 | | 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
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 51, Issue 4 / 2016 | Next article >> |
| M.F. Baburchenkov and N.M. Borodachev, "Infinite Systems in Problems for a Stiffened Rectangular Plate," Mech. Solids. 51 (4), 436-450 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
4 |
Pages |
436-450 |
| DOI |
10.3103/S0025654416040075 |
| Title |
Infinite Systems in Problems for a Stiffened Rectangular Plate |
| Author(s) |
M.F. Baburchenkov (Smolensk Auto Aggregate Plant AMO ZIL, ul. Gubenko 26, Smolensk, 214011 Russia, babur_mf@mail.ru)
N.M. Borodachev (National Aviation University, pr. Kosmonavta Komarova 1, Kiev, 03680 Ukraine) |
| Abstract |
A method is proposed for obtaining analytic solutions of a set of infinite systems of linear algebraic equations arising in problems of elasticity for stiffened rectangular plates with stiffening ribs. The method is based on a transformation of a set of infinite systems to a single system and on determining a majorant of the function generating the system series with regard to the order of the unknowns. It is proved that the constructed solution satisfies the infinite system for large indices of the unknowns. The amount of computations is decreased, and the reliability of the results increases. Some realization examples are given. |
| Keywords |
interaction mechanics, stiffened rectangular plate, infinite systems of equations |
| References |
| 1. | V. M. Aleksandrov,
"On a Method of Reducing Dual Integral Equations and Dual Series Equations
to Infinite Algebraic Systems,"
Prikl. Mat. Mekh.
39 (2), 324-332 (1975)
[J. Appl. Math. Mech. (Engl. Transl.)
39 (2), 303-311 (1975)]. |
| 2. | V. M. Alexandrov,
"Analytic Methods in Problems for Finite Bodies
with Improperly Mixed Boundary Conditions,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 2, 51-57 (2014)
[Mech. Solids (Engl. Transl.)
49 (2), 156-161 (2014)]. |
| 3. | L. A. Galin (Editor)
The Development of Theory of Contact Problems in USSR
(Nauka, Moscow, 1976)
[in Russian]. |
| 4. | M. F. Baburchenkov and N. M. Borodachev,
"Approach to Solving Plane Contact Problems for a Rectangular Domain,"
in Contemporary Problems of Mechanics and Aviation
(Mashinostroenie, Moscow, 1982),
pp. 55-64
[in Russian]. |
| 5. | B. M. Koyalovich,
"Study of Infinite Systems of Linear Equations,"
Trudy Fiz.-Mat. Inst. im. Steklova
3, 41-167 (1930). |
| 6. | B. M. Koyalovich,
"To the Theory of Infinite Systems of Linear Equations (Answer to Prof. R. O. Kuz'min),"
Trudy Fiz.-Mat. Inst. im. Steklova
2 (4), 1-16 (1932). |
| 7. | R. O. Kuz'min,
"To the Theory of Infinite Systems of Linear Equations,"
Trudy Fiz.-Mat. Inst. im. Steklova
2 (2), 18-41 (1931). |
| 8. | V. T. Grinchenko,
Equilibrium and Steady-State Oscillations of Finite-Dimensional Elastic Bodies
(Naukova Dumka, Kiev, 1978)
[in Russian]. |
| 9. | A. N. Tsvetkov and M. I. Chebakov,
"An Efficient Technique for Solving a Class of Infinite Systems in Contact Problems in the Theory of Elasticity,"
Prikl. Mat. Mekh.
55 (2), 344-347 (1991)
[J. Appl. Math. Mech. (Engl. Transl.)
55 (2), 279-282 (1991)]. |
| 10. | L. V. Kantorovich and V. I. Krylov,
Approximate Methods of Higher Analysis
(Fizmatgiz, Moscow-Leningrad, 1962; Interscience, New York, 1964). |
| 11. | G. A. Korn and T. M. Korn,
Mathematical Handbook for Scientists and Engineers
(McGraw-Hill, New York, 1961; Nauka, Moscow, 1979). |
| 12. | E. Melan,
"Ein Beitrag zur Theorie geschweisster Verbindungen,"
Ingenieur - Archiv
3 (2), 123-129 (1932) |
| 13. | R. Muki and E. Sternberg,
"On the Diffusion of Load from a Transverse Tension bar
into a Semi-Infinite Elastic,"
Trans. ASME. Ser. E
35 (4), 737-746 (1968). |
| 14. | B. L. Abramyan,
"On a Contact Problem for Half-Plane,"
Izv. Nauk SSSR. Mekh. Tverd. Tela,
No. 5, 4-10 (1972)
[Mech. Solids (Engl. Transl.)]. |
| 15. | N. K. Arutunyan and S. M. Mkhitaryan,
"Some Contact Problems for a Semi-Plane with Elastic Stiffeners,"
in Trends in Elasticity and Thermoelasticity,
Witold Nowacki Anniversary Volume
(Wolters, Noordhoff Publ., 1971),
pp. 3-20. |
| 16. | V. Yu. Salamatova,
"Interaction of a Deformable Patch with a Stressed Strip,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 62-67 (2009)
[Mech. Solids (Engl. Transl.)
44 (1), 57-61 (2009)]. |
| 17. | B. M. Nuller,
"Contact Problems for Bar-Reinforced Strips and Rectangular Plates,"
Prikl. Mat. Mekh.
39 (3), 559-564 (1975)
[J. Appl. Math. Mech. (Engl. Transl.)
39 (3), 534-539 (1975)]. |
| 18. | D. Bartuszat,
"Beitrag zur Spannungsermittlung an Bleichfeldern mit eingeschweisster Aussteifung,"
ZIS - Mitteilungen
17 (9), 1025-1031 (1975). |
| 19. | B. Budiansky and Wu Tai Te,
"Transfer of Load to a Sheet from a Rivet - Attached Stiffener,"
J. Math. Phys.
40 (2), 142-162 (1961). |
| 20. | L. S. Rybakov,
"Contact Problems of Discrete Interaction of a Plate with a Rod,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 2, 160-171 (1983)
[Mech. Solids (Engl. Transl.)]. |
| 21. | E. I. Grigolyuk and V. M. Tolkachev,
Contact Problems of Theory of Plates and Shells
(Mashinostroenie, Moscow, 1980)
[in Russian]. |
| 22. | I. S. Gradshtein and I. M. Ryzhik,
Tables of Integrals, Sums, Series, and Products
(Nauka, Moscow, 1971)
[in Russian]. |
| 23. | M. F. Baburchenkov,
"Boundary Effect in Car Frame Components,"
Gruzovik. Transp. Kompl. Spetstekhn.,
No. 4, 33-37 (2013). |
| 24. | V. Z. Vlasov,
Thin-Walled Elastic Rods,
(Fizmatgiz, Moscow, 1959)
[in Russian]. |
|
| Received |
22 November 2013 |
| Link to Fulltext |
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