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IssuesArchive of Issues2002-5pp.100-109

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V. G. Bazhenov, S. A. Pirogov, and D. T. Chekmarev, "An explicit scheme with a stabilizing operator for solving nonstationary problems of structural dynamics," Mech. Solids. 37 (5), 100-109 (2002)
Year 2002 Volume 37 Number 5 Pages 100-109
Title An explicit scheme with a stabilizing operator for solving nonstationary problems of structural dynamics
Author(s) V. G. Bazhenov (Nizhni Novgorod)
S. A. Pirogov (Nizhni Novgorod)
D. T. Chekmarev (Nizhni Novgorod)
Abstract A method is justified and developed to increase the efficiency of explicit schemes for the numerical solution of nonstationary nonlinear problems of continuum dynamics and the theory of Timoshenko-type shells. The effectiveness of this method is illustrated by solving 2D dynamic problems for multilayered composite plates and shells subject to impulsive and impact loading.
References
1.  G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow, 1989.
2.  U. V. Rakitskii, S. M. Ustinov, and I. G. Chernorutskii, Numerical Methods for Solving Stiff Problems [in Russian], Nauka, Moscow, 1979.
3.  E. G. Evseev and A. U. Semenov, "A method for the numerical solution of equations of dynamics of thin-walled shells based on separating rapidly oscillating components," Doklady AN SSSR, Vol. 310, No. 4, pp. 485-487, 1990.
4.  V. G. Bazhenov and V. P. Stolov, "Numerical simulation of nonstationary axially symmetric wave processes in multilayered composite plates and shells of revolution," in Applied Problems of Strength and Plasticity. Numerical Simulation of Physico-mechanical Processes [in Russian], pp. 80-88, Izd-vo Gorkovsk. Un-ta, Gorky, 1989.
5.  V. G. Bazhenov and M. B. Prokopenko, "Numerical solution of axially symmetric nonlinear nonstationary problems of dynamics of composite elastic-plastic structures," in Applied Problems of Strength and Plasticity. Numerical Simulation of Physico-mechanical Processes [in Russian], No. 49, pp. 55-63, Izd-vo Nizhegorodsk. Un-ta, Nizhni Novgorod, 1991.
6.  S. V. Sheshenin and Fu Minkhuei, "A semi-implicit method for solving problems of elasticity for thin-walled axisymmetric bodies," Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 78-85, 1995.
7.  V. G. Bazhenov and D. T. Chekmarev, Variational-difference Schemes in Nonstationary Wave Problems of Dynamics of Plates and Shells [in Russian], Izd-vo Nizhegorodsk. Un-ta, Nizhni Novgorod, 1992.
8.  D. T. Chekmarev, "Construction of finite-difference schemes equivalent to numerical schemes of the finite element method," in Applied Problems of Strength and Plasticity. Numerical Modeling of Physical and Mechanical Processes [in Russian], pp. 129-138, Tovarishch. Nauchn. Izd. KMK, Moscow, 1999.
9.  M. L. Wilkins, "Numerical analysis of elastoplastic flows," in B. Alder, S. Fernbach, and M. Rotenberg (Editors), Fundamental Methods in Hydrodynamics [Russian translation], pp. 212-263, Mir, Moscow, 1967.
10.  V. G. Bazhenov and D. T. Chekmarev, "On the index commutativity of the numerical differentiation," Zh. Vychisl. Matematiki i Matemat. Fiziki [Journal of Computational Mathematics and Mathematical Physics], Vol. 29, No. 5, pp. 662-674, 1989.
11.  V. G. Bazhenov and A. I. Kibets, "Numerical simulation of 3D problems of nonstationary deformation of elastic-plastic structures by the finite-element method," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 52-59, 1994.
12.  V. I. Tsypkin, V. N. Rusak, A. G. Ivanov, A. G. Fedorenko, and O. S. Vorontsova, "Deformation and fracture of two-layered metallic/plastic shells subjected to an internal impulsive loading," Mekhanika Komposit. Materialov, No. 5, pp. 833-838, 1987.
13.  V. V. Adishchev, V. M. Kornev, and L. A. Talzi, Evaluation of Maximal Stresses in Closed Cylindrical Vessels Subjected to an Axially Symmetric Explosive Loading [in Russian], No. 6588-83, VINITI, Moscow, 1983.
Received 18 April 2000
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