Summary
The behaviour of viscoelastic plates can be described by several engineering theories, based on different assumptions and theoretical conceptions. One of them — the direct approach — is used in this paper to modelize the viscoelastic behaviour of plates. This theory is physically and mathematically correct, but there are other problems, especially the identification of the effective properties in the constitutive equations. The paper deals with a Timoshenko-Reissner-Mindlin type theory, so the main problem is the determination of the classical-plate-properties for stretching, plane shear, bending and torsion and the properties for transverse shear. It is shown by a simple analytical method, that all properties can be found out for viscoelastic plates without any restrictions for the distribution of the material properties in the thickness (symmetric, unsymmetric) and the linear-viscoelastic behaviour (differential or integral relations, complex moduli). The proposed theory is suitable for homogeneous and inhomogeneous (e.g. laminated) plates. For some special cases there are given examples.
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
Goldenveizer, A.L., Methods of motivation and increasing accuracy of shell theories, PMM 32, (1968), 4, 684–695 (in Russian); (engl. transl. PMM 32, (1969), 4, 704-718).
Naghdi, P.M., The Theory of Plates and Shells, Flügge, S., (ed.), Handbuch der Physik VIa/2 (Festkörpermechanik), S. 425–640, Berlin, Heidelberg, New York, Springer 1972.
Wunderlich, W., Vergleich verschiedener Approximationen der Theorie dünner Schalen (mit numerischen Beispielen), Tech.-Wiss. Mitt. d. Instituts für Konstructiven Ingenieurbau der Ruhruniversität Bochum, 73-1.
Reissner, E., Reflections on the theory of elastic plates, Appl. Mech. Rev. 38, (1985), 11, 1453–1464.
Grigoriuk, E., Kogan, F.A., Contemporary state of theories of multilayered shells, Prik. mekh., VIII (1972), 6, 3–17 (in Russian); (engl. transl. Sov. Appl. Mech. 8, (1974), 6, 583-595).
Dudtchenko, A.A., Lurie, S.A., Obrazcov, I.F., Anisotropic multilayered plates and shells, Itogi nauki i tekhniki, Seria ”Mekh. tverd. defor. tiela”, 15, 2-63, Moskva, WINITI 1983 (in Russian).
Noor, A.K., Burton, W.S., Assessment of computational models for multilayered composite shells, Appl. Mech. Rev. 43, (1990), 4, 87–97.
Zhilin, P.A., Mechanics of Deformahle Directed Surfaces, Int. J. Solids Struct. 12, (1976), 635–648.
Altenbach, H., Eine direkt formulierte lineare Theorie für viskoelastische Platten und Schalen Ing.-Arch. 58, (1988), 215–228.
Altenbach, H., Determination of given properties for multilayered viisco-plastic plates, Mekh. komp. mat., (1988), 1, 58–66 (in Russian).
Altenbach, H., Zilin, P.A., The general theory of elastic simple shells, Advances in Mechanics 11, (1988), 4, 107–148 (in Russian).
Christensen, R.M., Theory of Viscoelasticity, New York, Academic Press 1971.
Altenbach, H., Dtermination of elastic moduli for plates made of anisotropic, nonhomogenous, in respect to the thickness, material, Izw. AN SSSR Mekh. tv. tiela (1987), 1, 139–146 (in Russian).
Altenbach, H., Die Ermittlung effektiver Eigenschaften für viskoelastische ebene Flächentragwerke, Technische Mechanik 8, (1987), 1, 33–39.
Altenbach, H., Eine direkt formulierte Biegetheorie für viskoelastische Ein-und Mehrschichtschalen, Technische Mechanik 7, (1986), 3, 38–43.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag, Berlin Heidelberg
About this paper
Cite this paper
Altenbach, H. (1991). Modelling of Viscoelastic Behaviour of Plates. In: Życzkowski, M. (eds) Creep in Structures. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84455-3_59
Download citation
DOI: https://doi.org/10.1007/978-3-642-84455-3_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-84457-7
Online ISBN: 978-3-642-84455-3
eBook Packages: Springer Book Archive