Static problems for toroidal shells with elliptical cross-section made of elastic orthotropic composites are considered. Variational difference and Lagrange multiplayer methods with mixed functionals are used. The ellipticity of the cross-section is significant. Emphasis is placed on the accuracy of the results. The agreement between the internal and external forces in the transverse and longitudinal sections is used as an integral criterion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. N. Guz, A. S. Kosmodamianskii, V. P. Shevchenko, et. al., Stress Concentration, Vol. 7 of the twelve-volume series Composite Mechanics [in Russian], A.S.K., Kyiv (1998).
Yu. Yu. Abrosov, V. A. Maximyuk, and I. S. Chernyshenko, “Influence of cross-sectional ellipticity on the deformation of a long cylindrical shell,” Int. Appl. Mech., 52, No. 5, 529–534 (2016).
P. A. Bakusov and A. A. Semenov, “Stability of toroidal shell segments at variation of a deflection angle,” PNRPU Mechanics Bulletin, No. 3, 17–36 (2017).
I. S. Chernyshenko and V. A. Maximyuk, “On the stress-strain state of toroidal shells of elliptical cross-section formed from nonlinear elastic orthotropic materials,” Int. Appl. Mech., 36, No. 1, 90–97 (2000).
C. P. Fowler, A. C. Orifici, and C. H. Wang, “A review of toroidal composite pressure vessel optimization and damage tolerant design for high pressure gaseous fuel storage,” Int. J. Hydrogen Energy, 41, No. 47, 22067–22089 (2016).
Y. Kisioglu, “Burst pressure determination of vehicle toroidal oval cross-section LPG fuel tanks,” J. Pressure Vessel Technol., 133, No. 3, 031202-1–031202-5 (2011).
I. V. Lutskaya, V. A. Maximuk, E. A. Storozhuk, and I. S. Chernyshenko, “Nonlinear elastic deformation of thin composite shells of discretely variable thickness,” Int. Appl. Mech., 52, No. 6, 616–623 (2016).
V. A. Maximyuk and I. S. Chernyshenko, “Nonlinear elastic state of thin-walled toroidal shells made of orthotropic composites,” Int. Appl. Mech., 35, No.12, 1238–1245 (1999).
V. A. Maximyuk, “Study of the nonlinearly elastic state of an orthotropic cylindrical shell with a hole using mixed functionals,” Int. Appl. Mech., 37, No. 12, 1602–1606 (2001).
V. F. Maximyuk, E. A. Storozhuk, and I. S. Chernyshenko, “Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review),” Int. Appl. Mech., 48, No. 6, 613–687 (2012).
M. D. Pazhooh, M. A. Dokainish, and S. Ziada, “Finite element modal analysis of on inflatable, self-rigidizing toroidal satellite component,” Exper. Appl. Mech., 6, No. 1, 281–288 (2011).
S. Roychowdhury and A. DasGupta, “Inflating a flat toroidal membrane,” Int. J. Solids Struct., 67–68, 182–191 (2015).
E. J. Ruggiero, A. Jha, G. Park, and D. J. Inman, “A literature review of ultra-light and inflated toroidal satellite components,” The Shock and Vibration Digest, 35, No. 3, 171–181 (2003).
E. A. Storozhuk and A. V. Yatsura, “Exact solutions of boundary-value problems for noncircular cylindrical shells,” Int. Appl. Mech., 52, No. 4, 386–397 (2016).
E. A. Storozhuk and A. V. Yatsura, “Analytical-numerical solution of static problems for noncircular cylindrical shells,” Int. Appl. Mech., 53, No. 3, 313–325 (2017).
W. J. Sutcliffe, “Stress analysis of toroidal shells of elliptical cross-section,” Int. J. Mech. Sci., 13, No. 11, 951–958 (1971).
V. T. Vu, “Minimum weight design for toroidal shells with strengthening component,” J. Pressure Vessel Technol., 138, No. 2, 21202-1–021202-7 (2015).
A. C. Young, W. G. Davids, D. J. Whitney, J. D. Clapp, and A. G. Goupee, “Structural testing and analysis of a braided, inflatable fabric torus structure,” Acta Astronaut., 139, 189–200 (2017).
A. Zingoni, N. Enoma, and N. Govender, “Equatorial bending of an elliptic toroidal shell,” Thin-Walled Struct., 96, 286–294 (2015).
L. Zu, S. Koussios, and A. Beukers, “A novel design solution for improving the performance of composite toroidal hydrogen storage tanks,” Int. J. Hydrogen Energy, 37, No. 19, 14343–14350 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 54, No. 6, pp. 57–62, November–December, 2018.
Rights and permissions
About this article
Cite this article
Lutskaya, I.V., Maximuk, V.A. & Chernyshenko, I.S. Modeling the Deformation of Orthotropic Toroidal Shells with Elliptical Cross-Section Based on Mixed Functionals. Int Appl Mech 54, 660–665 (2018). https://doi.org/10.1007/s10778-018-0920-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-018-0920-0