Abstract
The set of equations for the geometrically non-linear theory of thin elastic shells is usually expressed in terms of displacements as basic independent variables of the shell deformation. Various general and reduced displacemental forms of bending shell equations are summarized, for example, by MUSHTARI and GALIMOV [1], KOITER [2], PIETRASZKIEWICZ [3, 4], SCHMIDT [5] and BA§AR and KRÄTZIG [6], where further references may be found. When displacement field is determined from the shell equations, strains, rotations and stresses may be obtained by prescribed algebraic or differential procedures.
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References
MUSHTARI K.M. and GALIMOV K.Z., Non-linear theory of elastic shells (in Russian), Tatknigoizdat, Kazań 1957.
KOITER W.T., On the nonlinear theory of thin elastic shells, Proc. Koninkl. Ned. Ak. Wet. B69 (1966 ), 1, 1–54.
PIETRASZKIEWICZ W., Finite rotations in the non-linear theory of thin shells, in: Thin Shell Theory, New Trends and Applications, 155–208, ed. by W. Olszak, CISM Course No 240, Springer-Verlag, Wien 1980.
PIETRASZKIEWICZ. W., Lagrangian description and incremental formulation in the non-linear theory of thin shells, Int. J. Non-Linear Mech., 19(1984), 2, 115–141.
SCHMIDT R., A current trend in shell theory: constrained geometrically nonlinear Kirchhoff-Love type theories based on polar decomposition of strains and rotations, Comp. and Str., 20 (1985 ), 1–3, 265–275.
BA§AR Y. and KRÄTZIG W.B., Mechanik der Flächentragwerke, Vieweg, Braunschweig 1985.
ALUMÄE N.A., Differential equations of equilibrium states of thin--walled elastic shells in the post-critical stage (in Russian), Prikl.Mat.Mekh 13(1949), 1, 95–106.
REISSNER E., On axisymmetric deformations of thin shells of revolution, Proc. Symp. Appl. Math., 3(1950), 27–52.
WEMPNER G., Finite elements, finite rotations and small strains, Int. J. Solids and Str., (1969), 5, 117–153.
SIMMONDS J.G. and DANIELSON D.A., Nonlinear shell theory with a finite rotation and stress-function vectors, J. Appl. Mech., Trans. ASME E39(1972), 4, 1085–1090.
SIMMONDS J.G. and DANIELSON D.A., Nonlinear shell theory with a: finite rotation vector, Proc. Koninkl. Ned. Ak. Wet. B73(1970), 5, 460–478.
PIETRASZKIEWICZ W., Introduction to the Non-linear Theory of Shells, Ruhr-Universität, Mitt. Inst. f. Mech. Nr 10, Bochum, Mai 1977, 1–154.
PIETRASZKIEWICZ W., Obroty skończone i opis Lagrange’a w nieliniowej teorii powłok, Biul. IMP PAN 172(880), Gdańsk 1976. English transi.: Finite Rotations and Lagrangean Description in the Non--Linear Theory of Shells, Polish Sci. Publ., Warszawa-Poznań 1979.
PIETRASZKIEWICZ W., Finite rotations in shells, in: Theory of Shells, 445–471, Ed. by W.T.Koiter and G.K.Mikhailov, North-Holland P.Co., Amsterdam 1980.
SHKUTIN L.I., An exact formulation of equations of the non-linear deformation of thin shells (in Russian), in: Applied Problems of Strength and Plasticity (in Russian), 7(1977), 3–9; 8(1978), 38–43; 9(1978), 19–25.
LIBAI A. and SIMMONDS J.G., Nonlinear elastic shell theory, in: Advances In Applied Mechanics, vol.23, 271–371, Academic Press, New York 1983.
ATLURI S.N., Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with application to plates and shells-I. Theory, Comp. and Str. 18(1984), 1, 93–116.
KAYUK Ya.F. and SAKHATSKIY V.G., On the non-linear theory of shells based on the notion of a finite rotation, Soviet Applied Mechanics, 21(1985), 4, 65–73.
MAKOWSKI J. and STUMPF H., Finite strains and rotations in shells, in: Finite Rotations in Structural Mechanics, ed, by W. Pietraszkiewicz, Springer-Verlag, Berlin 1986.
COSSERAT E. and COSSERAT F., Theorie des Corps deformables, Herman, Paris 1909.
NAGHDI P.M., The theory of shells and plates, in: Handbuch der Physik, vol. VI/2, Springer-Verlag, Berlin 1972.
SCHROEDER F.H., Cosserat theory of shells with large rotations and displacements, lecture presented at the Euromech Colloquium 165 “Flexible Shells”, 17–20 May, München 1983.
ERINGEN A.C. and KAFADAR C.B., Polar field theories, in: Continuum Physics, vol IV, 1–73, ed. by A.C. Eringen, Academic Press, New York 1976.
TOUPIN R.A., Theories of elasticity with couple-stresses, Arch. Rat. Mech. Anal., 17 (1964), 2, 85–110.
KOITER W.T., Couple-stresses in the theory of elasticity, Proc. Koninkl. Ned. Ak. Wet., B67 (1964), 1, 17–29;. B67 (1964), 1, 30–48.
SHKUTIN L.I., Non-linear models for deformable continuum with couple-stresses (in Russian), Zhurnal Prikl. Mekh. Tekh. Fiz., 1980, 6, 111–117.
KOITER W.T., A consistent first approximation in the general theory of thin elastic shells, in: The Theory of Thin Elastic Shells, 12–33, Ed. by W.T. Koiter, North-Holland P.Co., Amsterdam 1960.
PIETRASZKIEWICZ W. and BADUR J., Finite rotations in the description of continuum deformation, Int. J. Engng Sci., 21(1983), 9, 1097–1115.
TRUESDELL C. and NOLL W., The Nonlinear Field Theories of Mechanics, in: Handbuch der Physik, vol. III/3, Springer-Verlag, Berlin 1965.
HILL R., On constitutive inequalities for simple materials, Int. J. Mech. Phys. Solids, 16(1968), 5, 229–241.
BUDIANSKY B. and SANDERS J.L., On the “best” first-order linear shell theory, in: Progress in Applied Mechanics (Prager Anniv. Vol) 129–140, Macmillan, New York 1963.
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Badur, J., Pietraszkiewicz, W. (1986). On Geometrically Non-Linear Theory of Elastic Shells Derived from Pseudo-Cosserat Continuum with Constrained Micro-Rotations. 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_2
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DOI: https://doi.org/10.1007/978-3-642-82838-6_2
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