Engineering Transactions, 43, 1-2, pp. 183-204, 1995

A Comparative Study of Vibrations of Elasto-Viscoplastic Shells and Plates

P. Kłosowski
Gdańsk University of Technology, Gdańsk

K. Woźnica
Université des Sciences et Technologies de Lille, Villeneuve D'ascq

D. Weichert
Université des Sciences et Technologies de Lille, Villeneuve D'ascq

A method of solution of the problem of nonlinear vibrations of elasto-viscoplastic plates and shells is presented, based on the first order shear deformation-moderate rotation theory of the laminated shells. Viscoplastic material behaviour is taken into account by the models developed by Perzyna, Chaboche and Bodner-Partom, respectively. The equations of motion are integrated by the central difference method, while the constitutive equations are integrated by the trapezoidal rule in an iterative process. In both cases the same time step is used. Numerical examples and comparison with experimental results are presented.

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P. KLOSOWSKI, K. WOŹNlCA and D. WEICHERT, Dynamics of elasto-viscoplastic plates and shells, Arch. Appl. Mech., 1995 [in print].

E.A. WITMER, H.A. BALMER, J.W. LEECH and T.H.H. PIAN, Large dynamic deformations of beams, rings, plates and shells, AIAA J., 1, 8, 1848-1858, 1963.

T. WIERZBICKI, lmpulsive loading of rigid viscoplastic plates, Int. J. Solids Struct., 3, 635-647, 1967.

O.A. CALDER, J.M. KELLY and W. GOLDSMITH, Projectile impact on an infinite viscoplastic plate, Int. J. Solids Struct., 7, 1143-1152, 1971.

W. WOJEWÓDZKI and T. WIERZBICKI, Transient response of viscoplastic rectangular plates, Arch. Mech., 24, 4, 587-604, 1972.

T. WIERZBICKI and A.L. FLORENCE, A theoretical and experimental investigation of impulsively loaded clamped circular viscoplastic plates, Int. J. Solids Struct., 13, 865-876, 1977.

CH.T. CHON and P.S. SYMONDS, Large dynamic plastic deflection of plates by mode method, J. Engng. Mech. Division, Proc. ASCE, 103, DEMI, 3-14, 1977.

P.S. SYMONDS and CH.T. CHON, Finite viscoplastic deflections of an impulsively loaded plate by the mode approximation technique, J. Appl. Math. Phys. Solids, 27, 115-133, 1979.

W. IDCZAK, CZ. RYMARZ and A. SPYCHAŁA, Large deflection of a rigid-viscoplastic impulsively loaded circular plate, J. Tech. Phys., 21, 4, 473-487, 1980.

W. IDCZAK, Approximate solutions in dynamics of inelastic membranes. Part I [in Polish], Engng. Trans., 33, 4, 519-535, 1985.

T. WIERZBICKI, lmpulsive loading of a spherical container with rigid-viscoplastic and strain rate sensitive material, Arch. Mech., 15, 775-790, 1963.

A. PABJANEK, Analysis of viscoplastic cylindrical shells, IFTR Reports, Polish Academy of Sci., 43, 1971.

T. WIERZBICKI, An approximate linear theory of viscoplastic shells, Arch. Mech., 24, 5-6, 941-953, 1972.

W. WOJNO, Perturbation solution for a rigid-viscoplastic spherical container, Arch. Mech., 31, 3, 407-422, 1979.

W. WOJNO and T. WIERZBICKI, Perturbation solution for a rigid-viscoplastic spherical container and for impulsively loaded viscoplastic plates, Int. J. Appl. Non-Linear Mech., 15, 211-223, 1980.

W. WOJEWÓDZKI, L. KWAŚNIEWSKI and S. JEMIOŁO, Vibrations of elastic-viscoplastic spherical shell in the range of moderate deflections [in Polish], Prace Nauk. Polit. Warszawskiej, 114, 6-40, 1992.

T. WIERZBICKI and H. ANDRZEJEWSKI, Impulsive loading of viscoplastic cylindrical shells, Proc. Symp. Plastic Analysis of Struct., Jassy, 461-479, Septernber 1972.

S.R. BODNER and P .S. SYMONDS, Experiments on the viscoplastic response of circular plates to impulsive loading, J. Mech. Phys. Solids., 27, 91-113, 1979.

W. IDCZAK, CZ. RYMARZ and A. SPYCHAŁA, Studies on shock-wave loaded, clamped circular plates, J. Tech. Phys., 22, 2, 175-184, 1981.

J.W. LEECH, Finite-difference circulation method for large elastic-plastic dynamically-induced deformations of general thin shells, Ph. D. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 1966.

R. SCHMIDT and J.N. REDDY, A refined small strain moderate rotations theory of elastic anisotropic shell, ASME J.Appl. Mech., 55, 611-617, 1988.

A.F. PALMERJO, J.N. REDDY and R. SCHMIDT, On a moderate rotation theory of laminated anisotropic shells. Part I, II, Int. J. Non-linear Mech., 25, 687-714, 1990.

R. SCHMIDT and D. WERCHERT, A refined theory of elastic-viscoplastic shells at moderate rotations, ZAMM, 69, 1, 11-n, 1989.

P. PERZYNA, Fundamental problem3 of viscoplasticity, Adv. in Mech., 9, 243-377, 1966,

J. LEMAITRE and J.-L. CHABOCHE, Mechanics of solid materials, Cambridge University Press, Cambridge 1990.

S.R. BODNER and Y. PARTOM, Constitutive equations for elasto-vicoplastic strain­hardening materials, ASME J. Appl. Mech., 42, 3, 385-389, 1975.

K. WOŹNICA, Lois de comportement du solide elasto-viscoplastique, Cahiers de Mécanique, Univ. des Sciences et Techn. de Lille, EUDIL-LML, 2, 1993.

A. BEN-CHEICK, Elasto-viscoplasticité à température variable, Ph.D. Thesis, Universiteé Paris 6, 1987.

T.M. MILLY and D.H. ALLEN,. A comparative study of non-linear rate-dependent mechanical constitutive theories for crystalline solids at elevated temperatures, Rep. API-E-5-82, Virginia Politechnic Inst. and State University, Blackburg, Virginia 1982.

J. ARGYRIS, H. BALMER and I.ST. DOLTSINIS, On shell models for impact analysis, The Winter Annual Meeting of the American Society of Mechanical Engineers, Vol. 3, 443-456, Dec. 1989.

T. BELYTSCHKO, B.L. WONG and H.Y. CHIANG, lmprovements in low-order shell elements for explicit transient analysis, The Winter Annual Meeting of the American Society of Mechanical Enginners, Vol. 3, 383-398, Dec. 1989.

H.A. BALMER and E.A. WITMER, Theoretical-exprimental correlation of large dynamic and permanent deformation of impulsively loaded simple structure, Air Force Flight Dynamics Laboratory, Report FDP-64-108, 1964.

A.M. RAJNDRAN, S.J. BLESS and D.S. DAWICKE, Evaluation of Bodner-Partom model parameters at high strain rates, ASME, J. Engng. Mat. Tech., 108, 75-80, 1986.

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