Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2001-5pp.126-140

Archive of Issues

Total articles in the database: 12804
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8044
In English (Mech. Solids): 4760

<< Previous article | Volume 36, Issue 5 / 2001 | Next article >>
V. G. Bazhenov and D. T. Chekmarev, "Numerical methods for solving problems of unsteady dynamics of thin-walled structures," Mech. Solids. 36 (5), 126-140 (2001)
Year 2001 Volume 36 Number 5 Pages 126-140
Title Numerical methods for solving problems of unsteady dynamics of thin-walled structures
Author(s) V. G. Bazhenov (Nizhni Novgorod)
D. T. Chekmarev (Nizhni Novgorod)
Abstract A review of numerical methods for solving problems of unsteady dynamics of thin-walled shell structures is presented. Major attention is given to methodological issues concerning the construction of numerical schemes and improvement of their effectiveness. We consider the convergence and stability of the numerical methods, as well as basic problems arising in the numerical analysis of thin-walled structures.
References
1.  N. P. Abovskii, N. P. Andreev, and A. P. Deruga, Variational Principles in Elasticity and the Theory of Shells [in Russian], Nauka, Moscow, 1978.
2.  N. A. Abrosimov and V. G.Bazhenov, "Analysis of elastoplastic processes of deformation of plates and shells of rotation under impulsive loading in a non-classical statement," Prikladnaya Mekhanika, Vol. 21, No. 1, pp. 73-79, 1985.
3.  L. Ya. Ainola, "Timoshenko-type nonlinear theory for elastic shells," Izv. AN SSSR. Ser. Fiz.-mat. i Tekhn. Nauk, Vol. 14, No. 3, pp. 337-344, 1965.
4.  L. Ya. Ainolla and U. K. Nigul, "Wave processes in deformation of elastic plates and shells," Izv. AN ESSR. Ser. Fiz.-mat. i Tekhn. Nauk, Vol. 14, No. 1, pp. 3-63, 1965.
5.  S. A. Anisimov, "Vector splitting of plane dynamic problem of elasticity for regions consisting of arbitrary quadrangles," in Dynamics of Continuum, No. 75, pp. 17-26, In-t Gidrodinamiki SO AN SSSR, Novosibirsk, 1986.
6.  B. D. Annin, "Mechanics of solids in the Siberian Branch of the Russian Academy of Sciences during 1988-1997," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 38, No. 4, pp. 28-45, 1997.
7.  S. B. Afanas'ev and E. A. Kozlov, "An algorithm for solving two-dimensional wave elastoplastic problems by Godunov's method," in Applied Problems of Strength and Plasticity. Algorithmization and Automation in Plasticity [in Russian], No. 36, pp. 91-100, Izd-vo Gorkovsk. Un-ta, Gorky, 1987.
8.  K. I. Babenko, Fundamentals of the Numerical Analysis [in Russian], Nauka, Moscow, 1986.
9.  V. G. Bazhenov, "Numerical analysis of unsteady processes of deformation of elastoplastic shells," Problemy Prochnosti, No. 11, pp. 51-54, 1984.
10.  V. G. Bazhenov, "Numerical modeling of unsteady problems of dynamics of elastoplastic structures," in Applied Problems of Strength and Plasticity [in Russian], No. 53, pp. 17-30, Tovarishch. Nauchn. Izd. KMK, Moscow, 1995.
11.  V. G. Bazhenov, S. V. Zefirov, and V. K. Lomunov, "A modified variational-difference method for solving axisymmetric problems of dynamics of elastoplastic structures with a filler," in Proceedings of 17th International Conference on the Theory of Shells and Plates [in Russian], pp. 172-178, Vol. 1, Kazan, 1996.
12.  V. G. Bazhenov, S. V. Zefirov, and M. V. Petrov, "Numerical solution of problems of unsteady interaction of elastoplastic shells of revolution subject to large deformations," in Applied Problems of Strength and Plasticity. Algorithmization and Automation of Solving Problems in Elasticity and Plasticity [in Russian], No. 28, pp. 54-59, Izd-vo Gorkovsk. Un-ta, Gorky, 1984.
13.  V. G. Bazhenov, S. V. Zefirov, A. V. Kochetkov, S. V. Krylov, and V. K. Lomunov, "Software package Dinamika-2," in Applied Problems of Strength and Plasticity. Algorithmization and Automation of Investigations [in Russian], No. 36, pp. 4-13, Izd-vo Gorkovsk. Un-ta, Gorky, 1987.
14.  V. G. Bazhenov, A. I. Kibets, and I. N. Tsvetkova, "Numerical modeling of unsteady processes of impact interaction of elastic shells and structures," Problemy Mashinostoeniya i Nadezhnosti Mashin, No. 2, pp. 20-26, 1995.
15.  V. G. Bazhenov, A. I. Kibets, and O. V. Tulintsev, "Application of the FEM moment scheme for the analysis of 3D nonlinear dynamics of massive and shell-type structural members," in Applied Problems of Strength and Plasticity. Methods of Solution [in Russian], No. 47, pp. 46-53, Izd-vo Nizhegorodsk. Un-ta, Nizhni Novgorod, 1991.
16.  V. G. Bazhenov and M. B. Prokopenko, "Numerical solution of axisymmetric nonlinear unsteady problems of dynamics of compound elastic structures," in Applied Problems of Strength and Plasticity. Numerical Modeling of Physical and Mechanical Processes [in Russian], No. 49, pp. 55-63, Izd-vo Nizhegorodsk. Un-ta, Nizhni Novgorod, 1991.
17.  V. G. Bazhenov and V. P. Stolov, "Numerical modeling of unsteady axisymmetric wave processes in multi-layered composite plates and shells of revolution," in Applied Problems of Strength and Plasticity. Numerical Modeling of Physical and Mechanical Processes [in Russian], No. 43, pp. 80-88, Izd-vo Gorkovsk. Un-ta, Gorky, 1989.
18.  V. G. Bazhenov and D. T. Chekmarev, Variational-difference Schemes in Unsteady Wave Problems of Dynamics of Plates and Shells [in Russian], Izd-vo Nizhegorodsk. Un-ta, Nizhni Novgorod, 1992.
19.  V. G. Bazhenov and D. T. Chekmarev, "On a finite-difference solution of wave equations in the theory of Timoshenko-type shells," in Applied Problems of Strength and Plasticity. Algorithmization and Automation of Solving Problems in Elasticity and Plasticity [in Russian], No. 19, pp. 41-50, Izd-vo Gorkovsk. Un-ta, Gorky, 1981.
20.  V. G. Bazhenov and D. T. Chekmarev, "On the index commutativity of the numerical differentiation," Zh. Vychisl. Matematiki i Matemat. Fisiki [Journal of Computational Mathematics and Mathematical Physics], Vol. 29, No. 5, pp. 662-674, 1989.
21.  V. G. Bazhenov and D. T. Chekmarev, "Stability analysis of the explicit finite-difference scheme cross for solving unsteady problems of elasticity and the theory of shells," in Applied Problems of Strength and Plasticity. Algorithmization and Automation of Solving Problems in Elasticity and Plasticity [in Russian], No. 28, pp. 15-22, Izd-vo Gorkovsk. Un-ta, Gorky, 1984.
22.  V. G. Bazhenov and A. P. Shinkarenko, "A variational-difference method for solving two-dimensional problems of dynamics of elastoplastic shells," in Applied Problems of Strength and Plasticity [in Russian], No. 3, pp. 61-69, Izd-vo Gorkovsk. Un-ta, Gorky, 1984.
23.  V. G. Bazhenov and A. P. Shinkarenko, "Elastoplastic deformation of compound shell structures subject to impulsive loading," Problemy Prochnosti, No. 3, pp. 25-29, 1981.
24.  V. F. Bakulin, I. F. Obrztsov, and V. A. Potopakhin, Dynamic Problems in Nonlinear Theory of Shells. The Action of Intensive Thermal-force Loads and Concentrated Energy Fluxes [in Russian], Nauka, Fizmatlit, Moscow, 1998.
25.  N. V. Banichuk, V. V. Kobelev, and R. B. Rikards, Optimization of Structural Elements from Composite Materials [in Russian], Mashinostroenie, Moscow, 1988.
26.  N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel'kov, Numerical Methods [in Russian], Nauka, Moscow, 1987.
27.  N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in Periodic Media. Mathematical Problems of Mechanics of Composite Materials [in Russian], Nauka, Moscow, 1984.
28.  A. E. Bogdanovich, Nonlinear Problems in Dynamics of Cylindrical Composite Shells [in Russian], Zinatne, Riga, 1987.
29.  I. O. Bogul'skii, "On one scheme of splitting the solution of the two-dimensional problem of the dynamics of solids," No. 1816-B89, VINITI, Moscow, 1989.
30.  V. P. Boldychev, Efficiency improvement of the finite element method for solving singular problems," in Issues of Dynamics and Strength [in Russian], No. 42, pp. 38-48, Zinatne, Riga, 1983.
31.  V. M.Boiko, A. I. Gulidov, A. I. Papyrin, V. N. Fomin, and Yu. A. Shitov, "Experimental-theoretical study of rebound of short rods from a rigid obstacle," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 5, pp. 129-133, 1982.
32.  V. I. Borisenko and A. I. Klokova, "Supercritical deformation of a cylindrical shell subjected to an impact," Prikl. Mekhanika, Vol. 2, No. 10, pp. 29-35, 1966.
33.  K. Washizu, Variational Methods in Elasticity and Plasticity [Russian translation], Mir, Moscow, 1987.
34.  V. V. Vasil'ev, Mechanics of Structures from Composite Materials [in Russian], Mashinostroenie, Moscow, 1988.
35.  A. V. Vestyak, A. G. Gorshkov, and D. V. Tarlakovskii, "Unsteady interaction of deformable bodies with the environment," in Achievements in Science and Technology. Mechanics. Volume 15 [in Russian], pp. 69-148, VINITI, Moscow, 1983.
36.  Yu. M. Volchkov, G. V. Ivanov, and V. D. Kutuzov, "Numerical solution of problems of dynamics of elastoplastic deformation of bodies of revolution based on the local linear polynomial approximation," in Numerical Methods for Solving Problems of Elasticity and Plasticity. Materials of the 7th All-Union Conference [in Russian], pp. 233-247, ITPM SO AN SSSR, Novosibirsk, 1982.
37.  A. S. Vol'mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow, 1972.
38.  S. K. Godunov, A. V. Zabrodin, M. Ya. Ivanov, et al, Numerical Solution of Multi-dimensional Problems in Gas Dynamics [in Russian], Nauka, Moscow, 1976.
39.  S. K. Godunov and V. S. Ryaben'kii, Difference Schemes [in Russian], Nauka, Moscow, 1973.
40.  A. I. Golovanov and M. S. Kornishin, Introduction to Finite Element Method for Statics of Thin Shells [in Russian], Fiz.-tekhn. In-t, Kazan, 1990.
41.  B. A. Gordienko, "On the numerical finite-difference solution of problems of impact-induced buckling of elastic systems," Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 143-148, 1970.
42.  V. A. Gorel'skii, I. E. Khorev, and N. T. Yugov, "Dynamics of a 3D process of asymmetric interaction of deformable bodies with a rigid wall," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 4, pp. 112-118, 1985.
43.  E. I. Grigolyuk, "Equations of three-layered shells with a light filler," Izv. AN SSSR. OTN, No. 1, pp. 77-84, 1957.
44.  A. I. Gulidov and V. M. Fomin, "Numerical modeling of rebound of axisymmetric rods from a rigid obstacle," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 3, pp. 126-132, 1980.
45.  E. G. Evseev and A. Yu. Semenov, "A method for numerical solution of equations of dynamics of thin-walled shells on the basis of separation of strongly oscillating components," Doklady AN SSSR, Vol. 310, No. 4, pp. 785-788, 1990.
46.  O. Zienkiewicz and K. Morgan, Finite Elements and Approximation [Russian translation], Mir, Moscow, 1986.
47.  G. V. Ivanov, "Construction of schemes for solving the plane dynamic problem of elasticity on the basis of the linear polynomial approximation," in Dynamics of Continuum, No. 37, pp. 63-77, In-t Gidrodinamiki SO AN SSSR, Novosibirsk, 1978.
48.  A. A. Il'yushin, Plasticity [in Russian], Izd-vo AN SSSR, Moscow, 1963.
49.  A. M. Kovalev, "Linear axisymmetric response on a compound shell of revolution to an impact loading," Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 177-184, 1981.
50.  D. Kolarov, A. Baltov, and N. Boncheva, Mechanics of Plastic Media [Russian translation from Bulgarian], Mir, Moscow, 1979.
51.  V. D. Koshur and Yu. V. Nemirovskii, Continuous and Discrete Models of Dynamic Deformation of Structural Elements [in Russian], Nauka, Novosibirsk, 1990.
52.  V. N. Kukudzhanov, "Numerical modeling of dynamic process of deformation and fracture in elastoplastic media," Uspekhi Mekhaniki [Advances in Mechanics], Vol. 8, No. 4, pp. 21-65, 1985.
53.  V. N. Kukudzanov and V. I. Kondaurov, "Numerical Solution of non-one-dimensional problems of Dynamics of Solids," in Problems of Dynamics of Elastoplastic Media. Volume 5 [in Russian], pp. 39-84, Mir, Moscow, 1975.
54.  O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics [in Russian], Nauka, Moscow, 1973.
55.  P. Z. Lugovoi, V. P. Mukoid, and V. F. Meish, Dynamics of Shell Structures under Explosive Loads [in Russian], Naukova Dumka, Kiev, 1991.
56.  G. Maenchen and S. Sack, "Computational method Tensor," in B. Alder, S. Fernbach, and M. Rotenberg (Editors), Fundamental Methods in Hydrodynamics [Russian translation], pp. 185-211, Mir, Moscow, 1967.
57.  A. P. Malyshev, "Analysis of transient processes in shell structures on the basis of the least variance scheme," Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 66-73, 1981.
58.  A. P. Malyshev and V. I. Panichkin, "Nonlinear wave processes in shells of revolution," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 175-178, 1976.
59.  G. I. Marchuk, Methods of Computational Mathematics [in Russian], Nauka, Moscow, 1989.
60.  G. I. Marchuk, Splitting Methods [in Russian], Nauka, Moscow, 1988.
61.  I. K. Naval, V. I. Patsyuk, and V. K. Rimskii, Unsteady Waves in Deformable Media [in Russian], Shtintsa, Kishinev, 1986.
62.  V. V. Novozhilov, "Mathematical models and accuracy of engineering calculations," Sudostroenie, No. 7, pp. 5-12, 1979.
63.  V. V. Novozhilov and L. I. Slepyan, "On the Saint-Venant principle in dynamics of rods," PMM [Applied Mathematics and Mechanics], Vol. 29, No. 2, pp. 261-281, 1965.
64.  N. F.) Noh, "CLM - Combined Lagrange-Euler method for solving unsteady two-dimensional problems," in B. Alder, S. Fernbach, and M. Rotenberg (Editors), Fundamental Methods in Hydrodynamics [Russian translation], pp. 128-184, Mir, Moscow, 1967.
65.  J. T. Oden, Finite Elements in Nonlinear Continuum Mechanics [Russian translation], Mir, Moscow, 1976.
66.  V. V. Ostapenko, "On the divergence form of finite-difference operators," in Dynamics of Continuum [in Russian], No. 70, pp. 105-126, In-t Gidrodinamiki SO AN SSSR, Novosibirsk, 1985.
67.  V. V. Ostapenko, "On the standard approximation of differential operators," in Dynamics of Continuum [in Russian], No. 72, pp. 67-83, In-t Gidrodinamiki SO AN SSSR, Novosibirsk, 1985.
68.  V. I. Patsyuk, G. A. Rybalkova, and P. F. Sabodash, "Wave processes in a cylindrical shell subjected to a non-axisymmetric longitudinal impact," Prikl. Mekhanika, Vol. 21, No. 1, pp. 35-42, 1985.
69.  B. E. Pobedrya, Mechanics of Composite Materials [in Russian], Izd-vo MGU, Moscow, 1984.
70.  B. E. Pobedrya, Numerical Methods in Elasticity and Plasticity [in Russian], Izd-vo MGU, Moscow, 1981.
71.  A. I. Ruzanov, "Numerical modeling of high-speed processes of penetration and breaking through with the use of grid-free Lagrangian methods," in Applied Problems of Strength and Plasticity. Numerical Modeling of Physical and Mechanical Processes [in Russian], pp. 122-124, Tovarishch. Nauchn. Izd. KMK, Moscow, 1999.
72.  Yu. V. Rakitskii, S. M. Ustinov, and I. G. Chernorutskii, Numerical Methods for Solving Stiff Systems [in Russian], Nauka, Moscow, 1979.
73.  R. D. Richtmyer and K. N. Morton, Difference Methods for Initial-value Problems [Russian translation], Mir, Moscow, 1972.
74.  A. I. Sadyrin, "Application of triangular grids to solving dynamic problems of elastoplasticity," in Applied Problems of Strength and Plasticity. Statics and Dynamics of Deformable Systems [in Russian], No. 24, pp. 39-46, Izd-vo Gorkovsk. Un-ta, Gorky, 1983.
75.  V. M. Sadovskii, "Hyperbolic variational inequalities in problems of dynamics of elastoplastic media," PMM [Applied Mathematics and Mechanics], Vol. 55, No. 6, pp. 1041-1048, 1991.
76.  A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow, 1983.
77.  A. A. Samarskii and Yu. P. Popov, Difference Schemes for Gas Dynamics [in Russian], Nauka, Moscow, 1975.
78.  A. S. Sakharov, V. N. Kislookii, V. V. Kirichevskii, at al., Finite Element Method in Mechanics of Solids [in Russian], Vishcha Shkola, Kiev, 1982.
79.  G. Strang and G. Fix, Theory of the Finite Element Method [Russian translation], Mir, Moscow, 1977.
80.  Yu. M. Tarnopol'skii, I. G. Zhigun, and V. A. Polyakov, Spatially Reinforced Composite Materials. A Handbook [in Russian], Mashinostroenie, Moscow, 1987.
81.  S. P. Timoshenko, Vibrations in Engineering [Russian translation], Fizmatgiz, Moscow, 1959.
82.  A. G. Ugodchikov, V. G. Bazhenov, and A. I. Ruzanov, "On numerical methods and the results of solving unsteady problems in the theory of elasticity and plasticity," in Numerical Methods in Continuum Mechanics [in Russian], Vol. 16, No. 4, pp. 129-149, VTs SO AN SSSR, Novosibirsk, 1985.
83.  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.
84.  D. T. Chekmarev, "Analysis of some FEM schemes of the theory of Timoshenko-type shells," in Applied Problems of Strength and Plasticity. Numerical Modeling of Physical and Mechanical Processes [in Russian], pp. 124-132, Tovarishch. Nauchn. Izd. KMK, Moscow, 1995.
85.  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.
86.  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.
87.  Yu. I. Shokin and N. N. Yanenko, Method of Differential Approximation: Application to Gas Dynamics [in Russian], Nauka, Novosibirsk, 1985.
88.  W. D. Schultz, "Two-dimensional finite-difference equations in Lagrangian variables," in Computational Methods in Hydrodynamics [Russian translation], pp. 9-54, Mir, Moscow, 1967.
89.  T. Belytschko and J. I. Lin, "Tsay Shyn-Chin explicit algorithms for the nonlinear dynamics of shells," Comput. Meth. Appl. Mech. and Engng., Vol. 42, No. 2, pp. 225-251, 1984.
90.  D. P. Flanagan and T. Belytschko, "A uniform strain hexahedron and quadrilateral with orthogonal hourglass control," Intern. J. Num. Meth. Engng., Vol. 17, No. 5, pp. 679-706, 1981.
91.  A. G. Petschek and M. E. Hanson, "Difference equation for two-dimensional elastic flow," J. Comp. Phys., Vol. 3, No. 2, pp. 307-321, 1968.
92.  O. C. Zienkewicz, R. L. Taylor, and J. Too, "Reduced integration technique in general analysis of plates and shells," Intern. J. Num. Meth. Engng., Vol. 3, No. 2, pp. 275-290, 1971.
Received 06 June 1999
<< Previous article | Volume 36, Issue 5 / 2001 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100