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IssuesArchive of Issues2014-4pp.403-412

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G.M. Kulikov and S.V. Plotnikova, "Solution of Three-Dimensional Problems for Thick Elastic Shells by the Method of Reference Surfaces," Mech. Solids. 49 (4), 403-412 (2014)
Year 2014 Volume 49 Number 4 Pages 403-412
DOI 10.3103/S0025654414040050
Title Solution of Three-Dimensional Problems for Thick Elastic Shells by the Method of Reference Surfaces
Author(s) G.M. Kulikov (Tambov State Technical University, ul. Sovetskaya 106, Tambov, 392000 Russia, kulikov@apmath.tstu.ru)
S.V. Plotnikova (Tambov State Technical University, ul. Sovetskaya 106, Tambov, 392000 Russia)
Abstract A new method for solving the elasticity problem for thick and thin shells is proposed. The method is based on the concept of reference surfaces inside the shell. According to this method, N reference surfaces are introduced in the body of the shell so that they are parallel to the midsurface and located at the Chebyshev polynomial nodes, which permits taking the displacement vectors u1,u2,…,uN of these surfaces for the desired functions. This choice of the desired functions allows one to represent the resolving equations of the proposed theory of higher-order shells in a sufficiently concise form and obtain deformation relations which permit describing the shell displacements as motions of a rigid body.
Keywords theory of elasticity, theory of higher-order shells, method of reference surfaces
References
1.  V. V. Novozhilov, Theory of Thin Shells (Sudpromgiz, Leningrad, 1962) [in Russian].
2.  G. M. Kulikov and S. V. Plotnikova, "Solution of Static Problems for a Three-Dimensional Elastic Shell," Dokl. Ross. Akad. Nauk 439 (5), 613-616 (2011) [Dokl. Phys. (Engl. Transl.) 56 (8), 448-451 (2011)]
3.  G. M. Kulikov and S. V. Plotnikova, "On the Use of a New Concept of Sampling Surfaces in Shell Theory," Adv. Struct. Mater. 15, 715-726 (2011).
4.  H. Schoop, "Oberflächenorientierte Schalentheorien endlicher Verschiebungen," Ing.-Archiv. 56 (6), 427-437 (1986).
5.  M. U. Nikabadze, "Parameterization of Shells Based on Two Base Surfaces," Dep. VINITI AN SSSR 12.07.88 No. 5588-B88.
6.  Y. H. Kim and S. W. Lee, "A Solid Element Formulation for Large Deflection Analysis of Composite Shell Structures," Comp. Struct. 30 (1-2), 269-274 (1988).
7.  G. M. Kulikov and S. V. Plotnikova, "Comparative Analysis of Two Algorithms for Numerical Solution of Nonlinear Static Problems for Multilayer Anisotropic Shells of Revolution," Mekh. Komp. Mater. 35 (4), 435-446 (1999).
8.  M. U. Nikabadze, "Some Geometric Relations in the Theory of Shells with Two Reference Surfaces," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 129-139 (2000) [Mech. Solids (Engl. Transl.) 35 (4), 109-116 (2000)].
9.  G. M. Kulikov and S. V. Plotnikova. "Finite Deformation Plate Theory and Large Rigid-Body Motions," Int. J. Nonlin. Mech. 39 (7), 1093-1109 (2004).
10.  C. Runge, "Über empirische Functional and die Interpolation zwischen äquidistanten Ordinated," ZAMP, 46, 224-243 (1901).
11.  N. S. Bakhvalov, Numerical Methods, Vol. 1 (Nauka, Moscow, 1973).
12.  G. M. Kulikov, "Strain-Displacement Relationships That Exactly Represent Large Rigid Displacements of a Shell," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 130-140 (2004) [Mech. Solids (Engl. Transl.) 39 (5), 105-113 (2004)].
13.  G. M. Kulikov and S. V. Plotnikova, "Nonlinear Strain-Displacements Equations Exactly Representing Large Rigid-Body Motions. Part II. Enhanced Finite Element Technique," Comput. Meth. Appl. Engng 195 (19-22), 2209-2230 (2006).
14.  A. L. Goldenveizer, Theory of Elastic Thin Shells (Nauka, Moscow, 1976).
15.  G. M. Kulikov and S. V. Plotnikova, "Equivalent Single-Layer and Layer-Wise Shell Theories and Rigid-Body Motions," Mech. Adv. Mater. Struct. 12 (4), 275-283 (2005).
16.  G. M. Kulikov and E. Carrera, "Finite Deformation Higher Order Shell Models and Rigid-Body Motions," Int. J. Solids Struct. 45 (11-12), 3153-3172 (2008).
17.  B. E. Pobedrya and D. V. Georgievskii, Foundations of Continuum Mechanics. A Course of Lectures (Fizmatlit, Moscow, 2006) [in Russian].
18.  T. K. Varadan and K. Bhaskar, "Bending of Laminated Orthotropic Cylindrical Shells. An Elasticity Approach," Compos. Struct. 17 (2), 141-156 (1991).
Received 11 March 2012
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