 | | 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 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| Yu.I. Vinogradov and M.V. Konstantinov, "Scope of Inextensible Frame Hypothesis in Local Action Analysis of Spherical Reservoirs," Mech. Solids. 52 (3), 342-352 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
3 |
Pages |
342-352 |
| DOI |
10.3103/S0025654417030116 |
| Title |
Scope of Inextensible Frame Hypothesis in Local Action Analysis of Spherical Reservoirs |
| Author(s) |
Yu.I. Vinogradov (Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5, Moscow, 105005 Russia, yuvino@rambler.ru)
M.V. Konstantinov (Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5, Moscow, 105005 Russia) |
| Abstract |
Spherical reservoirs, as objects perfect with respect to their weight, are used in spacecrafts, where thin-walled elements are joined by frames into multifunction structures. The junctions are local, which results in origination of stress concentration regions and the corresponding rigidity problems. The thin-walled elements are reinforced by frame to decrease the stresses in them. To simplify the analysis of the mathematical model of common deformation of the shell (which is a mathematical idealization of the reservoir) and the frame, the assumption that the frame axial line is inextensible is used widely (in particular, in the manual literature). The unjustified use of this assumption significantly distorts the concept of the stress-strain state. In this paper, an example of a lens-shaped structure formed as two spherical shell segments connected by a frame of square profile is used to carry out a numerical comparative analysis of the solutions with and without the inextensible frame hypothesis taken into account. The scope of the hypothesis is shown depending on the structure geometric parameters and the load location degree. The obtained results can be used to determine the stress-strain state of the thin-walled structure with an a priori prescribed error, for example, in research and experimental design of aerospace systems. |
| Keywords |
spherical reservoir, mathematical model of frame deformation mechanics, frame rigidity |
| References |
| 1. | V. L. Biderman,
Mechanics of Thin-Walled Structures
(Mashinostroenie, Moscow, 1977)
[in Russian]. |
| 2. | G. B. Men'kov,
Solution of Problems of Deformable Shell Mechanics by Functional Normalization Method,
Candidate's Dissertation in Physics and Mathematics
(Kazan, 1999)
[in Russian]. |
| 3. | Yu. I. Vinogradov and G. B. Men'kov,
A Method for Functional Normalization for Boundary Value Problems in the Theory of Shells
(Editorial URSS, Moscow, 2001)
[in Russian]. |
| 4. | M. V. Konstantinov,
"Qunatitative Evaluation of Errors of Vlasov Mathematical Model for Depressed Spherical Shell,"
Nauka Obraz. MGTU im. N.E. Baumana. El. Zh.,
No. 12, 858-877 (2014). |
| 5. | Yu. I. Vinogradov, V. G. Georgievskii, and M. V. Konstantinov,
"Goldenweizer Asymptotics in Strength Calculations of Spherical Reservoirs,"
Vestnik MGTU im. N.E. Baumana. Mashinostr.,
No. 3, 119-133 (2015). |
| 6. | Yu. I. Vinogradov,
"Influence of Frame Rigidity on Deformation Mechanics of Cylindrical Shells,"
Izv. Vyssh. Uchebn. Zaved. Mashinostr.,
No. 9, 20-25 (2013). |
| 7. | L. H. Donnell,
Beams, Plates, and Shells
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| 8. | I. A. Birger and Ya. G. Panovko (Editors),
Strength, Stability, Vibrations,
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| 9. | A. P. Filin,
Elements of the Theory of Shells
(Stroiizdat, Leningrad Division, Leningrad, 1975)
[in Russian]. |
| 10. | Ya. M. Grigorenko, L. A. Il'in, and A. D. Kovalenko,
Theory of Thin Conical Shells and Their Applications in Machine Engineering
(Izdat. AN UkrSSR, Kiev, 1963)
[in Russian]. |
|
| Received |
30 April 2015 |
| Link to Fulltext |
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