Abstract
The problem of viscoplastic bending of reinforced plates with varying thickness is formulated. An original method for the integration of this initial-boundary-value problem is developed. The numerical solution is compared with an analytical solution obtained with a rigid-plastic model of an isotropic circular plate. The efficiency of the method is demonstrated by analyzing the inelastic dynamics of reinforced plates with constant and varying thickness. It is shown that the maximum residual deflections of plates can be reduced severalfold by means of rational profiling and reinforcement
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G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kyiv (1985).
V. Z. Vlasov and N. N. Leont’ev, Beams, Plates, and Shells on Elastic Foundation [in Russian], Fizmatgiz, Moscow (1960).
F. V. Warnock and J. A. Pope, “The change in mechanical properties of mild steel under repeated impact,” Proc. Inst. Mech. Eng., 157, 33 (1947).
H. G. Hopkins and W. Prager, “On the dynamics of plastic circular plates,” J. Appl. Math. Phys. (ZAMP), 5, 317–330 (1954).
H. G. Hopkins and W. Prager, “The load carrying capacities of circular plates,” J. Mech. Phys. Solids, 2, 1–13 (1953).
M. I. Erkhov, Theory of Perfectly Plastic Bodies and Structures [in Russian], Nauka, Moscow (1978).
N. N. Kalitkin, Numerical Methods, Nauka, Moscow (1978).
L. M. Kachanov, Fundamentals of Plasticity Theory [in Russian], Nauka, Moscow (1969).
L. M. Kachanov, Creep Theory [in Russian], Fizmatgiz, Moscow (1960).
K. L. Komarov and Yu. V. Nemirovskii, Dynamics of Rigid-Plastic Structural Members [in Russian], Nauka, Novosibirsk (1984).
D. M. Karpinos (ed.), Handbook of Composite Materials [in Russian], Naukova Dumka, Kyiv (1985).
V. D. Koshur and Yu. V. Nemirovskii, Continuum and Discrete Dynamic Deformation Models of Structural Members [in Russian], Nauka, Novosibirsk (1990).
N. N. Malinin, Applied Theory of Plasticity and Creep [in Russian], Mashinostroenie, Moscow (1968).
C. J. Maiden and S. J. Green, “Compressive strain-rate tests on six selected materials at strain rates from 10−3 to 104 in/in/s,” Trans. ASME, J. Appl. Mech., 33, 496–504 (1966).
Yu. V. Nemirovskii, “Elastoplastic behavior of a reinforced layer,” Prikl. Mekh. Tekhn. Fiz., No. 6, 81–89 (1969).
Yu. V. Nemirovskii and A. P. Yaankovskii, “Some features of the equations of shells reinforced with fibers of constant cross section,” Mekh. Komp. Mater. Konstr., 3, No. 2, 20–40 (1997).
Yu. V. Nemirovskii and A. P. Yankovskii, “Elasticoplastic bending of rectangular plates reinforced with fibers of constant cross section,” Mech. Comp. Mater., 41, No. 1, 9–22 (2005).
Yu. V. Nemirovskii and A. P. Yankovskii, “Generalized Runge-Kutta integration of initial-boundary-value problems with large solution gradients,” Mat. Met. Fiz.-Mekh. Polya, 47, No. 1, 43–62 (2004).
P. M. Ogibalov, Issues of Dynamics and Stability of Shells [in Russian], Izd. MGU, Moscow (1963).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).
G. I. Taylor, “The testing of materials at high rates of loading,” J. Inst. Civil Eng., 26, 486–519 (1946).
G. L. Komissarova, “Features of how surface waves form in a cylinder made of a hard material and filled with a fluid,” Int. Appl. Mech., 43, No. 9, 988–999 (2007).
M. P. Malezhik, I. S. Chernyshenko, and G. P. Sheremet, “Diffraction of stress waves by a free or reinforced hole in an orthotropic plate,” Int. Appl. Mech., 43, No. 7, 767–771 (2007).
I. K. Senchenkov and N. F. Andrushko, “Thermomechanical coupling effects in a materially nonlinear disk under impulsive radial loading,” Int. Appl. Mech., 42, No. 8, 951–958 (2006).
A. V. Voropai and E. G. Yanyutin, “Identification of several impulsive loads on a plate,” Int. Appl. Mech., 43, No. 7, 780–785 (2007).
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 85–98, February 2008.
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Nemirovskii, Y.V., Yankovskii, A.P. Viscoplastic deformation of reinforced plates with varying thickness under explosive loads. Int Appl Mech 44, 188–199 (2008). https://doi.org/10.1007/s10778-008-0030-5
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DOI: https://doi.org/10.1007/s10778-008-0030-5