Engineering Transactions, 29, 1, pp. 99-114, 1981

A Mode Solution for the Finite Deflections of a Circular Plate Loaded Impulsively

C. Guedes Soares
Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Lisboa

The mode approximation technique as originally presented by MARTIN and SYMONDS [7] is applicable to rigid-plastic structures undergoing infinitesimal deflections. The extension of the mode approach to the finite-deflection range can be done by considering a series of instantaneous modes [5-7], or by assuming a permanent mode shape [9, 16]. The method proposed in [9] is further developed here and applied to the study of a circular plate loaded impulsively. The final deflection is obtained using a method developed by Jones for beams and non-axisymmetric plates [10]. Comparison with experiments and other theoretical treatments show good correlation.

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E. H. LEE, P. S. SYMONDS, Large plastic deformations of beams under transverse impact, J. Appl. Mech, 19, 308, 1952

H. HOPKINS, W. PRAGER, On the dynamics of plastic circular plates, Z. Angew. Math. Phys, 5, 137, 1954.

J. B. MARTIN, lmpulsive loading theorems for rigid-plastic continua, J. Eng. Mech. Div., Am. Soc. Civ. Eng., 90, 27, 1964.

J. B. MARTIN, P S SYMONDS, Mode approximations for impulsively loaded rigid-plastic structures, J, Eng. Mech. Div., Am. Soc, Civ. Eng., 92, 43, 1966.

P. S. SYMONDS, C. T. CHON, Approximation techniques for impulsive loading of structures of time-dependent plastic behaviour with finite deflections, Mechanical properties of materials at high strain rates, J. Harding (Ed), Inst. of Physics, 299, London 1974.

C. T. CHON, Large dynamic plastic deflection of plates by mode method, J. Eng.

P. S. SYMONDS, C. T. CHON, Finite Viscoplastic deflections of an impulsively loaded plate by the mode approximation technique, J. Mech. Phys. Sol., 27, 1979.

C. GUEDES SOARES, Higher mode dynamic plastic response of beams with finite deflections, Ocean Engineer Thesis, Massachusetts Institute of Technology, 1976.

C. GUEDES SOARES, Discussion on large dynamic plastic deflection of plates by mode method, J. Eng. Mech. Div., Am. Soc. Civ. Eng., 103, 1194, 1977.

N. JONES, A theoretical study of the dynamic plastic behaviour of beams and plates with finite-deflections, Int. J. Sol. Struct., 1, 1007, 1971.

N. JONES, T. WIERZBICKI, A study of the higher modal dynamic plastic response of beams, Int. J. Mech. Sci., 18, 533, 1975.

N. JONES, C. GUEDES SOARES, Higher modal dynamic plastic behaviour of beams loaded impulsively, Int. J. Mech. Sci., 20, 135, 1978.

R. M. WALTERS, N. JONES, An approximate theoretical study of the dynamic plastic behaviour of shells, Int. J. Non-Linear Mech., 7, 255, 1972.

D. C. DRUCKER, W. PRAGER, H. J. GREENBERG, Extended limit design theorems for continuous media, Quart. App. Math., 9, 381, 1952.

J. B. MARTIN, A note on the uniqueness of solutions for dynamically loaded rigid-plastic and rigid-viscoplastic continua, J. Appl. Mech., 33, 207, 1966.

P. S. SYMONDS, T. WIERZBICKI, Membrane mode solutions for impulsively loaded circular plates, J. Appl. Mech., 46, 58, 1979.

N. JONES, Consistent equations for the large deflections of structures; Bull. Mech. Engng. Ed., 10, 9, 1971.

E. T. ONAT, W. PRAGER, Limit analysis of shells of revolution, Proc. Roy. Netherl. Acad. Sci., Ser. B, 57, 534, 1954.

P. G. HODGE, The linearization of plasticity problems by means of nonhomogeneous materials, Nonhomogeneity in Elasticity and Plasticity, Ed. W. OLSZAK, Pergamon Press, 147, London 1959.

D. C. DRUCKER, R. T. SHIELD, Limit analysis of symmetrically loaded thin shells of revolution, J. Appl. Mech., 26, 61, 1959.

P. G. HOOGE, Yield conditions for rotationally symmetric shells under axisymmetric loading, J. Appl. Mech., 27, 323, 1960.

A. J. WANG, The permanent deflection of a plastic plate under biast loading, J. Appl. Mech., 22, 375, 1955.

J. B. MARTIN, Mode approximations for impulsively loaded structures in the inelastic range, Structures, Solid Mechanics and Engineering Design, M.TE'ENI (Ed) J. Wiley and Sons Inc., 2, 1227, New York 1969.

P. S. SYMONDS, C. T. CHON, On dynamic plastic mode-form solutions, J. Mech. Phys. Sol., 26, 21, 1978.

A. L. FLORENCE, Annular plate under a transverse line impulse, AIAAJ, 3, 1726, 1965.

N. JONES, lmpulsive loading of a simply supported circular rigid plastic plate, J. Appl. Mech., 35, 59, 1968.

A. L. FLORENCE, Circular plate under a uniformly distributed impulse, Int. J. Sol. Struct., 2, 37, 1966.

T. WIERZBICKI, A method of approximation in the large deflection analysis of impulsively loaded rigid plastic structures, Act. Tech. Acad. Sci. Hung., 68, 403, 1970.

S. KALISZKY, Large deformations of rigid-viscoplastic structures under impulsive and pressure loading, J. Struct. Mech., 1, 295, 1973.

M. TAYA, T. MURA, Plastic behaviour of structures under impact loading investigated by the extended Hamilton's principle, Int. J. Sol. Struct. 10, 197, 1974.

A. J. WANG, H. G. HOPKINS, On the plastic deformation of built-in circular plates under impulsive load, J. Mech. Phys. Sol., 3, 22, 1954.