Buckling of a ring joint with the cylindrical shell under internal pressure in the shell

Authors

  • Maria L. Boyarskaya St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;
  • Sergey B. Filippov St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;

DOI:

https://doi.org/10.21638/11701/spbu01.2016.210

Abstract

Buckling under the uniform internal pressure of a thin circular cylindrical shell supported by the rings with T-shaped cross-section is studied. As a model of the ring the annular plate supported on outer edge by a circular beam is used. The classical model of a ring — a beam with T-shaped cross-section does not allow to solve the given problem, because the buckling deformations are localized on the surface of the ring. It is impossible to find the critical pressure corresponding to such loss of stability by means of the beam model. In the first approximation the buckling problem for the annular plate joint with the cylindrical shell is reduced to the solution of an eigenvalue problem for the bending equation of the annular plate. In the assumption, that the width of the plate is much less than its internal radius the approximate formulas for calculation of the critical pressure are obtained. The results found by Rayleigh—Ritz method and shooting procedure differ a little from each other. It is shown, that the critical pressure for the rings with the rectangular cross-section section is greater, than for the rings with T-shaped cross-section. Refs 9. Figs 3. Tables 2.

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References

Литература

1. Андрианов И.В., Лесничая В.А., Маневич Л.И. Метод усреднения в статике и динамике ребристых оболочек. М.: Наука, 1985. 224 с.

2. Tian J., Wang C.M., Swaddiwudhipohg S. Elastic buckling analysis of ring-stiffened cylindrical shell under general pressure loading via the Ritz method // Thin Walled Structures, 1999. Vol. 35. P. 1-24.

3. Teng J.G., Rotter J.M. Buckling of Thin Metal Shells. CRC Press, 2003. 520 p.

4. Вольмир А.С. Устойчивость деформируемых систем. М.: Наука, 1967. 984 с.

5. Пустовой Н.В., Матвеев К.А., Моховнев Д.В. Устойчивость кольцевых ортотропных пластин // Прикладная механика и техническая физика. 2000. Т. 41, № 2. С. 166-170.

6. Боярская М.Л., Филиппов С.Б. Устойчивость цилиндрической оболочки, подкрепленной шпангоутами с тавровым поперечным сечением // Вестник С-Петерб. ун-та. Сер. 1. 2015. Т. 2(60), вып. 3. С. 431-442.

7. Filippov S.B. Optimal design of stiffened cylindrical shells based on an asymptotic approach // Technische Mechanik. 2004. Band 24, Heft 3-4. P. 221-230.

8. Mansfield E.H. On the buckling of an annular plate // Quart. J. Mech. and Applied Math. 1960. Vol. 13. P. 16-23.

9. Tovstik P.E., Smirnov A.L. Asymptotic methods in the buckling theory of elastic shells. Singapore; New Jersey; London; Hong Kong: World Scientific Publishing Co Ltd., 2001. 347 p.

References

1. Andrianov I.V., Lesnichaya V. A., Manevich L. I., Averaging in statics and dynamics of ringstiffened shells (Nauka, Moscow, 1985) [in Russian].

2. Tian J., Wang C.M., Swaddiwudhipohg S., “Elastic buckling analysis of ring-stiffened cylindrical shell under general pressure loading via the Ritz method”, Thin Walled Structures 35, 1–24 (1999).

3. Teng J. G., Rotter J.M., Buckling of Thin Metal Shells (CRC Press, 2003).

4. Volmir A. S., Stability of deformable systems (Nauka, Moscow, 1967) [in Russian].

5. Pustovoi N.V., Matveev K.A., Mokhovnev D.V., “Buckling of annular orthotropic plates”, Prikladnaya mekhanika i tekhnicheskaya phisika 41, 166–170 (2000) [in Russian].

6. Boyarskaya M. L., Filippov S.B., “Buckling of cylindrical shell stiffened by rings with T-shaped cross-section”, Vestnik Sankt-Peterburgskogo Universiteta. Series 1 2(60), Issue 3, 431–442 (2015) [in Russian].

7. Filippov S.B., “Optimal design of stiffened cylindrical shells based on an asymptotic approach”, Technische Mechanik 24(3–4), 221–230 (2004).

8. Mansfield E.H., “On the buckling of an annular plate”, Quart. J. Mech. and Applied Math. 13, 16–23 (1960).

9. Tovstik P.E., Smirnov A. L., Asymptotic methods in the buckling theory of elastic shells (World Scientific Publishing Co Ltd., Singapore, New Jersey, London, Hong Kong, 2001).

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Published

2020-10-19

How to Cite

Boyarskaya, M. L., & Filippov, S. B. (2020). Buckling of a ring joint with the cylindrical shell under internal pressure in the shell. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 3(2), 1. https://doi.org/10.21638/11701/spbu01.2016.210

Issue

Vol. 3 No. 2 (2016)

Section

Mechanics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.