Numerical analysis of buckling under axial compression of orthogrid-stiffened cylindrical shells made of aluminum alloys


Аuthors

Anisimov S. A.

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

e-mail: ser85@bk.ru

Abstract

In the introductory part of the article, it is noted that orthogrid-stiffened (reinforced on the inner surface by an orthogonal mesh of ribs) cylindrical shells made of aluminum alloys are widespread structural elements of rocket and space technology products, which under operating conditions are subject to large axial compressive loads. An important (in terms of strength) problem here is the calculation of this type of shell for buckling (or load-bearing capacity). Such calculations are usually performed using well-known commercial finite element systems. The corresponding computational models are built using both shell and volumetric elements. It is noted that the use of these detailed finite element models when carrying out the necessary parametric studies may turn out to be ineffective due to the large expenditure of computer time on the calculation of a separate option. This especially applies to cases of large-sized structures. Recent publications are pointed out, in which calculations for the buckling of the type of shell under consideration are carried out within the framework of models based on the “smearing” hypothesis. With this approach, the shell, supported by a network of ribs, is approximately considered according to the scheme of an axisymmetric structural-orthotropic shell, which makes it possible to construct a more computationally efficient calculation model. It is noted that in this article, a similar calculation model is constructed based on the numerical integration method.

The main content of the article is devoted to the description of the designated computational model and the calculated results obtained using it. Assuming that the reinforcing ribs are located quite often, using the “smearing” hypothesis, the ribbed cylindrical structure under consideration is reduced to a design of a structurally orthotropic shell, working in accordance with the Kirchhoff-Love hypotheses. The problem of buckling under axial compression of the shell model accepted for consideration is formulated in the traditional Eulerian (bifurcation) formulation, taking into account the linearity of the subcritical stress-strain state. The resulting linear homogeneous boundary value problem for a system of eight first-order ordinary differential equations (as a result of applying the procedure of expansion into Fourier series along the circumferential coordinate) for each harmonic number n is solved using the orthogonal sweep procedure of S.K. Godunov, including numerical integration according to the Kutta-Merson scheme. The numerical solution algorithm developed (in the form of a Fortran program) determines the harmonic number n and the smallest (critical) value of the compressive load Q, at which the specified homogeneous boundary value problem has a non-zero solution.

In order to check the reliability of the results obtained using the described computational model, a calculation of an axially compressible cylindrical orthogrid- stiffened shell was carried out and a comparison was made with the known solution obtained using a finite-difference computational model. Additionally, an alternative finite element model was built in the MSC Patran/Nastran software package based on a tetrahedral element (Tet10). A practical coincidence of the results of the buckling calculations using all three of these computational models was noted.

Next, the question is considered concerning the degree of consistency with experiment of the buckling calculation results obtained using the developed computational model. Calculations were carried out to determine the critical loads for nine different structures of samples of orthogrid-stiffened shells (made of aluminum alloy) that passed axial compression tests. A slight overestimation (by about 20%) of the calculated values of critical loads compared to the experiment was noted. The analysis carried out for the considered set of samples established the desired value of the “knockdown factor” in the form k = 0.75.

The final part of the article contains conclusions on the research performed. It is noted here that the article presents a computational model constructed using the “smearing” hypothesis and the numerical integration method for calculating the buckling of axially compressed cylindrical orthogrid-stiffened shells. The main results obtained using the developed model are also indicated.

Keywords:

buckling under axial compression, orthogrid-stiffened cylindrical shell, numerical integration method, finite element method

References

  1. Wang B., Tian K., Hao P., Zheng Y., Ma Y., Wang J. Numerical-based smeared stiffener method for global buckling analysis of grid-stiffened composite cylindrical shells, Composite Structures, 2016, no. 152, pp. 807-815. DOI: 10.1016/j.compstruct.2016.05.096

  2. Wang B., Du K., Hao P., Zhou C., Tian K., Xu S., Ma Y., Zhang X. Numerically and experimentally predicted knockdown factors for stiffened shells under axial compression, Thin-Walled Structures, 2016, no. 109, pp. 13-24. DOI: 10.1016/J.TWS.2016.09.008

  3. Wagner H.N.R., Huhne C., Niemann S., Tian K., Wang B., Hao P. Robust knockdown factors for the design of cylindrical shells under axial compression: Analysis and modeling of stiffened and unstiffened cylinders, Thin-Walled Structures, 2018, no. 127, pp. 629-645. DOI: 10.1016/j.tws.2018.01.041

  4. Tian K., Wang B., Hao P., Waas A.M. A high-fidelity approximate model for determining lower-bound buckling loads for stiffened shells, International Journal of Solids and Structures, 2018, no. 148-149, pp. 14–23. DOI: 10.1016/j.ijsolstr.2017.10.034

  5. Egorov I.A. Trudy MAI, 2022, no. 122. URL: https://www.trudymai.ru/eng/published.php?ID=164103. DOI: 10.34759/trd-2022-122-04

  6. Malinin G.V. Trudy MAI, 2021, no. 121. URL: https://www.trudymai.ru/eng/published.php?ID=162655. DOI: 10.34759/trd-2021-121-08

  7. Firsanov V.V., Vo A.Kh. Trudy MAI, 2018, no. 104. URL: https://www.trudymai.ru/eng/published.php?ID=102130

  8. Petrov I.I., Serdyuk D.O., Skopintsev P.D. Trudy MAI, 2022, no. 124. URL: https://www.trudymai.ru/eng/published.php?ID=167066. DOI: 10.34759/trd-2022-124-11

  9. Kabanov V.V., Zheleznov L.P. Voprosy prochnosti i dolgovechnosti elementov aviatsionnykh konstruktsyi (Questions of strength and durability of elements of aviation designs), Kuibyshev, KuAI, 1990, pp. 3-12.

  10. Yudin A.S., Ponomarev S.E., Yudin S.A. Izvestiya vysshikh uchebnykh zavedenii. Severo-Kavkazskii region. Estestvennye nauki, 2002, no. 1, pp. 45-49.

  11. Petrokovskii S.A. Nauchno-tekhnicheskie razrabotki OKB-23 – KB “Salyut ” (Scientific and technical developments OKB-23 – KB “Salyut ”), Moscow, Vozdushnyi transport, 2006, pp. 204-240.

  12. Petrokovskii S.A. Nauchno-tekhnicheskie razrabotki KB “Salyut” 2012-2013 gg (Scientific and technical developments KB “Salyut” 2012-2013 years), Moscow, Mashinostroenie, 2014, pp. 90-97.

  13. Hilburger M.W., Lovejoy A.E., Thornburgh R.P., Rankin C. Design and analysis of subscale and full-scale buckling-critical cylinders for launch vehicle technology development, AIAA Paper, 2012. DOI: 10.2514/6.2012-1865

  14. Hilburger M.W., Haynie W.T., Lovejoy A.E., Roberts M.G., Norris J.P., Waters W.A., Herring H.M. Subscale and full-scale testing of buckling-critical launch vehicle shell structures, AIAA Paper, 2012. URL: https://archive.org/details/NASA_NTRS_Archive_20120008177/page/n2/mode/1up

  15. Hilburger M.W., Waters W.A.J., Haynie W.T. Buckling Test Results from the 8-Foot-Diameter Orthogrid-Stiffened Cylinder Test Article TA01. [Test Dates: 19-21 November 2008], NASA/TP-2015-218785, L-20490, NF1676L-20067 - 2015.

  16. Hilburger M.W., Waters W.A.J., Haynie W.T., Thornburgh R.P. Buckling Test Results and Preliminary Test and Analysis Correlation from the 8-Foot-Diameter Orthogrid-Stiffened Cylinder Test Article TA02, NASA/TP-2017-219587, L-20801, NF1676L-26704 - 2017.

  17. Vasyukov E.V., Vladimirov S.A., Ezhov S.A. et at. Kosmonavtika i raketostroenie, 2022, no. 5 (128), pp. 54-66.

  18. Karmishin A.V., Lyaskovets V.A., Myachenkov V.I., Frolov A.N. Statika i dinamika tonkostennykh obolochechnykh konstruktsii (Statics and dynamics of thin-walled shell designs), Moscow, Mashinostroenie, 1975, 376 p.

  19. Godunov S.K. Uspekhi matematicheskikh nauk, 1961, vol. XVI, no. 3, pp. 171-174.

  20. Lans Dzh.N. Chislennye metody dlya bystrodeistvuyushchikh vychislitel'nykh mashin (Numerical methods for high-speed computers), Moscow, IL, 1962, 208 p.

  21. Sukhinin S.N. Prikladnye zadachi ustoichivosti mnogosloinykh kompozitnykh obolochek (Applied problems of buckling of multilayer composite shells), Moscow, Fizmatlit, 2010, 248 p.

  22. Stepkin V.I., Sukhinin S.N. Raketno-kosmicheskaya tekhnika, 1995, no. 1, pp. 89-101.

  23. Hilburger M.W. Developing the next generation shell buckling design factors and technologies, Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, 2012. DOI: 10.2514/6.2012-1686


Download

mai.ru — informational site MAI

Copyright © 2000-2024 by MAI

 Вход