Engineering Transactions, 42, 1-2, pp. 33-59, 1994

Interaction of Membrane and Bending Forces in Plates at Nonlinear Vibration

W. Dornowski
Military University of Technology, Warszawa

The subject of this paper is the analysis of the dynamic response of circular and rectangular elastic-viscoplastic plates subjected to impulsive loading. The range of what is referred to as moderately large deflections has been considered. All the displacement components and their time derivatives in the description of the kinematics are included. The equations of motion have been formulated by using the principle of virtual work. Approximate solutions are found by the orthogonalization principle. As regards the numerical aspects of this method, they are characterized by the necessity of applying typical techniques of numerical integration of the equations of motion and the constitutive relations. Principal emphasis is laid on the study of the co-operation between membrane and bending forces over a wide range of plate deflection. The influence of such factors as the type of edge support, the character of dynamic load and the kind of material of the plate have been discussed. It has been found that plates on hinged supports are more sensitive to membrane e:lfects than those with clamped edges. Intensive dynamic loads with long periods of action lead in most cases to membrane-type mechanisms of deformation. lnitial velocity pulses make the plate move with a strongly non-stationary displacement velocity field, the deformation being characterized by a flexural way of producing deformation.

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N. JONES, A literature review of the dynamic plastic response of structures, Shock Vib. Dig., 13, IO, 3-16, 1975.

T. WIERZBICKI, Large deflections of structures umder dynamic load. Critical review of methods [in Polish], Engng. Trans., 24, 2, 667-730, 1976.

G.N. NURICK and J.B. MARTIN, Deformation of thin plates subjected to impulsive loading - a review. Part I. Theoretical considerations, Int. J. lmpact Engng., 8, 2, 159-170, 1989.

G.N. NURICK and J .B. MARTIN, Deformation of thin plates subjected to impulsive loading - a review. Part I. E:xperimental studies, Int. J. lmpact Engng., 8, 2, 171- 186, 1989.

M. KLEIBER and CZ. WOŹNIAK, Nonlinear mechanics of structures, PWN-Warszawa, Kluwer Academic Publishers, Dordrecht/Boston/London 1991.

J.H. ARGYRIS, J.S. DOLTSINIS and K.J. WILIAM, New developments in the inelastic analysis of quasistatic and dynamic problems, Int. J. Num. Engng., 14, 12, 1813-1850, 1979.

J.W. LEECH, E.A. WITMER and T.H. PIAN, Numerical calculation technique for large elastic-plastic transient deformations of thin shells, AIAA J., 12, 6, 2352-2359, 1974.

G. BĄK and W. DORNOWSKI, An analytical-numerical method for describing moderately large deflections of elastic-viscoplastic plates under pulse loads [in Polish], Arch. Inż. Ląd., 3-4, 305-315, 1991.

W. DORNOWSKI and G. BĄK, Analytical-numerical solutions for elastic-viscoplastic circular and rectangular plates under pulse loads within the range of moderately large deflections [in Polish], Arch. Inż. Ląd., 3-4, 373-392, 1991.

Y.C. FUNG, Foundations of solid mechanics [in Polish], PWN, Warszawa 1969.

Z. KĄCZKOWSKI, Plates. Structural analysis [in Polish], Arkady, Warszawa 1968.

A.S. VOLMIR, Flexible plates and shells [in Russian], Gossizdat, Moskva 1956.

CHEN-YUAN CHIA, Nonlinear analysis of plates, McGraw Hill, New York.

P. PERZYNA, Theory of viscoplasticity [in Polish], PWN, Warszawa 1966.

M. DUSZEK, Equations of the theory of large deflections of plastic shell8 [in Polish], IFTR Reports, 13, 1971.

G.BĄK, An analytical-numerical method for solving problems of dynamics of elastic­plastic beams and plates [in Polish], Arch. Inż. Ląd., 1, 51-62, 1986.

A. STOLARSKI, Dynamics of clamped rectangular elastic-viscoplastic plate [in Polish], Arch. Inż Ląd., 2, 203-217, 1988.