Abstract
Specialization of the general thin-shell theory for the class of large deformations realizable by small strain is considered. This leads in three different ways to the intrinsic nonlinear theory of flexible shells. As an illustration, large displacements and rotations culminating in collapse of finite-length tubes are investigated.
This work is dedicated to the recent 70th birthday of Professor W.T. Koiter.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
REISSNER E., On axisymmetrical deformations of thin shells of revolution. Proc. Symposia in Appl. Math. 3 (1950), 27–52.
MUSHTARY KH.M.,GALIMOV K.Z., Nonlinear theory of thin elastic shells. Kasan 1957 (In Russian). Translation NASA-TT-F62 (1961).
KOITER W.T., On the nonlinear theory of thin elastic shells. Proc. Koninkl. Nederl. Akad. van Wet.; Ser. B 69 (1966), 1–54.
KOITER W.T., Foundations and basic equations of shell theory.Proc. 2nd IUTAM Symp. on the Theory of Thin Shells. Springer 1969, 93–105.
KOITER W.T., The intrinsic equations of shell theory with some applications. Mechanics Today, Ed. S. Nemat-Nasser, Pergamon Press, 1980, 139–154.
LIBAI A., SIMMONDS J.G., Nonlinear elastic shell theory. Adv. in Appl. Mech. 23 (1983) 271–371.
SIMMONDS J.G., Special cases of nonlinear shell equations. Trends in Solid Mechanics. (Edited by J.F. Besseling and A.M.A. van der Heijden). (Proc. of the Symp. dedicated to the 65th birthday of W.T. Koiter). Sijthoff & Nordhoff (1979), 211–224.
AXELRAD E.L., Flexible shells. Theoretical and Applied Mechanics. Proc. of the 15th Intern. Congr., Toronto 1980; ed. by F.P.J. Rimrott, B. Tabarrok. North-Holland 1980.
HALMOS P.R., How to write mathematics. L’Enseignement Mathematique. 16 (1970), 123–152.
GOLDENVEIZER A.L., Theory of Elastic Thin Shells. Translation from the Russian Edition (1953); ed. by G. Herrmann. Oxford Pergamon Press (1961).
SIMMONDS J.G., A set of simple, accurate equations for circular cylindrical elastic shells. Int. J. Solids & Structures, 2 (1966), 525–541.
AXELRAD E.L., EMMERLING F.A., Eine geometrische nichtlineare Halbmembrantheorie elastischer Schalen. Forschung im Ing.Wes. 49 (1983), 31–36.
AXELRAD E.L., Elastic tubes-assumptions, equations, edge conditions. Thin-Walled Structures 3 (1985), 193–215.
AXELRAD E.L., Flexible shells. In “Flexible shells, Theory and Applications”, eds. E.L. Axelrad, F.A. Emmerling, Springer, Berlin, 1984, 44–63.
KARMAN v. TH., über die Formänderung dünnwandiger Rohre, insbesondere federnder Ausgleichsrohre. VDI-Z. 55 (1911), 1889–1895.
BESKIN L., Bending of curved thin tubes. J. Appl. Mech., Tr. ASME, 65 (1943), A 105 — A 120.
AXELRAD E.L., Refinement of critical-load analysis for tube flexure by way of considering precritical deformation. Izv. AN SSSR OTN, Mekh. i. Mash. (1965), n4, 133–139 (In Russian).
NOVOZHILOV V.V., Thin Shell Theory. Groningen, P. Noordhoff 1970.
AXELRAD E.L., Nonlinear equations of axisymmetric shells and bending of thin-walled beams. Izv. AN SSSR, OTN, Mekh. i.Mash. (1960), n4, 84–92 (in Russian). Translation in: Amer. Rocket Soc. J. Supplement 32 (1962) 1147–1151.
AXELRAD E.L., Schalentheorie. B.G. Teubner, Stuttgart, 1983.
BRAZIER L.G., On the flexure of thin cylindrical shells and other “thin” sections. Proc. Roy. Soc. London, Ser. A. 116 (1927) 104–114.
STEPHENS W.B., STARNES J.H., ALMROTH B.O., Collapse of long cylindrical shells under combined bending and pressure loads. AIAA J., 13 (1975), 20–25.
ATLURI S.N., Computational analysis of finitely deformed solids with application to plates and shells — I. Computer & Structures, 18 (1984), 93–116.
EMMERLING F.A., Nonlinear bending of curved tubes. In “Flexible Shells, Theory and Applications”, eds. E.L. Axelrad, F.A. Emmerling. Springer, Berlin 1984, 175–192.
AXELRAD E.L., EMMERLING F.A., Finite bending and collapse of elastic pressurized tubes. Ing.-Arch. 53, (1983), 41–52.
AXELRAD E.L., On local buckling of thin shells. Int. J. Non-Linear Mechanics, 20 (1985) 249–259.
EMMERLING F.A., Nichtlineare Biegung und Beulen von Zylindern und krummen Rohren bei Normaldruck. Ing.-Arch. 52, (1982), 1–16.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin, Heidelberg
About this paper
Cite this paper
Axelrad, E.L., Emmerling, F.A. (1986). Intrinsic Shell-Theory Formulation Effective for Large Rotations and an Application. In: Pietraszkiewicz, W. (eds) Finite Rotations in Structural Mechanics. Lecture Notes in Engineering, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82838-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-82838-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16737-2
Online ISBN: 978-3-642-82838-6
eBook Packages: Springer Book Archive