, Vestn. St. Petersbourg Univ. Math. 40(3), 188192 (2007).
  • [152]
    P.E. Tovstik and T.P. Tovstik, On the 2D models of plates and shells including the transversal shear, Z. Angew. Math. Mech. 87(2), 160171 (2007).
  • [153]
    V.A. Trenogin, Functional Analysis (in Russian) (Physmatlit, Moscow, 2002).
  • [154]
    W.B. Krätzig and D. Jun, On “best” shell models – from classical shells, degenerated and multi-layer concepts to 3D, Arch. Apppl. Mech 73, 125 (2003).
  • [155]
    Y.A. Ustinov, On the completeness of a system of homogeneous solutions of the plates theory, J. Appl. Math. Mech. 40(3), 489496 (1976).
  • [156]
    T. Vashakmadze, The Theory of Anisotropic Plates (Kluwer Academic Publishers, Dordrecht-London-Boston, 1999).
  • [157]
    V.V. Vassiliev and S.A. Lurie, The method of homogeneous solutions and biorthogonal expansions in the plane problem of the theory of elasticity for an orthotropic body, J. Appl. Math. Mech. 60, 105112 (1996).
  • [158]
    I.N. Vekua, On the method of analysis for prismatic shells (in Russian), Proc. Tbilis. Mathem. Inst. 21, 191259 (1955).
  • [159]
    I.N. Vekua, On the Variant of Thin Shallow Shells Theory (in Russian) (Gos. Univ., Novosibirsk, 1964).
  • [160]
    I.N. Vekua, Theory of Thin Shallow Shells with Variable Thickness (in Russian) (Gos. Univ., Novosibirsk, 1964).
  • [161]
    I.N. Vekua, Thin and Shallow Elastic Shells with Variable Thickness, in: Application of Theory of Functions to the Continuum Mechanics (Nauka, Moscow, 1965).
  • [162]
    I.N. Vekua, Fundamentals of Tensor Analysis and Theory of Covariants (in Russian) (Nauka, Moscow, 1978).
  • [163]
    I.N. Vekua, Shell Theory: General Methods of Construction (Pitman Advanced Publ. Program, Boston, 1985).
  • [164]
    M. Vogelius and I. Babuŝka, On a dimensional reduction method, Math. Comput. 37, 3168 (1981).
  • [165]
    I.I. Vorovich, Some Mathematical Problems of the Theory of Plates and Shells (Nauka, Moscow, 1966).
  • [166]
    I.I. Vorovich, Some Results and Problems of the Asymptotic Plate and Shell Theory (in Russian), in: Proc. I School for Plate and Shell Theory and Numer. Meth., Gegechkori 1974 (Tbil. State Univ., Tbilisi, 1974), pp. 51–149.
  • [167]
    I.I. Vorovich and O.K. Aksentian, The state of stress in a thin plate, J. Appl. Math. Mech. 27(6), 16211643 (1963).
  • [168]
    M.V. Wilde, L.Y. Kossovich, and Y.V. Shevtsova, Asymptotic integration of dynamic equations of elasticity theory for thin multilayer shells (in Russian), Vestn. Saratov. Univ. New Ser., Math., Mekh., Inform. 12(2), 5664 (2012).
  • [169]
    S.I. Zhavoronok, Generalized Lagrange equations of the second kind of three-dimensional anisotropic shell theory (in Russian), J. Compos. Mech. Design 17(1), 116132 (1999).
  • [170]
    S.I. Zhavoronok, High-order anisotropic shells models (in Russian), J. Compos. Mech. Design 14(4), 561571 (2008).
  • [171]
    S.I. Zhavoronok, Investigation of harmonic waves in elastic layer using N-th order three-dimensional shells theory (in Russian), J. Compos. Mech. Design 16(4/2), 693701 (2010).
  • [172]
    S.I. Zhavoronok, Investigation of propagating modes of harmonic waves in elastic layer using N-th order three-dimensional shells theory (in Russian), J. Compos. Mech. Design 17(2), 278287 (2011).
  • [173]
    S.I. Zhavoronok, Variational equations for 3D theory for anisotropic shells (in Russian), Vestn. UNN 5, 21532155 (2011).
  • [174]
    S.I. Zhavoronok, A formulation of the three-dimensional approximated shells theory of N-th order using generalized displacements and its application to steady dynamics (in Russian), J. Compos. Mech. Design 18(3), 333344 (2012).
  • [175]
    S.I. Zhavoronok, Kinematics of normal modes in elastic layer for some wavenumbers investigation based on N-th order three-dimensional shells theory (in Russian), J. Compos. Mech. Design 18(1), 4556 (2012).
  • [176]
    S.I. Zhavoronok, M.Y. Kuprikov, A.L. Medvedsky, and L.N. Rabinsky, Analytical and Numerical Methods of Solution for Problems of Diffraction of Acoustical Waves on Solids and Shells (in Russian) (Physmatlit, Moscow, 2010).
  • [177]
    S.I. Zhavoronok, A.N. Leontiev, and K.A. Leontiev, Analysis of thick-walled rotation's shells based on Legendre polynomials, Int. J. Comput. Civil Struct. Eng. 6(1–2), 105111 (2010).
  • [178]
    S.I. Zhavoronok and L.N. Rabinskiy, An axisymmetric problem of interaction of acoustical wave and elastic shell of revolution, J. Compos. Mech. Design 12(4), 12511265 (2006).
  • [179]
    V.S. Zhgenti, To investigation of stress state of isotropic thick-walled shells of nonhomogeneous structure, Appl. Mech. 27(5), 3744 (1991).
  • [180]
    P.A. Zhilin, Simple edge effect on the basis of shell theories and three-dimensional elasticity theory, Mech. Solids 5, 137142 (1983).
  • [181]
    E.I. Zveriaev and G.I. Makarov, A general method for constructing Timoshenko-type theories, J. Appl. Math. Mech. 72(2), 197207 (2008).