Electronic Scientific Journal
Diagnostics, Resource and Mechanics 
         of materials and structures


advanced search

IssuesAbout the JournalAuthorContactsNewsRegistration

2018 Issue 1

All Issues
2024 Issue 3
2024 Issue 2
2024 Issue 1
2023 Issue 6
2023 Issue 5
2023 Issue 4
2023 Issue 3
2023 Issue 2
2023 Issue 1
2022 Issue 6
2022 Issue 5
2022 Issue 4
2022 Issue 3
2022 Issue 2
2022 Issue 1
2021 Issue 6
2021 Issue 5
2021 Issue 4
2021 Issue 3
2021 Issue 2
2021 Issue 1
2020 Issue 6
2020 Issue 5
2020 Issue 4
2020 Issue 3
2020 Issue 2
2020 Issue 1
2019 Issue 6
2019 Issue 5
2019 Issue 4
2019 Issue 3
2019 Issue 2
2019 Issue 1
2018 Issue 6
2018 Issue 5
2018 Issue 4
2018 Issue 3
2018 Issue 2
2018 Issue 1
2017 Issue 6
2017 Issue 5
2017 Issue 4
2017 Issue 3
2017 Issue 2
2017 Issue 1
2016 Issue 6
2016 Issue 5
2016 Issue 4
2016 Issue 3
2016 Issue 2
2016 Issue 1
2015 Issue 6
2015 Issue 5
2015 Issue 4
2015 Issue 3
2015 Issue 2
2015 Issue 1






A. A. Semenov


DOI: 10.17804/2410-9908.2018.1.016-033

The paper analyzes the possibility of applying five different strength criteria (maximum stress criterion, Mises-Hill, Pisarenko-Lebedev, Fisher, Goldenblat-Kopnov) to calculating the strength of orthotropic shell structures. We consider shallow shells of double curvature, square in plan, panels of cylindrical and conical shells. A geometrically nonlinear mathematical model of their deformation, taking into account transverse shearing, is used. For calculations, the characteristics of modern orthotropic materials are used, such as fiberglass and CFRP. An increase in the areas of the failure of strength conditions with increasing load is shown.

Acknowledgments: The study was supported by the RF Ministry of Education and Science within the frame-work of the state order, project No. 9.5605.2017/8.9.

Keywords: strength, strength criterion, theory of strength, shell, CFRP


1.Goldenblat I.I., Kopnov V.A. Strength criterion for anisotropic materials. Izv. AN SSSR. Mekhanika, 1965, no. 6, pp. 77–83. (In Russian).

2.Bazhanov V.L., Goldenblat I.I., Kopnov V.A., Pospelov A.D., Sinyukov A.M. Plastinki i Obolochki iz Stekloplastikov [Fiberglass Plates and Shells]. M, Vysshaya Shkola Publ., 1970, 408 p. (In Russian).

3.Kopnov V.A., Belov G.P. Evaluating the strength of composite materials and other media with different types of anisotropy. Izvestiya RAN. MTT, 2014, no. 2 (32), pp. 73–80. (In Russian).

4.Giginjak F.F., Kovalchuk B.I., Lamashevsky V.P., Lebedev A.A. Handbook of Mechanical Properties of Structural Materials at a Complex Stress State. Begell House Inc. Publ., 2001, 504 p.

5.Pisarenko G.S., Lebedev A.A. Deformation and strength of materials at a complex stress state. Prikladnaya Mekhanika, 1968, no. 4, iss. 3, pp. 45–50. (In Russian).

6.Fisher L. How to predict structural behavior of R.P. Laminates. Modern Plastics, 1960, no. 6.

7.Zakharov K.V. Strength criterion for layered masses. Plasticheskie Massy, 1961, no. 8. (In Russian).

8.Malmeyster A.K. Geometry of strength theories. Mekhanika Polimerov, 1966, no. 4. (In Russian).

9. Alikin V.N., Litvin I.E., Sesyunin S.G., Sokolovsky M.I., Ushin N.V. Kriterii Prochnosti i Nadezhnost Konstruktsiy, pod red. chl.-korr. RAN M.I. Sokolovskogo [Criteria for the Strength and Reliability of Structures, M.I. Sokolovskiy, cor. memb. RAS, ed.]. Moscow, Nedra-Biznestsentr Publ., 2005, 164 p. (In Russian).

10.Aliev M.M., Shafieva S.V., Karimova N.G. Criteria for the strength and fracture of various materials with due regard for the effect of comprehensive pressure. Vestnik CHGPU im. I.Ya. Yakovleva. Ser. Mekhanika predelnogo sostoyaniya, 2012, no. 3 (13), pp. 64–71. (In Russian).

11.Aliev M.M., Bayburova M.M. Anisotropic materials short-time strength criteria and their application to limit state problems. Vestnik SamGU – Estestvennonauchnaya seriya, 2007, no. 6 (56), pp. 22–29. (In Russian).

12.Bendyukov V.V., Osyayev O.G. Strength criteria for anisotropic composite materials. Nauchnyy vestnik MGTU GA, 2011, no. 163, pp. 151–156. (In Russian).

13.Makovenko S.Ya. The Comparative Analysis of two Criteria of Anisotropic Material Strength. Stroitelnaya Mekhanika Inzhenernykh Konstruktsiy i Sooruzheniy, 2005, no. 1, pp. 65–70. (In Russian).

14.Nekliudova E.A., Semenov A.S., Melnikov B.E., Semenov S.G. Experimental research and finite element analysis of elastic and strength properties of fiberglass composite material. Magazine of Civil Engineering, 2014, no. 3, pp. 25–39. DOI: 10.5862/MCE.47.3.

15.Polilov A.N., Tatus N.A. Experimental substantiation of strength criteria for FRP showing directional type of fracture. Vestnik PNIPU, Mekhanika, 2012, no. 2, pp. 140–166. (In Russian).

16.Grebenyuk S.N., Melashchenko O.P. The use of various criteria for calculating the strength of fibrous composites. Zbіrnyk Naukovykh Prats Kharkіvskogo Unіversitetu Povіtryanykh Sil, 2012, no. 3 (32), pp. 134–136. (In Russian).

17.Galicki J., Czech M. A new approach to formulate the general strength theories for anisotropic discontinuous materials. Part A: The experimental base for a new approach to formulate the general strength theories for anisotropic materials on the basis of wood. Applied Mathematical Modelling, 2013, vol. 37, no. 3, pp. 815–827. DOI: 10.1016/j.apm.2012.03.004.

18. Niu J., Liu G., Tian J., Zhang Y., Meng L. Comparison of yield strength theories with experimental results. Engineering Mechanics, 2014, vol. 31, no. 1, pp. 181–187. DOI: 10.6052/j.issn.1000-4750.2012.09.0622.

19.Liu G. A novel limiting strain energy strength theory. Transactions of Nonferrous Metals Society of China, 2009, vol. 19, no. 6, pp. 1651–1662. DOI: 10.1016/S1003-6326(09)60084-4.

20.Zhang S., Song B., Wang X., Zhao D., Chen X. Deduction of geometrical approximation yield criterion and its application. Journal of Mechanical Science and Technology, 2014, vol. 28, no. 6, pp. 2263–2271. DOI: 10.1007/s12206-014-0515-6.

21.Zhu X.-K., Leis B.N. Average shear stress yield criterion and its application to plastic collapse analysis of pipelines. International Journal of Pressure Vessels and Piping, 2006, vol. 83, no. 9, pp. 663–671. DOI: 10.1016/j.ijpvp.2006.06.001.

22.Kalnins A., Updike D.P. Limit Pressures of Cylindrical and Spherical Shells. Journal of Pressure Vessel Technology, 2001, vol. 123, no. 3, pp. 288–292. DOI: 10.1115/1.1367273.

23.Zezin Y.P. Experimental investigation of the strength properties of particulate polymeric composites, 2016, vol. 1785, pp. 030036. DOI: 10.1063/1.4967057.

24.Yan L., Junhai Z., Ergang X., Xueye C. Research on burst pressure for thin-walled elbow and spherical shell made of strength differential materials. Materials Research Innovations, 2015, vol. 19, no. 5, pp. 80–87. DOI: 10.1179/1432891715Z.0000000001340.

25.Shroff S., Kassapoglou C. Progressive failure modelling of impacted composite panels under compression. Journal of Reinforced Plastics and Composites, 2015, vol. 34, no. 19, pp. 1603–1614. DOI: 10.1177/0731684415592485.

26.Sengupta J., Ghosh A., Chakravorty D. Progressive Failure Analysis of Laminated Composite Cylindrical Shell Roofs. Journal of Failure Analysis and Prevention, 2015, vol. 15, no. 3, pp. 390–400. DOI: 10.1007/s11668-015-9951-6.

27.Shokrieh M.M., Karamnejad A. Investigation of Strain Rate Effects on the Dynamic Response of a Glass/Epoxy Composite Plate under Blast Loading by Using the Finite-Difference Method. Mechanics of Composite Materials, 2014, vol. 50, no. 3, pp. 295–310. DOI: 10.1007/s11029-014-9415-1.

28.Günel M., Kayran A. Non-linear progressive failure analysis of open-hole composite laminates under combined loading. Journal of Sandwich Structures & Materials, 2013, vol. 15, no. 3, pp. 309–339. DOI: 10.1177/1099636213483651.

29.Van der Meer F.P., Sluys L.J., Hallett S.R., Wisnom M.R. Computational modeling of complex failure mechanisms in laminates. Journal of Composite Materials, 2012, vol. 46, no. 5, pp. 603–623. DOI: 10.1177/0021998311410473.

30.Pietropaoli E. Progressive Failure Analysis of Composite Structures Using a Constitutive Material Model (USERMAT) Developed and Implemented in ANSYS ©. Applied Composite Materials, 2012, vol. 19, no. 3–4, pp. 657–668. DOI: 10.1007/s10443-011-9220-0.

31.Garnich M.R., Akula V.M. Review of Degradation Models for Progressive Failure Analysis of Fiber Reinforced Polymer Composites. Applied Mechanics Reviews, 2009, vol. 62, no. 1, pp. 010801. DOI: 10.1115/1.3013822.

32.Bleyer J., de Buhan P. A numerical approach to the yield strength of shell structures. European Journal of Mechanics – A/Solids, 2016, vol. 59, pp. 178–194. DOI: 10.1016/j.euromechsol.2016.03.002.

33.Sun H.-H., Tan P.-L. Background of ABS Buckling Strength Assessment Criteria for Cylindrical Shells in Offshore Structures. Journal of Offshore Mechanics and Arctic Engineering, 2008, vol. 130, no. 2, pp. 021012. DOI: 10.1115/1.2913349.

34.Mellor P.B. The ultimate strength of thin-walled shells and circular diaphragms subjected to hydrostatic pressure. International Journal of Mechanical Sciences, 1960, vol. 1, nos. 2–3, pp. 216–228. DOI: 10.1016/0020-7403(60)90041-2.

35.Noh H.C. Ultimate strength of large scale reinforced concrete thin shell structures. Thin-Walled Structures, 2005, vol. 43, no. 9, pp. 1418–1443. DOI: 10.1016/j.tws.2005.04.004

36.Zhang B., Sun Q. The Ultimate Strength of Stiffened Panel with Overall Buckling. Advanced Materials Research, 2011, vol. 308–310, pp. 1297–1301. DOI: 10.4028/www.scientific.net/AMR.308-310.1297.

37.Ueda Y., Rashed S.M.H., Paik J.K. Buckling and ultimate strength interaction in plates and stiffened panels under combined inplane biaxial and shearing forces. Marine Structures, 1995, vol. 8, no. 1, pp. 1–36. DOI: 10.1016/0951-8339(95)90663-F.

38.Abrosimov N.A., Elesin A.V. Numerical analysis of dynamic strength of composite cylindrical shells under multiple-pulse exposures. PNRPU Mechanics Bulletin, 2016, no. 4, pp. 7–19. DOI: 10.15593/perm.mech/2016.4.01.

39.Karpov V.V., Semenov A.A. Strength criteria for thin orthotropic shells. Part 2: Calculation and analysis. Vestnik Grazhdanskikh Inzhenerov, 2015, no. 1 (48), pp. 60–70. (In Russian).

40.Tsvetkov S.V., Kulish G.G. Strength Criteria of Unidirectional Organic Plastic in Three-Axis Stress State. Vestnik MGTU im. N.E. Baumana. Seriya: Mashinostroe, 2011, no. SP, pp. 19–28. (In Russian).

41.Yu M.-H. Advances in strength theories for materials under complex stress state the 20th sentury. Appl. Mech. Rev., 2002, vol. 55, no. 3, pp. 169–218. DOI: 10.1115/1.1472455.

42.Yu M.-H., Li J.-C. Computational plasticity: with emphasis on the application of the unified strength theory. Hangzhou, Zhejiang Univ. Press, 2012, 529 p.

43.Kolupaev V.A., Yu M.-H., Altenbach H. Visualization of the Unified Strength Theory. Archive of Applied Mechanics, 2013, vol. 83, no. 7, pp. 1061–1085. DOI: 10.1007/s00419-013-0735-8.

44.Tsvetkov S.V. Strength criteria for transversely isotropic materials of different symmetry classes of structure. Vestnik MGTU im. N.E. Baumana. Seriya: Mashinostroenie, 2009, no. 1, pp. 86–99. (In Russian).

45.Karpov V.V., Semenov A.A. Strength criteria for thin orthotropic shells. Part 1: Analysis of the basic strength criteria for isotropic and orthotropic materials. Vestnik Grazhdanskikh Inzhenerov, 2014, no. 6 (47), pp. 43–51. (In Russian).

46.Smerdov A.A., Buyanov I.A., Chudnov I.V. Analysis of optimal combinations of requirements to developed CFRP for large space-rocket designs. Izvestiya Vuzov. Mashinostroenie, 2012, no. 8, pp. 70–77. (In Russian).

47.Tyshkevich V.N. The choice of strength criteria for pipes made of reinforced plastics. Izvestiya Volgogradskogo Gosudarstvennogo Tekhnicheskogo Universiteta, 2011, no. 5 (78), pp. 76–79. (In Russian).

48.Karpov V.V., Semenov A.A. Mathematical models and algorithms for studying strength and stability of shell structures. Journal of Applied and Industrial Mathematics, 2017, vol. 11, no. 1, pp. 70–81. DOI: 10.1134/S1990478917010082.

49.Kuznetsov E.B. Continuation of solutions in multiparameter approximation of curves and surfaces. Computational Mathematics and Mathematical Physics, 2012, vol. 52, no. 8, pp. 1149–1162. DOI: 10.1134/S0965542512080076.


Article reference

Semenov A. A. Analysis of the Strength of Shell Structures, Made from Modern Materials, According to Various Strength Criteria // Diagnostics, Resource and Mechanics of materials and structures. - 2018. - Iss. 1. - P. 16-33. -
DOI: 10.17804/2410-9908.2018.1.016-033. -
URL: http://eng.dream-journal.org/issues/2018-1/2018-1_135.html
(accessed: 07/24/2024).


impact factor
RSCI 0.42


MRDMS 2024
Google Scholar



Founder:  Institute of Engineering Science, Russian Academy of Sciences (Ural Branch)
Chief Editor:  S.V. Smirnov
When citing, it is obligatory that you refer to the Journal. Reproduction in electronic or other periodicals without permission of the Editorial Board is prohibited. The materials published in the Journal may be used only for non-profit purposes.
Home E-mail 0+

ISSN 2410-9908 Registration SMI Эл № ФС77-57355 dated March 24, 2014 © IMACH of RAS (UB) 2014-2024, www.imach.uran.ru