Abstract
A great deal of interest in the substantiation of refined theories of elastic an-isotropic plates and shells has been manifested in the specialized literature in the last two decades. This interest is largely due to the need for more adequate methods of analysis of structural elements exposed to severe and complex operational conditions in various branches of the advanced technology. In addition, the increased use of new exotic composite materials has provided a new impetus for such refined theories. As it was conclusively shown, the classical methods of analysis based on the Kirchhoff-Love assumptions are inadequate in many important instances. This is especially true whenever the material of the structure exhibits high degrees of anisotropy in its physical and mechanical properties. Such features are typical for the composite and refractory type materials used with increased frequency in the aerospace, naval, nuclear industries, etc. In such cases, refined models allowing a more adequate description of the structural response are needed. They should include transverse shear and transverse normal deformations and should account for the higher-order effects.
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References
NAGHDI P.M., The Theory of Shells and Plates, in “Handbuch der Physik”, vol. VI a/2, ed. S. Flügge, 425–640, Springer-Verlag, Berlin — Heidelberg — New York, 1972.
LIBRESCU L., Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff Int. Publ., Leyden, 1975.
LIBRESCU L., Refined Geometrically Non-Linear Theories of Anisotropie Laminated Shells, Quarterly of Applied Mathematics, (in print).
YOKOO Y., MATSUNAGA H., A General Theory of Elastic Shells, Int. J. Solids Structures 10 (1974), 261–274.
HABIP L.M., Theory of Elastic Shells in the Reference State, Ingenieur-Archiv 34 (1965), 228–237.
HABIP L.M., Theory of Elastic Plates in the Reference State, Int. J. Solids Structures 2 (1966), 157–166.
HABIP L.M., EBCIOGLU I.K., On the Equations of Motion of Shells in the Reference State, Ingenieur-Archiv 34 (1965), 28–32.
AINOLA L. IA., Nonlinear Timoshenko Type Theory of Elastic Shells (in Russian), Izv. Akad. Nauk. Eston. SSR 14 (1965), 337–344.
GALIMOV K.Z., Foundations of the Nonlinear Theory of Shells (in Russian), Kazan’ University Press, Kazan’ 1975.
GALIMOV K.Z., Theory of Shells with Transverse Shear Deformation Effect (in Russian), Kazan’ University Press, Kazan’ 1977.
PIETRASZKIEWICZ W., Finite Rotations and Lagrangean Description in the Non-Linear Theory of Shells, Polish Scientific Publishers, Warszawa — Poznan, 1979.
SANDERS J.L., Nonlinear Theories for Thin Shells, Quart. Appl. Math. 21 (1963), 21–36.
KOITER W.T., On the Nonlinear Theory of Thin Elastic Shells, Proc. Kon. Ned. Ak. Wet., Series B, 69 (1966), 1–54.
REISSNER E., Rotationally Symmetric Problems in the Theory of Thin Elastic Shells, Proc. 3rd U.S. Nat. Congr. of Appl. Mech., 1958, 51–69.
PIETRASZKIEWICZ W., Finite Rotations in the Non-Linear Theory of Thin Shells, in “Thin Shell Theory, New Trends and Applications”, ed. W. Olszak, 153–208, Springer-Verlag, Wien — New York, 1980.
PIETRASZKIEWICZ W., Lagrangian Description and Incremental Formulation in the Non-Linear Theory of Thin Shells, Int. J. Non-Linear Mechanics 19 (1984), 115–140.
SCHMIDT R., Variational Principles for General and Restricted Kirchhoff-Love Type Shell Theories, Proc. Int. Conf. on Finite Element Methods, Shanghai (China) 1982, eds. He Guangqian, Y.K. Cheung, 621–626, Gordon and Breach, New York, 1982.
SCHMIDT R., On Geometrically Nonlinear Theories for Thin Elastic Shells, in “Flexible Shells, Theory and Applications”, Proc. EUROMECH-Colloquium Nr. 165, Munich (Germany) 1983, eds. E.L. Axelrad, F.A. Emmerling, 76–90, Springer-Verlag, Berlin — Heidelberg — New York — Tokyo, 1984.
SCHMIDT R., A Current Trend in Shell Theory: Constrained Geometrically Nonlinear Kirchhoff-Love Type Theories Based on Polar Decomposition of Strains and Rotations, Proc. Symp. on Advances and Trends in Structures and Dynamics, Arlington, Virginia (USA), 1984, eds. A.K. Noor, R.J. Hayduk, 265–275, Pergamon Press, New York, 1985, reprinted in Computers and Structures 20 (1985), 265–275.
KAUL R.K., Finite Thermal Oscillations of Thin Plates, Int. J. Solids Structures 2 (1966), 337–350.
WEMPNER G.A., Mechanics of Solids with Applications to Thin Bodies, McGraw-Hill, New York, 1973.
NAGHDI P.M., VONGSARNPIGOON L., A Theory of Shells with Small Strains Accompanied by Moderate Rotations, Arch, for Rational Mechanics and Analysis 83 (1983), 245–283.
YU Y.-Y., Generalized Hamilton’s Principle and Variational Equation of Motion in Nonlinear Elasticity Theory, with Application to Plate Theory, J. of the Acoustical Society of America 36 (1964), 111–120.
VINSON J.R., CHOU T.W., Composite Materials and Their Use in Structures, J. Wiley and Sons, New York — Toronto, 1974.
NOOR A.K., Stability of Multilayered Composite Plates, Fibre Science and Technology 8 (1975), 81–89.
REDDY J.N., Analysis of Layered Composite Plates Accounting for Large Deflections and Transverse Shear Strains, in “Recent Advances in Non-Linear Computational Mechanics”, eds. E. Hinton, D.R.J. Owen and C. Taylor, Pineridge Press Ltd., Swansea, U.K., 1982.
REDDY J.N., CHAO W.C., Nonlinear Oscillations of Laminated Anisotropic Rectangular Plates, Journal of Applied Mechanics, Trans. ASME, 49 (1982), 396–402.
BRULL M.A., LIBRESCU L., Strain Measures and Compatibility Equations in the Linear High-Order Shell Theories, Quarterly of Appl. Mathematics, 40 (1982), 15–25.
AMBARTSUMIAN S.A., Theory of Anisotropic Plates (English Transl.), Technomic, Stamford, Conn., 1970.
BRUNELLE E.J., ROBERTSON S.R., Initially Stressed Mindlin Plates, AIAA Journal 12 (1974), 1036-l045.
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Librescu, L., Schmidt, R. (1986). Higher-Order Moderate Rotation Theories for Elastic Anisotropic Plates. 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_13
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DOI: https://doi.org/10.1007/978-3-642-82838-6_13
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