Nonlinear Static Analysis of Spherical Shells with Variable Thickness under Hydrostatic Pressure
Article Sidebar
Main Article Content
Abstract
This paper presents a nonlinear static analysis of spherical shells with variable thickness under hydrostatic pressure. The shell geometry with variable thickness along the meridian coordinate can be defined using differential geometry. The energy functional is formulated in terms of shell displacements based on the principle of virtual work. Nonlinear numerical results can be obtained by finite element method and direct iterative procedure. The results indicate that the spherical shells with variable thickness exhibit reduced tangential and normal displacements near the support condition when compared to those with constant thickness. However, the membrane forces and bending moments along the meridian and circumferential coordinates show only minor differences. Consequently, the present results are applicable to the design of spherical shells with variable thickness. Moreover, the maximum circumferential membrane force is occurred in the range of 070o, and then decreases rapidly. The maximum meridian and circumferential bending moments are occurred in the range of 60o90o, and the maximum bending moments is occurred at the support.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The content within the published articles, including images and tables, is copyrighted by Rajamangala University of Technology Rattanakosin. Any use of the article's content, text, ideas, images, or tables for commercial purposes in various formats requires permission from the journal's editorial board.
Rajamangala University of Technology Rattanakosin permits the use and dissemination of article files under the condition that proper attribution to the journal is provided and the content is not used for commercial purposes.
The opinions and views expressed in the articles are solely those of the respective authors and are not associated with Rajamangala University of Technology Rattanakosin or other faculty members in the university. The authors bear full responsibility for the content of their articles, including any errors, and are responsible for the content and editorial review. The editorial board is not responsible for the content or views expressed in the articles.
References
Zingoni, A. (2015). Liquid-containment shells of revolution: A review of recent studies on strength, stability and dynamics. Thin-Walled Structures, 87, 102-114. https://doi.org/10.1016/j.tws.2014.10.016
Jiammeepreecha, W., Tiyasangthong, S., Chaidachatorn, K., Choeipo, S., Lerdchaipong, K., & Jamnam, S. (2025). Large displacement analysis of internally pressurized multi-segmented spherical shells with lagrange’s multiplier technique. The Journal of KMUTNB, 35(1), 1-19. https://doi.org/10.14416/j.kmutnb.2024.08.010
Artioli, E., & Viola, E. (2006). Free Vibration Analysis of Spherical Caps Using A G.D.Q. Numerical Solution. Journal of Pressure Vessel Technology, 128(3), 370-378. https://doi.org/10.1115/1.2217970
Jiammeepreecha, W., & Chucheepsakul, S. (2017). Nonlinear axisymmetric free vibration analysis of liquid-filled spherical shell with volume constraint. Journal of Vibration and Acoustics, 139(5), 051016. http://dx.doi.org/10.1115/1.4036500
Jiammeepreecha, W., Chaidachatorn, K., & Chucheepsakul, S. (2022). Large amplitude axisymmetric free vibration of a closed two-dimensional spherical pressure vessel with a constrained volume. International Journal of Structural Stability and Dynamics, 22(6), 2250077. https://doi.org/10.1142/S0219455422500778
Al-Gahtani, H., Khathlan, A., Sunar, M., & Naffa'a, M. (2014). Local pressure testing of spherical vessels. International Journal of Pressure Vessels and Piping, 114-115, 61-68. https://doi.org/10.1016/j.ijpvp.2013.12.004
Evkin, A.Y., & Lykhachova, O.V. (2019). Design buckling pressure for thin spherical shells: development and validation. International Journal of Solids and Structures, 156-157, 61-72. https://doi.org/10.1016/j.ijsolstr.2018.06.035
Wang, Y., Tang, W., Zhang, J., Zhang, S., & Chen, Y. (2019). Buckling of imperfect spherical caps with fixed boundary under uniform external pressure. Marine Structures, 65, 1-11. https://doi.org/10.1016/j.marstruc.2019.01.004
Du, X., Zhao, G., Wang, W., Guo, M., Zhang, R., & Yang, J. (2020). Study on dented hemispheres under external hydrostatic pressure. Marine Structures, 74, 102819. https://doi.org/10.1016/j.marstruc.2020.102819
Liang, C.C., Shiah, S.W., Jen, C.Y., & Chen, H.W. (2004). Optimum design of multiple intersecting spheres deep-submerged pressure hull. Ocean Engineering, 31(2), 177-199. https://doi.org/10.1016/S0029-8018(03)00120-3
Jiammeepreecha, W., Chucheepsakul, S., & Huang, T. (2015). Parametric study of an equatorially anchored deepwater fluid-filled periodic symmetric shell with constraint volume. Journal of Engineering Mechanics, 141(8), 04015019. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000920
Phadke, A., & Cheung, K. (2003). Nonlinear response of fluid-filled membrane in gravity waves. Journal of Engineering Mechanics, 129(7), 739-750. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:7(739)
Wang, C.M., Vo, K.K., & Chai, Y.H. (2006). Membrane analysis and minimum weight design of submerged spherical domes. Journal of Structural Engineering, 132(2), 253-259. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:2(253)
Jiammeepreecha, W., Chucheepsakul, S., & Huang, T. (2014). Nonlinear static analysis of an axisymmetric shell storage container in spherical polar coordinates with constraint volume. Engineering Structures, 68, 111-120. http://dx.doi.org/10.1016/j.engstruct.2014.02.014
Jiammeepreecha, W., Chucheepsakul, S., & Huang, T. (2014). Nonlinear static analysis of deep water axisymmetric spherical half drop shell. KMUTT Research and Development Journal, 37(2), 239-255.
Zingoni, A. (2001). Stresses and deformations in egg-shaped sludge digestors: membrane effects. Engineering Structures, 23(11), 1365-1372. https://doi.org/10.1016/S0141-0296(01)00055-4
Zingoni, A. (2001). Stresses and deformations in egg-shaped sludge digestors: discontinuity effects. engineering structures, 23(11), 1373-1382. https://doi.org/10.1016/S0141-0296(01)00056-6
Zingoni, A., Mokhothu, B., & Enoma, N. (2015). A theoretical formulation for the stress analysis of multi-segmented spherical shells for high-volume liquid containment. Engineering Structures, 87, 21-31. http://dx.doi.org/10.1016/j.engstruct.2015.01.002
Jiammeepreecha, W., Chaidachatorn, K., & Chucheepsakul, S. (2021). Nonlinear static response of an underwater elastic toroidal storage container. International Journal of Solids and Structures, 228, 111134. https://doi.org/10.1016/j.ijsolstr.2021.111134
Jiammeepreecha, W., Chaidachatorn, K., & Chucheepsakul, S. (2023). Large displacement analysis of egg-shaped containment shells using lagrange multipliers. International Journal of Solids and Structures, 279, 112390. https://doi.org/10.1016/j.ijsolstr.2023.112390
Jiammeepreecha, W., Chaidachatorn, K., & Chucheepsakul, S. (2023). Nonlinear static analysis of multi-segmented toroidal shells under external pressure. Thin-Walled Structures, 189, 110920. https://doi.org/10.1016/j.tws.2023.110920
Jiammeepreecha, W., Chaidachatorn, K., Klaycham, K., Athisakul, C., & Chucheepsakul, S. (2024). Multi-segmented fifth-order polynomial–shaped shells under hydrostatic pressure. Thin-Walled Structures, 203, 112214. https://doi.org/10.1016/j.tws.2024.112214
Sekhon, G.S., & Bhatia, R.S. (2000). Generation of exact stiffness matrix for a spherical shell element. Computers and Structures, 74(3), 335-349. https://doi.org/10.1016/S0045-7949(98)00316-2
Langhaar, H.L. (1964). Foundations of practical shell analysis. University of Illinois at Urbana-Champaign.
Tangbanjongkij, C., Jiammeepreecha, W., & Chucheepsakul, S. (2019). Large displacement analysis of ellipsoidal pressure vessel heads using the fundamental of differential geometry. International Journal of Pressure Vessels and Piping, 172, 337-347. https://doi.org/10.1016/j.ijpvp.2019.04.001
Chaidachatorn, K., Ngohpok, C., Jiammeepreecha, W., Lerdchaipong, K., Chupkhunthod, W., & Jamnam, S. (2025). Large amplitude free vibration of spherical dome structures with variable thickness. The Journal of King Mongkut's University of Technology North Bangkok, 35(1), 1-15. https://doi.org/10.14416/j.kmutnb.2024.08.007
Mase, G.T., & Mase, G.E. (1999). Continuum mechanics for engineers. CRC Press.
Langhaar, H.L. (1962). Energy methods in applied mechanics. John Wiley & Sons.
Cook, R.D., Malkus, D.S., Plesha, M.E., & Witt, R.J. (2002). Concepts and applications of finite element analysis. John Wiley & Sons.
Jiammeepreecha, W., Chaidachatorn, K., Tiyasangthong, S., & Jamnam, S. (2023). Nonlinear static analysis of egg-shaped toroidal shells under internal pressure. Rattanakosin journal of science and technology (RJST), 5(3), 14-36. Search at https://ph02.tci-thaijo.org/index.php/RJST/article/view/250556
Reddy, J.N. (2004). An introduction to nonlinear finite element analysis. Oxford University Press.
Young, W.C., & Budynas R.G. (2002), Roark’s formulas for stress and strain. McGraw-Hill.
