On equations of the linear theory of shells with surface stresses taken into account

We construct equations of equilibrium and constitutive relations of linear theory of plates and shells with transverse shear strain taken into account, which are based on reducing the spatial elasticity relations with surface stresses taken into account to two-dimensional equations given on the shel...

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Published inMechanics of solids Vol. 45; no. 3; pp. 331 - 342
Main Authors Altenbach, H., Eremeev, V. A., Morozov, N. F.
Format Journal Article
LanguageEnglish
Published Heidelberg Allerton Press, Inc 01.06.2010
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ISSN0025-6544
1934-7936
DOI10.3103/S0025654410030040

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Abstract We construct equations of equilibrium and constitutive relations of linear theory of plates and shells with transverse shear strain taken into account, which are based on reducing the spatial elasticity relations with surface stresses taken into account to two-dimensional equations given on the shell median surface. We analyze the influence of surface elasticity moduli on the effective stiffness of plates and shells.
AbstractList We construct equations of equilibrium and constitutive relations of linear theory of plates and shells with transverse shear strain taken into account, which are based on reducing the spatial elasticity relations with surface stresses taken into account to two-dimensional equations given on the shell median surface. We analyze the influence of surface elasticity moduli on the effective stiffness of plates and shells.
Author Eremeev, V. A.
Morozov, N. F.
Altenbach, H.
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  surname: Eremeev
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  organization: St. Petersburg State University
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Cites_doi 10.1016/j.ijsolstr.2005.07.036
10.1103/PhysRevB.73.235409
10.1088/0957-4484/11/3/301
10.1103/PhysRevB.69.165410
10.1007/BF00380381
10.1016/j.surfrep.2005.08.002
10.1016/j.ijsolstr.2007.08.006
10.1016/j.jmps.2008.01.004
10.1098/rspa.2005.1637
10.1063/1.2071453
10.1007/s00419-007-0192-3
10.1016/S0065-2156(08)00001-X
10.1093/qjmam/29.3.245
10.1017/CBO9780511574511
10.1016/S0020-7683(99)00057-8
10.1098/rspa.1999.0320
10.1016/j.jmps.2005.02.009
10.1016/S0039-6028(99)01174-7
10.1016/j.ijsolstr.2008.10.012
10.1016/0167-5729(95)00007-0
10.1016/j.physe.2008.06.025
10.1002/9780470172872
10.1103/PhysRevLett.96.075505
10.1098/rspa.1970.0091
10.1016/0022-5096(93)90037-G
10.1007/BF00250426
10.1098/rstl.1805.0005
10.1007/978-3-642-69567-4_5
10.1007/BF00261375
10.1007/978-1-4613-8584-4
10.1007/978-94-015-9379-3
10.1007/978-3-662-08589-9
10.1142/7826
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Keywords surface stresses
plates
shells
effective stiffnesses
surface tension
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References Wang, Reddy, Lee (CR49) 2000
Steigmann, Ogden (CR22) 1999; 455
Eremeyev, Altenbach, Morozov (CR32) 2009; 424
Zubov (CR37) 1982
Orowan (CR12) 1970; 316
Young (CR10) 1805; 95
Altenbach, Altenbach, Kissing (CR47) 2004
Guo, Zhao (CR30) 2005; 98
Zhilin (CR43) 2001
Chen, Shi, Zhang (CR7) 2006; 96
Gurtin, Murdoch (CR18) 1975; 59
Goldenveizer (CR39) 1976
Altenbach, Eremeyev (CR50) 2009; 9
Dahmen, Lehwald, Ibach (CR28) 2000; 446
Grigolyuk, Selezov (CR45) 1973
Wilson (CR42) 1901
Cuenot, Frétigny, Demoustier-Champagne, Nysten (CR5) 2004; 69
Landau, Lifshitz (CR2) 1986
Miller, Shenoy (CR29) 2000; 11
Huang (CR26) 2008; 45
Laplace (CR8) 1805
Rusanov (CR15) 1996; 23
Lu, Lim, Chen (CR31) 2009; 46
Zubov, Karyakin (CR44) 2006
Rubin (CR55) 2000
Gurtin, Murdoch (CR17) 1975; 57
Duan, Wang, Huang, Karihaloo (CR4) 2005; 53
Podio-Guidugli, Caffarelli (CR20) 1990; 109
Lu, He, Lee, Lu (CR24) 2006; 43
Timoshenko, Woinowsky-Krieger (CR38) 1959
Finn (CR14) 1986
Lebedev, Cloud, Eremeyev (CR41) 2010
Gibbs (CR11) 1928
Altenbach, Zhilin (CR33) 1988; 11
Peng, Wu, Hwang (CR27) 2008; 56
Grigolyuk, Chulkov (CR46) 1973
CR54
Laplace (CR9) 1805
Duan, Wang, Karihaloo (CR1) 2008; 42
Rusanov (CR16) 2005; 58
Murdoch (CR19) 1976; 29
Jing, Duan, Sun (CR6) 2006; 73
Podstrigach, Povstenko (CR13) 1985
Chróścielewski, Makowski, Pietraszkiewicz (CR51) 2004
Pietraszkiewicz (CR53) 1979
Altenbach, Eremeyev (CR36) 2008; 78
Povstenko (CR21) 1993; 41
Wang, Duan, Huang, Karihaloo (CR3) 2006; 462
Zhilin (CR35) 2006
Novozhilov, Chernykh, Mikhailovskii (CR40) 1991
Shi, Guo, Ru (CR25) 2008; 41
Libai, Simmonds (CR52) 1998
Szilard (CR48) 2004
Eremeev, Zubov (CR23) 2008
Altenbach (CR34) 2000; 37
J. Peng (6140_CR27) 2008; 56
6140_CR54
R. E. Miller (6140_CR29) 2000; 11
E. B. Wilson (6140_CR42) 1901
S. P. Timoshenko (6140_CR38) 1959
Yu. Z. Povstenko (6140_CR21) 1993; 41
H. Altenbach (6140_CR36) 2008; 78
J. Chróścielewski (6140_CR51) 2004
H. Altenbach (6140_CR47) 2004
L. M. Zubov (6140_CR37) 1982
Ya. S. Podstrigach (6140_CR13) 1985
T. Young (6140_CR10) 1805; 95
G. Y. Jing (6140_CR6) 2006; 73
K. Dahmen (6140_CR28) 2000; 446
A. I. Rusanov (6140_CR15) 1996; 23
A. Libai (6140_CR52) 1998
L. M. Zubov (6140_CR44) 2006
S. Cuenot (6140_CR5) 2004; 69
C. Q. Chen (6140_CR7) 2006; 96
D. W. Huang (6140_CR26) 2008; 45
P. A. Zhilin (6140_CR43) 2001
P. S. Laplace (6140_CR8) 1805
E. Orowan (6140_CR12) 1970; 316
L. D. Landau (6140_CR2) 1986
H. Altenbach (6140_CR34) 2000; 37
C. M. Wang (6140_CR49) 2000
M. E. Gurtin (6140_CR18) 1975; 59
W. Pietraszkiewicz (6140_CR53) 1979
A. I. Rusanov (6140_CR16) 2005; 58
P. Lu (6140_CR24) 2006; 43
J. G. Guo (6140_CR30) 2005; 98
H. Altenbach (6140_CR33) 1988; 11
E. I. Grigolyuk (6140_CR45) 1973
H. L. Duan (6140_CR1) 2008; 42
V. A. Eremeyev (6140_CR32) 2009; 424
R. Finn (6140_CR14) 1986
J. Wang (6140_CR3) 2006; 462
J. W. Gibbs (6140_CR11) 1928
P. A. Zhilin (6140_CR35) 2006
D. J. Steigmann (6140_CR22) 1999; 455
A. I. Murdoch (6140_CR19) 1976; 29
P. S. Laplace (6140_CR9) 1805
R. Szilard (6140_CR48) 2004
M. B. Rubin (6140_CR55) 2000
H. Altenbach (6140_CR50) 2009; 9
A. L. Goldenveizer (6140_CR39) 1976
E. I. Grigolyuk (6140_CR46) 1973
H. L. Duan (6140_CR4) 2005; 53
P. Podio-Guidugli (6140_CR20) 1990; 109
V. V. Novozhilov (6140_CR40) 1991
V. A. Eremeev (6140_CR23) 2008
M. E. Gurtin (6140_CR17) 1975; 57
C. F. Lu (6140_CR31) 2009; 46
L. P. Lebedev (6140_CR41) 2010
Y. J. Shi (6140_CR25) 2008; 41
References_xml – year: 1805
  ident: CR9
  article-title: À la Théorie de L’action Capillaire
  publication-title: Supplément au TraitédeMécanique Céleste
– volume: 43
  start-page: 4631
  issue: 16
  year: 2006
  end-page: 4647
  ident: CR24
  article-title: Thin Plate Theory Including Surface Effects
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/j.ijsolstr.2005.07.036
– volume: 73
  start-page: 235409
  issue: 23
  year: 2006
  end-page: 6
  ident: CR6
  article-title: Surface Effects on Elastic Properties of Silver Nanowires: Contact Atomic-Force Microscopy
  publication-title: Phys. Rev. B
  doi: 10.1103/PhysRevB.73.235409
– volume: 11
  start-page: 139
  issue: 3
  year: 2000
  end-page: 147
  ident: CR29
  article-title: Size-Dependent Elastic Properties of Nanosized Structural Elements
  publication-title: Nanotech.
  doi: 10.1088/0957-4484/11/3/301
– year: 1901
  ident: CR42
  publication-title: Vector Analysis, Founded upon the Lectures of J. W. Gibbs
– volume: 69
  start-page: 165410
  issue: 16
  year: 2004
  end-page: 5
  ident: CR5
  article-title: Surface TensionEffect on the Mechanical Properties of Nanomaterials Measured by Atomic Force Microscopy
  publication-title: Phys. Rev. B
  doi: 10.1103/PhysRevB.69.165410
– year: 1959
  ident: CR38
  publication-title: Theory of Plates and Shells
– volume: 109
  start-page: 343
  issue: 4
  year: 1990
  end-page: 383
  ident: CR20
  article-title: Surface Interaction Potentials in Elasticity
  publication-title: Arch. Rational Mech. Anal.
  doi: 10.1007/BF00380381
– year: 2004
  ident: CR51
  publication-title: Statics and Dynamics of Multifold Shells: Nonlinear Theory and Finite Element Method
– year: 2004
  ident: CR47
  publication-title: Mechanics of Composite Structural Elements
– ident: CR54
– year: 1805
  ident: CR8
  article-title: Sur L’action Capillaire
  publication-title: Supplément au Traitéde Mécanique Céleste
– year: 2006
  ident: CR35
  publication-title: Applied Mechanics. Foundations of Shell Theory
– year: 2010
  ident: CR41
  publication-title: Tensor Analysis with Applications in Mechanics
– volume: 58
  start-page: 111
  issue: 5–8
  year: 2005
  end-page: 239
  ident: CR16
  article-title: Surface Thermodynamics Revisited
  publication-title: Surf. Sci. Rep.
  doi: 10.1016/j.surfrep.2005.08.002
– volume: 45
  start-page: 568
  issue: 2
  year: 2008
  end-page: 579
  ident: CR26
  article-title: Size-Dependent Response of Ultra-Thin Films with Surface Effects
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/j.ijsolstr.2007.08.006
– year: 1986
  ident: CR2
  publication-title: , Vol. 6:
– year: 1985
  ident: CR13
  publication-title: Introduction to Mechanics of Surface Phenomena in Strained Rigid Bodies
– volume: 56
  start-page: 2213
  issue: 6
  year: 2008
  end-page: 2224
  ident: CR27
  article-title: Can a Single-Wall Carbon Nanotube be Modeled as a Thin Shell?
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/j.jmps.2008.01.004
– volume: 462
  start-page: 1355
  issue: 2069
  year: 2006
  end-page: 1363
  ident: CR3
  article-title: A Scaling Law for Properties of Nano-Structured Materials
  publication-title: Proc. Roy. Soc. London. Ser. A
  doi: 10.1098/rspa.2005.1637
– year: 1986
  ident: CR14
  publication-title: Equilibrium Capillary Surfaces
– volume: 98
  start-page: 074306
  issue: 7
  year: 2005
  end-page: 11
  ident: CR30
  article-title: The Size-Dependent Elastic Properties of Nanofilms with Surface Effects
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.2071453
– year: 2008
  ident: CR23
  publication-title: Mechanics of Elastic Shells
– volume: 78
  start-page: 775
  issue: 10
  year: 2008
  end-page: 794
  ident: CR36
  article-title: Direct Approach Based Analysis of Plates Composed of Functionally Graded Materials
  publication-title: Arch. Appl. Mech.
  doi: 10.1007/s00419-007-0192-3
– volume: 42
  start-page: 1
  year: 2008
  end-page: 63
  ident: CR1
  article-title: Theory of Elasticity at the Nanoscale
  publication-title: Adv. Appl. Mech.
  doi: 10.1016/S0065-2156(08)00001-X
– volume: 29
  start-page: 245
  issue: 3
  year: 1976
  end-page: 274
  ident: CR19
  article-title: A Thermodynamical Theory of Elastic Material Interfaces
  publication-title: Quart. J. Mech. Appl. Math.
  doi: 10.1093/qjmam/29.3.245
– year: 2006
  ident: CR44
  publication-title: Tensor Calculus. Foundations of the Theory
– year: 1973
  ident: CR46
  publication-title: Stability and Vibrations of Three-Layer Shells
– year: 1998
  ident: CR52
  publication-title: The Nonlinear Theory of Elastic Shells
  doi: 10.1017/CBO9780511574511
– volume: 37
  start-page: 3503
  issue: 25
  year: 2000
  end-page: 3520
  ident: CR34
  article-title: An Alternative Determination of Transverse Shear Stiffness for Sandwich and Laminated Plates
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/S0020-7683(99)00057-8
– year: 1973
  ident: CR45
  article-title: Nonclassical Theories of Rod, Plate, and Shell Vibrations
  publication-title: , Vol. 5
– volume: 455
  start-page: 437
  issue: 1982
  year: 1999
  end-page: 474
  ident: CR22
  article-title: Elastic Surface-Substrate Interactions
  publication-title: Proc. Roy. Soc. London. Ser.A
  doi: 10.1098/rspa.1999.0320
– volume: 53
  start-page: 1574
  issue: 7
  year: 2005
  end-page: 1596
  ident: CR4
  article-title: Size-Dependent Effective Elastic Constants of Solids Containing Nano-Inhomogeneities with Interface Stress
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/j.jmps.2005.02.009
– volume: 11
  start-page: 107
  issue: 4
  year: 1988
  end-page: 148
  ident: CR33
  article-title: General Theory of Elastic Simple Shells
  publication-title: Uspekhi Mekh.
– year: 2000
  ident: CR49
  publication-title: Shear Deformable Beams and Shells
– volume: 9
  start-page: 153
  issue: 2
  year: 2009
  end-page: 178
  ident: CR50
  article-title: Eigen-Vibrations of Plates Made of Functionally Graded Material
  publication-title: CMC
– volume: 446
  start-page: 161
  issue: 1–2
  year: 2000
  end-page: 173
  ident: CR28
  article-title: Bending of Crystalline Plates under the Influence of Surface Stress-a Finite Element Analysis
  publication-title: Surf. Sci.
  doi: 10.1016/S0039-6028(99)01174-7
– volume: 46
  start-page: 1176
  issue: 5
  year: 2009
  end-page: 1185
  ident: CR31
  article-title: Size-Dependent Elastic Behavior of FGM Ultra-Thin Films Based on Generalized Refined Theory
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/j.ijsolstr.2008.10.012
– year: 1976
  ident: CR39
  publication-title: Theory of Thin Elastic Shells
– volume: 23
  start-page: 173
  issue: 6–8
  year: 1996
  end-page: 247
  ident: CR15
  article-title: Thermodynamics of Solid Surfaces
  publication-title: Surf. Sci. Rep.
  doi: 10.1016/0167-5729(95)00007-0
– volume: 41
  start-page: 213
  issue: 2
  year: 2008
  end-page: 219
  ident: CR25
  article-title: Relevance of Timoshenko-Beam Model to Microtubules of Low Shear Modulus
  publication-title: Phys. E: Low-Dimens. Syst. Nanostruct.
  doi: 10.1016/j.physe.2008.06.025
– year: 2004
  ident: CR48
  publication-title: Theories and Applications of Plate Analysis. Classical, Numerical, and Engineering Methods
  doi: 10.1002/9780470172872
– volume: 96
  start-page: 075505
  issue: 7
  year: 2006
  end-page: 4
  ident: CR7
  article-title: Size Dependence of Young’s Modulus in ZnO Nanowires
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.96.075505
– volume: 316
  start-page: 473
  issue: 1527
  year: 1970
  end-page: 491
  ident: CR12
  article-title: Surface Energy and Surface Tension in Solids and Fluids
  publication-title: Proc. Roy. Soc. London. Ser. A
  doi: 10.1098/rspa.1970.0091
– volume: 424
  start-page: 618
  issue: 5
  year: 2009
  end-page: 621
  ident: CR32
  article-title: The Influence of Surface Tension on the Effective Stiffness of Nanosize Plates
  publication-title: Dokl. Ross. Akad. Nauk
– year: 1982
  ident: CR37
  publication-title: Methods of Nonlinear Elasticity in Shell Theory
– year: 2000
  ident: CR55
  publication-title: Cosserat Theories: Shells, Rods, and Points
– volume: 57
  start-page: 291
  issue: 4
  year: 1975
  end-page: 323
  ident: CR17
  article-title: A Continuum Theory of Elastic Material Surfaces
  publication-title: Rational Mech. Anal.
– year: 2001
  ident: CR43
  publication-title: Vector and Second-Rank Tensors in Three-Dimensional Space
– year: 1991
  ident: CR40
  publication-title: The Linear Theory of Thin Shells
– volume: 41
  start-page: 1499
  issue: 9
  year: 1993
  end-page: 1514
  ident: CR21
  article-title: Theoretical Investigation of Phenomena Caused by Heterogeneous Surface Tension in Solids
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/0022-5096(93)90037-G
– start-page: 55
  year: 1928
  end-page: 353
  ident: CR11
  article-title: On the Equilibrium of Heterogeneous Substances
  publication-title: The Collected Works of J. Willard Gibbs
– volume: 59
  start-page: 389
  issue: 4
  year: 1975
  end-page: 390
  ident: CR18
  article-title: Addenda to Our Paper: A Continuum Theory of ElasticMaterial Surfaces
  publication-title: Arch. Rational Mech. Anal.
  doi: 10.1007/BF00250426
– year: 1979
  ident: CR53
  publication-title: Finite Rotations and Lagrangian Description in the Nonlinear Theory of Shells
– volume: 95
  start-page: 65
  year: 1805
  end-page: 87
  ident: CR10
  article-title: An Essay on the Cohesion of Fluids
  publication-title: Phil. Trans. Roy. Soc. London
  doi: 10.1098/rstl.1805.0005
– volume: 96
  start-page: 075505
  issue: 7
  year: 2006
  ident: 6140_CR7
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.96.075505
– volume-title: Supplément au TraitédeMécanique Céleste
  year: 1805
  ident: 6140_CR9
– volume: 78
  start-page: 775
  issue: 10
  year: 2008
  ident: 6140_CR36
  publication-title: Arch. Appl. Mech.
  doi: 10.1007/s00419-007-0192-3
– volume: 95
  start-page: 65
  year: 1805
  ident: 6140_CR10
  publication-title: Phil. Trans. Roy. Soc. London
  doi: 10.1098/rstl.1805.0005
– volume: 316
  start-page: 473
  issue: 1527
  year: 1970
  ident: 6140_CR12
  publication-title: Proc. Roy. Soc. London. Ser. A
  doi: 10.1098/rspa.1970.0091
– volume-title: Vector Analysis, Founded upon the Lectures of J. W. Gibbs
  year: 1901
  ident: 6140_CR42
– volume-title: Results in Science and Technology. Mechanics of Deformable Solids, Vol. 5
  year: 1973
  ident: 6140_CR45
– volume-title: Statics and Dynamics of Multifold Shells: Nonlinear Theory and Finite Element Method
  year: 2004
  ident: 6140_CR51
– volume: 11
  start-page: 139
  issue: 3
  year: 2000
  ident: 6140_CR29
  publication-title: Nanotech.
  doi: 10.1088/0957-4484/11/3/301
– volume: 45
  start-page: 568
  issue: 2
  year: 2008
  ident: 6140_CR26
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/j.ijsolstr.2007.08.006
– ident: 6140_CR54
  doi: 10.1007/978-3-642-69567-4_5
– volume: 43
  start-page: 4631
  issue: 16
  year: 2006
  ident: 6140_CR24
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/j.ijsolstr.2005.07.036
– volume: 57
  start-page: 291
  issue: 4
  year: 1975
  ident: 6140_CR17
  publication-title: Rational Mech. Anal.
  doi: 10.1007/BF00261375
– volume: 11
  start-page: 107
  issue: 4
  year: 1988
  ident: 6140_CR33
  publication-title: Uspekhi Mekh.
– volume-title: Methods of Nonlinear Elasticity in Shell Theory
  year: 1982
  ident: 6140_CR37
– volume-title: Equilibrium Capillary Surfaces
  year: 1986
  ident: 6140_CR14
  doi: 10.1007/978-1-4613-8584-4
– volume: 455
  start-page: 437
  issue: 1982
  year: 1999
  ident: 6140_CR22
  publication-title: Proc. Roy. Soc. London. Ser.A
  doi: 10.1098/rspa.1999.0320
– volume-title: Cosserat Theories: Shells, Rods, and Points
  year: 2000
  ident: 6140_CR55
  doi: 10.1007/978-94-015-9379-3
– volume: 41
  start-page: 1499
  issue: 9
  year: 1993
  ident: 6140_CR21
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/0022-5096(93)90037-G
– volume: 41
  start-page: 213
  issue: 2
  year: 2008
  ident: 6140_CR25
  publication-title: Phys. E: Low-Dimens. Syst. Nanostruct.
  doi: 10.1016/j.physe.2008.06.025
– volume-title: Finite Rotations and Lagrangian Description in the Nonlinear Theory of Shells
  year: 1979
  ident: 6140_CR53
– volume-title: Theory of Plates and Shells
  year: 1959
  ident: 6140_CR38
– volume-title: Applied Mechanics. Foundations of Shell Theory
  year: 2006
  ident: 6140_CR35
– volume-title: Mechanics of Composite Structural Elements
  year: 2004
  ident: 6140_CR47
  doi: 10.1007/978-3-662-08589-9
– volume: 424
  start-page: 618
  issue: 5
  year: 2009
  ident: 6140_CR32
  publication-title: Dokl. Ross. Akad. Nauk
– volume-title: Theory of Thin Elastic Shells
  year: 1976
  ident: 6140_CR39
– volume-title: Introduction to Mechanics of Surface Phenomena in Strained Rigid Bodies
  year: 1985
  ident: 6140_CR13
– volume: 56
  start-page: 2213
  issue: 6
  year: 2008
  ident: 6140_CR27
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/j.jmps.2008.01.004
– volume: 58
  start-page: 111
  issue: 5–8
  year: 2005
  ident: 6140_CR16
  publication-title: Surf. Sci. Rep.
  doi: 10.1016/j.surfrep.2005.08.002
– volume-title: Theories and Applications of Plate Analysis. Classical, Numerical, and Engineering Methods
  year: 2004
  ident: 6140_CR48
  doi: 10.1002/9780470172872
– volume-title: The Linear Theory of Thin Shells
  year: 1991
  ident: 6140_CR40
– volume-title: Shear Deformable Beams and Shells
  year: 2000
  ident: 6140_CR49
– volume: 37
  start-page: 3503
  issue: 25
  year: 2000
  ident: 6140_CR34
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/S0020-7683(99)00057-8
– volume-title: Tensor Calculus. Foundations of the Theory
  year: 2006
  ident: 6140_CR44
– volume: 42
  start-page: 1
  year: 2008
  ident: 6140_CR1
  publication-title: Adv. Appl. Mech.
– volume-title: Course of Theoretical Physics, Vol. 6: Hydrodynamics
  year: 1986
  ident: 6140_CR2
– volume: 109
  start-page: 343
  issue: 4
  year: 1990
  ident: 6140_CR20
  publication-title: Arch. Rational Mech. Anal.
  doi: 10.1007/BF00380381
– volume-title: Stability and Vibrations of Three-Layer Shells
  year: 1973
  ident: 6140_CR46
– volume: 53
  start-page: 1574
  issue: 7
  year: 2005
  ident: 6140_CR4
  publication-title: J. Mech. Phys. Solids
  doi: 10.1016/j.jmps.2005.02.009
– volume-title: The Nonlinear Theory of Elastic Shells
  year: 1998
  ident: 6140_CR52
  doi: 10.1017/CBO9780511574511
– start-page: 55
  volume-title: The Collected Works of J. Willard Gibbs
  year: 1928
  ident: 6140_CR11
– volume: 98
  start-page: 074306
  issue: 7
  year: 2005
  ident: 6140_CR30
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.2071453
– volume-title: Vector and Second-Rank Tensors in Three-Dimensional Space
  year: 2001
  ident: 6140_CR43
– volume: 446
  start-page: 161
  issue: 1–2
  year: 2000
  ident: 6140_CR28
  publication-title: Surf. Sci.
  doi: 10.1016/S0039-6028(99)01174-7
– volume: 73
  start-page: 235409
  issue: 23
  year: 2006
  ident: 6140_CR6
  publication-title: Phys. Rev. B
  doi: 10.1103/PhysRevB.73.235409
– volume: 23
  start-page: 173
  issue: 6–8
  year: 1996
  ident: 6140_CR15
  publication-title: Surf. Sci. Rep.
  doi: 10.1016/0167-5729(95)00007-0
– volume: 9
  start-page: 153
  issue: 2
  year: 2009
  ident: 6140_CR50
  publication-title: CMC
– volume: 462
  start-page: 1355
  issue: 2069
  year: 2006
  ident: 6140_CR3
  publication-title: Proc. Roy. Soc. London. Ser. A
  doi: 10.1098/rspa.2005.1637
– volume: 69
  start-page: 165410
  issue: 16
  year: 2004
  ident: 6140_CR5
  publication-title: Phys. Rev. B
  doi: 10.1103/PhysRevB.69.165410
– volume: 59
  start-page: 389
  issue: 4
  year: 1975
  ident: 6140_CR18
  publication-title: Arch. Rational Mech. Anal.
  doi: 10.1007/BF00250426
– volume-title: Supplément au Traitéde Mécanique Céleste
  year: 1805
  ident: 6140_CR8
– volume-title: Tensor Analysis with Applications in Mechanics
  year: 2010
  ident: 6140_CR41
  doi: 10.1142/7826
– volume: 29
  start-page: 245
  issue: 3
  year: 1976
  ident: 6140_CR19
  publication-title: Quart. J. Mech. Appl. Math.
  doi: 10.1093/qjmam/29.3.245
– volume-title: Mechanics of Elastic Shells
  year: 2008
  ident: 6140_CR23
– volume: 46
  start-page: 1176
  issue: 5
  year: 2009
  ident: 6140_CR31
  publication-title: Int. J. Solids Struct.
  doi: 10.1016/j.ijsolstr.2008.10.012
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Snippet We construct equations of equilibrium and constitutive relations of linear theory of plates and shells with transverse shear strain taken into account, which...
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SubjectTerms Classical Mechanics
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Title On equations of the linear theory of shells with surface stresses taken into account
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