The Problem of Bending of Fibre Composite Viscoelastic Plates
A method is proposed for solving the problems of bending of prestressed fibrereinforced viscoelastic plates, subjected to durable loads. The plate considered is made of the primary material (the matrix, phase I), reinforced with densely spaced fibres (phase II) distributed in planes parallel to the middle plane of the plate. The compatibility condition of the two phases is introduced: ε = εI = εII, σ = σI + σII. A numerical algorithm has been prepared, the finite element method being applied. The problem is discretized with respect to time. The paper includes some examples of analysis and inferences.
References
J. BIALKIEWICZ, Rheology of discs and circularly symmetrical plates in civil engineering structures, Zesz. Nauk. Politechniki Krakowskiej, Monografia 40, Kraków 1986.
R. CUPJSZ and S. OCHELSKI, Statical and rheological studies of polymer composites reinforced in a single direction [in Polish], VIII Sympozjum Poświęcone Reologii, Wrocław 1981.
S.A.A. AMBARCUMJAN, Theory of anisotropic shells [in Russian], lzd. Fiz. Ma.t. Lit., Moscov 1961.
Z. HASHIN and B.W. ROSEN, The elastic moduli of fibre-reinforced materials, Trans. ASME, J. Appl. Mech., 31, 2, 225-232, 1964.
R. HILL, Elastic properties of the reinforced solids. Same theoretical principles, J. Mech. Phys. Solids, 12, 199-212, 1964.
W. BARAŃSKI, Microstresses in homogenization, Arch. Mech., 38, 4, 369-382, 1986.
R.M. CHRISTENSEN, Mechanics of composite materials, Wiley-lnterscience, New York 1979.
R. JONES, Mechanics of composite materials, Mc Graw Hill, New York 1975.
CZ. WOŹNIAK, Nonstandard analysis in mechanics, Advances in Mech., 1, 1986.
M. MARKS, Composite elements of minimal deformability, reinforced with two families of fibres, Engng. Trans., 36, 3, 541-562, 1988.
J. ROLNICKI-SZULC, The prestressing problem of two-phase bodies, Mech. Teoret. i Stosowana, 16, 1, 41-55, 1978.
J. HOLNICKJ-SZULC, Distortion in structural systems, analysis, control, modelling, PWN, Warszawa-Poznań 1990.
R. ŚWITKA, Equations of fibre composite plates, Engng. Trans., 40, 2, 178-201, 1992.
M. OLEJNICZAK, Analysis of discs made of prestressed two-phase viscoelastic materials, Doctor's Thesis, Politechnika Poznańska. 1990.
M. OLEJNICZAK, The influence of fibrous phase on stress redistribution in the viscoelastic disc, X Polish Conf. "Comp. Methods in Mechanics", Świnoujście-Szczecin, 2, 575-582, 1991.
O.C. ZIENKIEWICZ, The method of finite elements, Arkady, Warszawa 1972.
R. ŚWITKA and B. HUSIAR, Discrete analysis of rheological models, Mech. Teoret. i Stosowana, 22, 1/2, 209-233, 1984.
R. ŚWITKA, A proposal for discretization of viscoelastic problems [in Polish], Materiały Sympozjum, Zielonka. 21-22 X 1982, Akademia Rolnicza, Poznań 1984.
R.H. GALLAGHER, Finite element analysis, Prentice-Hall Englewood Cliffs, New York 1975.
M. KUCZMA, The problem of unilateral contact between beams and plates resting on a viscoelastic foundation, A Doctor's Thesis, Politechnika. Poznańska 1990.
I. KISIEL, Rheology in building, Arkady, Warszawa 1967.