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Mat. Sb., 2000, Volume 191, Number 7, Pages 129–159 (Mi msb495)  

This article is cited in 18 scientific papers (total in 18 papers)

Asymptotic analysis of an arbitrary anisotropic plate of variable thickness (sloping shell)

S. A. Nazarov

Saint-Petersburg State University

Abstract: The leading terms of the asymptotics of the solution of the problem of elasticity theory for a thin plane with curved bases are constructed; in addition, the resulting problem (a two-dimensional model) is written out explicitly. Arbitrary anisotropy of elastic properties is allowed; moreover, these properties may depend on the “rapid” transversal and the “slow” longitudinal variables. The substantiation of these asymptotics is carried out on the basis of Korn's weighted inequality. The cases of laminated plates, sloping shells, and plates with sharp edges are discussed separately.


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English version:
Sbornik: Mathematics, 2000, 191:7, 1075–1106

Bibliographic databases:

UDC: 517.946+539.3
MSC: 74B05, 74E10, 35B40
Received: 25.01.1999

Citation: S. A. Nazarov, “Asymptotic analysis of an arbitrary anisotropic plate of variable thickness (sloping shell)”, Mat. Sb., 191:7 (2000), 129–159; Sb. Math., 191:7 (2000), 1075–1106

Citation in format AMSBIB
\by S.~A.~Nazarov
\paper Asymptotic analysis of an~arbitrary anisotropic plate of variable thickness (sloping shell)
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 7
\pages 129--159
\jour Sb. Math.
\yr 2000
\vol 191
\issue 7
\pages 1075--1106

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    This publication is cited in the following articles:
    1. Akimova E.A., Nazarov S.A., Chechkin G.A., “Weighted Korn inequality: The Tetris procedure for an arbitrary periodic plate”, Dokl. Math., 64:2 (2001), 205–207  mathnet  mathscinet  zmath  isi  elib
    2. S. A. Nazarov, A. S. Slutskij, “Arbitrary Plane Systems of Anisotropic Beams”, Proc. Steklov Inst. Math., 236 (2002), 222–249  mathnet  mathscinet  zmath
    3. Nazarov S.A., “Estimating the convergence rate for eigenfrequencies of anisotropic plates with variable thickness”, C. R., Méc., Acad. Sci. Paris, 330:9 (2002), 603–607  crossref  zmath  isi  elib  scopus  scopus
    4. Jaiani G., Kharibegashvili S., Natroshvili D., Wendland W.L., “Two-dimensional hierarchical models for prismatic shells with thickness vanishing at the boundary”, J. Elasticity, 77:2 (2004), 95–122  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. S. A. Nazarov, J. Sokolowski, “The topological derivative of the Dirichlet integral under formation of a thin ligament”, Siberian Math. J., 45:2 (2004), 341–355  mathnet  crossref  mathscinet  zmath  isi  elib
    6. S. A. Nazarov, “Estimates for second order derivatives of eigenvectors in thin anisotropic plates with variable thickness”, J. Math. Sci. (N. Y.), 132:1 (2006), 91–102  mathnet  crossref  mathscinet  zmath  elib  elib
    7. S. A. Nazarov, “Weighted anisotropic Korn's inequality for a junction of a plate and a rod”, Sb. Math., 195:4 (2004), 553–583  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. S. A. Nazarov, “Korn inequalities for elastic junctions of massive bodies, thin plates, and rods”, Russian Math. Surveys, 63:1 (2008), 35–107  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Cardone G., Nazarov S.A., Taskinen J., “A criterion for the existence of the essential spectrum for beak-shaped elastic bodies”, J. Math. Pures Appl. (9), 92:6 (2009), 628–650  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    10. Cardone G., Nazarov S.A., Taskinen J., ““Absorption” effect for elastic waves by the beak-shaped boundary irregularity”, Dokl. Phys., 54:3 (2009), 146–150  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
    11. G. Buttazzo, S. A. Nazarov, “An optimization problem for the Biharmonic equation with Sobolev conditions”, J Math Sci, 2011  crossref  mathscinet  elib  scopus  scopus  scopus
    12. S. A. Nazarov, G. H. Sweers, A. S. Slutskij, “Homogenization of a thin plate reinforced with periodic families of rigid rods”, Sb. Math., 202:8 (2011), 1127–1168  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. Leugering G.R., Nazarov S.A., Slutskij A.S., “Asymptotic Analysis of 3D Thin Anisotropic Plates with a Piezoelectric Patch”, Math. Meth. Appl. Sci., 35:6 (2012), 633–658  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    14. S. A. Nazarov, “Asymptotics of eigen-oscillations of a massive elastic body with a thin baffle”, Izv. Math., 77:1 (2013), 87–142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. Buttazzo G., Cardone G., Nazarov S.A., “Thin Elastic Plates Supported Over Small Areas. i: Korn'S Inequalities and Boundary Layers”, J. Convex Anal., 23:2 (2016), 347–386  mathscinet  zmath  isi
    16. Buttazzo G., Cardone G., Nazarov S.A., “Thin Elastic Plates Supported Over Small Areas. II: Variational-Asymptotic Models”, J. Convex Anal., 24:3 (2017), 819–855  mathscinet  zmath  isi
    17. S. A. Nazarov, “‘Blinking’ and ‘gliding’ eigenfrequencies of oscillations of elastic bodies with blunted cuspidal sharpenings”, Sb. Math., 210:11 (2019), 1633–1662  mathnet  crossref  crossref  adsnasa  isi
    18. S. A. Nazarov, “Construction of a trapped mode with a small frequency in an elastic waveguide”, Funct. Anal. Appl., 54:1 (2020), 31–44  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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