Abstract
In this paper we analyze the deformation of cylindrical multi-layered elastic shells using the direct approach to shell theory. In this approach, the thin shell-like bodies are modeled as deformable surfaces with a triad of vectors (directors) attached to each point. This triad of directors rotates during deformation and describes the rotations of the thickness filament of the shell. We consider a general set of constitutive equations which can model orthotropic multi-layered shells. For this type of shells we investigate the equilibrium of thin-walled tubes (not necessarily circular) subjected to external body loads and to resultant forces and moments applied to the end edges. We present a general procedure to derive the analytical solution of this problem. We consider that the external body loads are given polynomials in the axial coordinate, which coefficients can be arbitrary functions of the circumferential coordinate. We illustrate our method in the case of circular cylindrical three-layered shells and obtain the solution in closed form. For isotropic shells, the solution is in agreement with classical known results.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Altenbach, H.: An alternative determination of transverse shear stiffnesses for sandwich and laminated plates. Int .J. Solids Struct. 37, 3503–3520 (2000)
Altenbach, H., Eremeyev, V.A.: Direct approach-based analysis of plates composed of functionally graded materials. Arch. Appl. Mech. 78, 775–794 (2008)
Altenbach, H., Eremeyev, V.A.: On the bending of viscoelastic plates made of polymer foams. Acta Mech. 204, 137–154 (2009)
Altenbach, H., Eremeyev, V.A.: On the effective stiffness of plates made of hyperelastic materials with initial stresses. Int. J. Non-Lin Mech. 45, 976–981 (2010)
Altenbach, H., Zhilin, P.A.: The theory of simple elastic shells. In: Kienzler, R., Altenbach, H., Ott, I. (eds) Theories of Shells and Plates, Lecture Notes in Applied and Computational Mechanics 16: 1–12., Springer, Berlin (2004)
Berdichevsky, V., Armanios, E., Badir, A.: Theory of anisotropic thin-walled closed-cross-section beams. Comp. Eng. 2, 411–432 (1992)
Bîrsan, M., Altenbach, H.: A mathematical study of the linear theory for orthotropic elastic simple shells. Math. Meth. Appl. Sci. 33, 1399–1413 (2010)
Bîrsan, M., Altenbach, H.: On the dynamical theory of thermoelastic simple shells. ZAMM. (2011).DOI: 10.1002/zamm.201000057
Cosserat, E., Cosserat, F.: Théorie des corps déformables. Herman et Fils, Paris (1909)
Ieşan, D.: Classical and Generalized Models of Elastic Rods. Chapman & Hall / CRC Press, Boca Raton - London - New York (2009)
Ieşan, D.: Deformation of porous Cosserat elastic bars. Int. J. Solids Struct. 48, 573–583 (2011)
Lurie, A.I.: Theory of Elasticity. Springer, Berlin (2005)
Naumenko, K., Altenbach, H.: Modeling of Creep for Structural Analysis. Springer-Verlag, Berlin (2007)
Reissner, E., Tsai, W.T.: Pure bending, stretching, and twisting of anisotropic cylindrical shells. J. Appl. Mech. 39, 148–154 (1972)
Sokolnikoff, I.S.: Mathematical Theory of Elasticity. McGraw-Hill, New York (1956)
Timoshenko, S., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, New York (1951)
Zhilin, P.A.: Mechanics of deformable directed surfaces. Int. J. Solids Struct. 12, 635–648 (1976)
Zhilin, P.A.: Applied Mechanics: Foundations of Shell Theory (in Russian). Politekhn Univ Publ, Sankt Petersburg (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bîrsan, M., Altenbach, H. (2011). Analysis of the Deformation of Multi-layered Orthotropic Cylindrical Elastic Shells Using the Direct Approach. In: Altenbach, H., Eremeyev, V. (eds) Shell-like Structures. Advanced Structured Materials, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21855-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-21855-2_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21854-5
Online ISBN: 978-3-642-21855-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)