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
 


IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2008-1pp.75-85

Archive of Issues

Total articles in the database: 9198
In Russian (. . ): 6504
In English (Mech. Solids): 2694

<< Previous article | Volume 43, Issue 1 / 2008 | Next article >>
A. V. Nalimov and Yu. V. Nemirovskii, "Closed system of limit equilibrium equations for axisymmetric shells," Mech. Solids. 43 (1), 75-85 (2008)
Year 2008 Volume 43 Number 1 Pages 75-85
DOI 10.3103/S002565440801007X
Title Closed system of limit equilibrium equations for axisymmetric shells
Author(s) A. V. Nalimov (Biysk Technological Institute, Polzunov Altai State Technical University, Trofimova 27, Biysk, Altaiskii kray, 659305, Russia, nalimov@bti.secna.ru)
Yu. V. Nemirovskii (Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian Academy of Sciences, Institutskaya 4/1, Novosibirsk, 630090, Russia, shulgin@itam.nsc.ru)
Abstract We consider rigid-plastic axisymmetric shells and use methods of control theory to construct the carrying capacity loss condition for such shells in formalized form.

We show that solving limit equilibrium problems for such structures can be reduced to solving a multipoint boundary value problem for a system of nonlinear differential-algebraic equations with unknown matching boundaries between different plastic modes as well as between rigid and plastic domains.

We present a complete system of resolving equations for the problem on the carrying capacity of axisymmetric shells, including the matching conditions for domains in different states.
References
1.  G. P. Cherepanov, Mechanics of Brittle Fracture (Nauka, Moscow, 1974; McGraw-Hill, New York, 1979).
2.  L. M. Kachanov, Foundations of Fracture Mechanics (Nauka, Moscow, 1974) [in Russian].
3.  Yu. N. Rabotnov, Creep of Construction Elements (Nauka, Moscow, 1966) [in Russian].
4.  D. D. Ivlev, Mechanics of Plastic Media, Vol. 1: Theory of Ideal Plasticity (Fizmatlit, Moscow, 2001); Vol. 2: General Problems. Rigid-Plastic and Elastoplastic State of Bodies. Reinforcement. Strain Theories. Compound Media (Fizmatlit, Moscow, 2002) [in Russian].
5.  J. L. Bogdanoff and F. Kozin, Probabilistic Models of Cumulative Damage (Wiley, New York, 1985; Mir, Moscow, 1989).
6.  Yu. N. Rabotnov, Mechanics of Deformable Solids (Nauka, Moscow, 1979) [in Russian].
7.  I. T. Vokhmyanin and Yu. V. Nemirovskii, "The Carrying Capacity of Smooth and Reinforced Cylindrical Shells," Prikl. Mekh. 3(1), 18-23 (1967) [Int. Appl. Mech. (Engl. Transl.) 3 (1), 9-12 (1967)].
8.  U. R. Lepik, "Application of Pontryagin maximum principle in problems of strength, stability, and oscillations of thin-walled constructions," Period. Sb. Perevodov Inostr. Statei. Mekhanika, No. 6, 126-141 (1974).
9.  S. A. Ambartsumyan, General Theory of Anisotropic Shells (Nauka, Moscow, 1974) [in Russian].
10.  A. Savchuk, "On Plastic Analysis of Shells," in: Mechanics of Strained Solids. Development Directions (Mir, Moscow, 1983) [in Russian].
11.  Yu. V. Nemirovskii, "Limiting Equilibrium of Multi-Layer Reinforced Axisymmetric Shells," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 6, 80-89 (1969) [Mech. Solids (Engl. Transl.)].
12.  V. Olshak and A. Savchuk, Inelastic Behavior of Shells (Mir, Moscow, 1969) [in Russian].
13.  D. D. Ivlev, Theory of Ideal Plasticity (Nauka, Moscow, 1966) [in Russian].
14.  E. T. Onat, "Limit Equilibrium of Slanted Conic Shells," Period. Sb. Perevodov Inostr. Statei. Mekhanika, No. 4, 105-115 (1961).
15.  W. T. Koiter, General Theorems for Elastic-Plastic Solids (Izd-vo Inostr. Lit., Moscow, 1961) [in Russian].
16.  A. R. Rzhanitsyn, Limit Equilibrium of Plastes and Shells (Nauka, Moscow, 1983) [in Russian].
17.  Yu. V. Nemirovskii and A. V. Nalimov, "Ideally Plastic Reinforcement of Compound Shell Constructions," in Materials of 11th All-Union Conference: Numerical Methods for Solving Problems of the Theory of Elasticity and Plasticity (ITPM SO AN SSSR, Novosibirsk, 1990), pp. 162-170.
18.  L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze, and Y. F. Mishchenko, The Mathematical Theory of Optimal Processes (J. Wiley and Sons, Interscience, New York, 1962; Nauka, Moscow, 1983).
19.  M. I. Reitman, "Optimal Design of Shells Using Maximum Principle," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3, 175-179 (1971) [Mech. Solids (Engl. Transl.)].
20.  V. S. Chernina, Statics of Thin-Walled Shells of Rotation (Nauka, Moscow, 1968) [in Russian].
21.  A. V. Nalimov and Yu. V. Nemirovskii, "Approximate Solutions for Cylindrical Shells of Minimal Weight," in Materials of 13th Inter-Republic Conference: Numerical Methods for Solving Problems of the Theory of Elasticity and Plasticity (ITPM SO AN SSSR, Novosibirsk, 1995), pp. 120-124.
22.  R. T. Shield, "Optimal Design of Shells," Trans. ASME. Ser. E. J. Appl. Mech. 27(2), 316-322 (1960).
23.  R. Hill, "Discontinuity Relations in Mechanics of Solids," Period. Sb. Perevodov Inostr. Statei. Mekhanika, No. 3, 117-142 (1963) [Progress in Solid Mechanics, Vol. 2 (North Holland Publ. Co., Amsterdam, 1961) pp. 246-276].
24.  Yu. V. Nemirovskii and A. V. Nalimov, "Limit Equilibrium of Reinforced Shells of Zero Gaussian Curvature," Prikl. Mekh. 25(9), 72-79 (1989) [Int. Appl. Mech. (Engl. Transl.) 25 (9), 913-919 (1989)].
25.  U. Ascher, J. Christiansen, and R. D. Russell, "Collocation Software for Boundary-Value ODES," ACM Trans. on Math. Software 7(2), 209-222 (1981).
26.  N. Wirth, Algorithms + Data Structures = Programs (Printice-Hall, Englewood Cliffs, New Jersey, 1976; Mir, Moscow, 1985).
27.  E. I. Grigolyuk and V. I. Shalashilin, "Method of Continuation with Respect to Parameter in Problems of Nonlinear Strain of Rods, Plates, and Shells," Uspekhi Mekhaniki 4(2), 89-122 (1981).
28.  G. Holl and G. Watt, Nodern Numerical Methods of Ordinary Differential Equations (Clarendon, Oxford, 1976; Mir, Moscow, 1979).
29.  E. T. Onat and W. Prager, "Limit of Economy of Materials in Shells," De Ingenieur 67(10), 46-49 (1955).
Received 27 January 2005
Link to Fulltext http://www.springerlink.com/content/y1j8m320315883g6
<< Previous article | Volume 43, Issue 1 / 2008 | 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, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100