A perfect rigid–plastic body is used as a model to develop a general procedure for analyzing the dynamic behavior of an arbitrary curvilinear plate of variable thickness with an arbitrary internal hole. The plate is subjected to an arbitrary, uniform, short-term dynamic surface load. Two plate deformation patterns are considered. Analytic formulas for plastic zones, ultimate loads, and residual deflections are presented. Numerical examples are given
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References
A. S. Grigor’ev, “Load-bearing capacity of annular plates,” Inzh. Sb., 16, 177–182 (1953).
M. I. Erkhov, Theory of Perfectly Plastic Bodies and Structures [in Russian], Nauka, Moscow (1978).
L. V. Kantorovich and G. P. Akilov, Functional Analysis, Pergamon Press, Oxford (1982).
Yu. V. Nemirovskii and T. P. Romanova, “Dynamic deformation of a curvilinear plate with a rigid insert,” Prikl. Mekh. Tekhn. Fiz., 47, No. 2, 126–138 (2006).
Yu. V. Nemirovskii and T. P. Romanova, “Dynamics of a rigid-plastic curvilinear plate of varying thickness with a free internal hole or a rigid ring,” in: Theoretical and Applied Mechanics (International Research-and-Technology Collection), issue 21, BNTU, Minsk (2006), pp. 60–66.
Yu. V. Nemirovskii and T. P. Romanova, “Modeling the dynamic behavior of a rigid–plastic curvilinear plate with an arbitrary free hole,” in: Theoretical and Applied Mechanics (International Research-and-Technology Collection), issue 23, BNTU, Minsk (2007), pp. 26–34.
Yu. V. Nemirovskii and T. P. Romanova, “Deformation of protective flat barriers with access hatches,” Strength of Materials, 39, No. 1, 12–23 (2007).
Yu. V. Nemirovskii and T. P. Romanova, “Dynamic deformation of rigid–plastic curvilinear plates of varying thickness,” Prikl. Mekh. Tekhn. Fiz., 48, No. 5, 108–120 (2007).
Yu. V. Nemirovskii and T. P. Romanova, “Dynamics of a rigid-plastic circular plate with an arbitrary free internal hole,” in: Proc. 9th All-Russian Research-and-Technology Conf. Science, Industry, and Defense (Novosibirsk, April 23–25, 2008) [in Russian], NGTU, Novosibirsk (2008), pp. 262–274.
A. R. Rzhanitsyn, Limit Equilibrium of Plates and Shells [in Russian], Nauka, Moscow (1983).
A. A. Savelov, Plane Curves [in Russian], Fizmatgiz, Moscow (1960).
N. Jones, “Finite deflections of a simply supported rigid-plastic annular plate loaded dynamically,” Int. J. Solids Struct., 4, 593–603 (1968).
V. N. Mazalov and Yu. V. Nemirovsky, “Dynamical bending of circular piece-wise nonhomogeneous plates,” Arch. Mech., 25, No. 3, 469–490 (1973).
V. N. Mazalov and Yu. V. Nemirovsky, “Dynamical bending of rigid-plastic annular plates,” Int. J. Non-Linear Mech., 11, No. 1, 25–39 (1976).
Z. Mroz, “Plastic deformations of annular plates under dynamic loads,” Arch. Mech., 10, No. 4, 499–516 (1958).
R. K. Narasimhan and V. Verreyya, “Yield line analysis of square slabs with central rectangular openings,” J. Inst. Eng. (India) Civil Eng. Div., 59, No. 2, 138–143 (1978).
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Translated from Prikladnaya Mekhanika, Vol. 46, No. 3, pp. 70–82, March 2010.
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Nemirovskii, Y.V., Romanova, T.P. Dynamics of a rigid-plastic curvilinear plate of varying thickness with an arbitrary hole. Int Appl Mech 46, 304–314 (2010). https://doi.org/10.1007/s10778-010-0311-7
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DOI: https://doi.org/10.1007/s10778-010-0311-7