Summary
For a general elastic laminate consisting of different transversely isotropic plane layers an exact (but expensive) method for the calculation of the deformations, stability and eigenvibrations is discussed. The specialization to a laminate composed of alternating stiff reinforcing sheets and soft matrix layers (special discrete model), however, allows a considerable simplification. It is shown how this regular laminate (=inhomogeneous classical continuum) may be approximated by a homogeneous continuum with couple stresses using a suitable limiting process (continuum model). This model corresponds to a restricted Cosserat continuum and enables the derivation of closed formulas for the displacements, critical loads and eigenfrequencies. Numerical results are worked out on the basis of the discrete and continuum model respectively and compared with each other.
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References
Neuber, H.: Theorie der Druckstabilität der Sandwichplatte I. ZAMM32, 325–337 (1952).
Neuber, H.: Theorie der Druckstabilität der Sandwichplatte II. ZAMM33, 10–26 (1953).
Bufler, H.: Die Bestimmung des Spannungs- und Verschiebungszustandes eines geschichteten Körpers mit Hilfe von Übertragungsmatrizen. Ing.-Archiv31, 229–240 (1962).
Bufler, H.: Die Druckstabilität rechteckiger Verbundplatten. Ing.-Archiv34, 109–128 (1965).
Bufler, H.: Theory of elasticity of a multilayered medium. J. of Elasticity1, 125–143 (1971).
Bufler, H.: Spannungs- und Stabilitätsproblem eines elastisch-querisotropen Schicht-systems. Ing.-Archiv41, 278–290 (1972).
Sun, C. T., Achenbach, J. D., Herrmann, G.: Continuum theory for a laminated medium. J. Appl. Mech.35, 467–475 (1968).
Achenbach, J. D., Sun, C. T., Herrmann, G.: On the vibrations of a laminated body. J. Appl. Mech.35, 689–696 (1968).
Sun, C. T.: On the equations for composite beams under initial stress. Int. J. Solids Struct.8, 385–399 (1972).
Chung, W. Y., Testa, R. B.: The elastic stability of fibers in a composite plate. J. Comp. Mat.3, 58–80 (1969).
Srinivas, S., Rao, A. K.: Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int. J. Solids Struct.6, 1463–1481 (1970).
Kiusalaas, J., Jaunzemis, W.: Internal buckling of a laminated medium, in: Developments in theoretical and applied mechanics (Rogers, A. L., ed.), Vol. 5, pp. 151–173. The University of North Carolina Press 1971.
Kiusalaas, J., Jaunzemis, W., Conway J. C.: A strain-gradient theory for prestrained laminates. Int. J. Solids Struct.9, 1317–1330 (1973).
Drumheller, D. S., Bedford, A.: On a continuum theory for a laminated medium. J. Appl. Mech.40, 527–532 (1973).
Whitney, J. M., Sun, C. T.: A higher order theory for extensional motion of laminated composites. J. Sound and Vibration30, 85–97 (1973).
Noor, A. K.: Stability of multilayered composite plates. Fibre Science and Technology8, 81–89 (1975).
Niven, H. D. M., Mengi, Y.: A mixture theory for elastic laminated composites. Int. J. Solids Struct.15, 281–302 (1979).
Biot, M. A.: Mechanics of incremental deformations. New York-London-Sydney: Wiley 1965.
Lee, E. H. (ed.): Dynamics of composite materials. ASME-Proceedings 1972.
Herrmann, G., Achenbach, J. D.: Applications of theories of generalized Cosserat continua to the dynamics of composite materials, in: Mechanics of generalized continua, Proceedings of the IUTAM Symposium Freudenstadt Stuttgart 1967 69–79. Berlin-Heidelberg-New York: Springer 1968.
Bufler, H., Kennerknecht, H.: Elastische Stabilität ebener Laminate. Ing.-Archiv (in press).
Kennerknecht, H.: Verformungen, Stabilität und Eigenschwingungen elastischer Laminate. Diss., Universität Stuttgart, 1981.
Pestel, E. C., Leckie, F. A.: Matrix methods in elastomechanics. New York-San Francisco-Toronto-London: McGraw-Hill 1963.
Pflüger, A.: Stabilitätsprobleme der Elastostatik, 3. Aufl. Berlin-Heidelberg-New York: Springer 1975.
Girkmann, K.: Flächentragwerke, 6. Aufl. Wien-New York: Springer 1963.
Koiter, W. T.: Couple-stresses in the theory of elasticity I and II. Proc. Koninkl. Nederl. Akad. Wetensch., AmsterdamB 67, 17–44 (1964).
Neuber, H.: On the general solution of linear-elastic problems in isotropic and anisotropic Cosserat continua. In: Applied mechanics (Görtler H., ed.), pp. 153–158. Proc. of the 11th intern. IUTAM Congress of applied mechanics. Berlin-Heidelberg-New York: Springer 1966.
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Bufler, H., Kennerknecht, H. Prestrained elastic laminates: Deformations, stability and vibrations. Acta Mechanica 48, 1–30 (1983). https://doi.org/10.1007/BF01178493
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DOI: https://doi.org/10.1007/BF01178493