Polar Decomposition and Finite Rotation Vector in First — Order Finite Elastic Strain Shell Theory
While large strain membrane theories are well established in literature since more than three decades, there exist considerably less papers which deal with large elastic strain shell theory incorporating also the bending effects into the nonlinear analysis. Recently, however, this topic has gained considerable interest. Important contributions have been given by CHERNYKH [1,2] , LIBAI and SIMMONDS [5,6] , and SIMMONDS  , where also additional references on related works may be found. The aforementioned authors agree that such a theory should be based on a refined Kirchhoff-Love type model which admits at least changes in shell thickness. Due to bending this thickness change is in general asymmetric about the undeformed midsurface so that its deformed configuration is no longer the geometrical midsurface of the deformed shell. This requires a representation of the position vector of the deformed shell space which incorporates at least quadratic terms with respect to the thickness coordinate.
KeywordsShell Thickness Shell Theory Polar Decomposition Moderate Rotation Rotational Part
Unable to display preview. Download preview PDF.
- 2.CHERNYKH K.F., Advances in Mechanics 6 (1983), 111–147 (in Russian).Google Scholar
- 3.CHERNYKH K.F., In: Mechanics of Deformable Continuum, 9–72 (in Russian), Kuybyshev State University 1976.Google Scholar
- 4.KORN G.A., KORN T.M., Mathematical Handbook for Scientists and Engineers, 2nd ed., Mc Graw-Hill, New York 1968.Google Scholar
- 7.LUR’E A.I., Analytical Mechanics (in Russian), Nauka, Moscow 1961.Google Scholar
- 9.PIETRASZKIEWICZ W., Finite Rotations and Langrangean Description in the Non-Linear Theory of Shells, Polish Scientific Publishers, Warszawa-Poznań 1979.Google Scholar
- 10.PIETRASZKIEWICZ W.,In: Theory of Shells, eds. W.T. Koiter; G.K. Mikhailov, 445–471, North-Holland Publ. Co., Amsterdam-New York-Oxford 1980.Google Scholar
- 11.PIETRASZKIEWICZ W., Mitteilungen aus dem Institut für Mechanik, Nr. l0, Ruhr-Universität Bochum 1977.Google Scholar
- 13.SCHMIDT R., Proc. of the Symp. on Advances and Trends in Structures and Dynamics, Washington 1984, eds. A.K. Noor; R.J. Hayduk, 265–275, Pergamon Press, New York, reprinted as Computers and Structures 20 (1985), 265–275.Google Scholar
- 14.SCHMIDT R., Contributions to the Nonlinear Theory of Thin Elastic Shells, Part II, Lecture XVI IUTAM Int.Congr. of Theoretical and Applied Mechanics, Lyngby, 19.-25.8.1984, to be published.Google Scholar
- 16.SCHROEDER F.-H., Cosserat Theory of Shells with Large Rotations and Displacements, Lecture EUROMECH-Colloquium Nr. 165 “Flexible Shells, Theory and Applications”, München, May 17–20, 1983.Google Scholar