Nonlinear Static Analysis of Egg-Shaped Toroidal Shells under Internal Pressure
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Abstract
This paper presents a nonlinear static analysis of egg-shaped toroidal shells under internal pressure. Strain- and curvature-displacement relations are considered in the energy functional of the egg-shaped toroidal shell system in terms of the metric tensor and curvature components, and are written in terms of the appropriate form for nonlinear analysis. Lagrange multiplier’s method is introduced in the present formulation to enforce the discontinuity effect. The numerical results in terms of the meridian and normal to the meridian displacements can be obtained by nonlinear finite element method. The toroidal shell displacements from the present formulation are found to be in close agreement with the finite element commercial software results. Finally, the effects of the internal pressure, cross-sectional radii ratio, and bend-to-cross-sectional radii ratio on the numerical results in terms of toroidal shell displacements are demonstrated in this paper.
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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. (2016). Finite element analysis of toroidal membrane under external pressure. UBU Engineering Journal, 9(2), 47-56. (in Thai).
Chaidachatorn, K., Jiammeepreecha, W., & Jamnam, S. (2021). Axisymmetric and antisymmetric free vibrations of inflated toroidal membrane. The Journal of KMUTNB, 31(4), 661-674. (in Thai).
Zingoni, A., & Enoma, N. (2020). On the strength and stability of elliptic toroidal domes. Engineering Structures, 207, 110241. https://doi.org/10.1016/j.engstruct.2020.110241
Zhang, J., Dai, M., Wang, F., Tang, W., & Zhao, X. (2021). Buckling performance of egg-shaped shells fabricated through free hydroforming. International Journal of Pressure Vessels and Piping, 193, 104435. https://doi.org/10.1016/j.ijpvp.2021.104435
Huang, H., Zou, M.S., & Jiang, L.W. (2021). Analysis of characteristic of acoustic radiation from axisymmetric pressure-resistant egg-shaped shells in the ocean environment. Applied Ocean Research, 116, 102890. https://doi.org/10.1016/j.apor.2021.102890
Zhang, J., Wang, M., Wang, W., & Tang, W. (2017). Buckling of egg-shaped shells subjected to external pressure. Thin-Walled Structures, 113, 122-128. https://doi.org/10.1016/j.ijpvp.2021.104435
Sanders Jr, J.L., & Liepins, A. (1963). Toroidal membrane under internal pressure. AIAA Journal, 1(9), 2105-2110. https://doi.org/10.2514/3.2001
Jiammeepreecha, W., & Chucheepsakul, S. (2017). Nonlinear static analysis of an underwater elastic semi-toroidal shell. Thin Walled Structures, 116, 12-18. https://doi.org/10.1016/j.tws.2017.03.001
Jiammeepreecha, W., Suebsuk, J., & Chucheepsakul, S. (2020). Nonlinear static analysis of liquid-containment toroidal shell under hydrostatic pressure. Journal of Structural Engineering, 146(1), 04019169. https://doi.org/10.1061/(ASCE)ST.1943-541X.000246
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
Sun, B. (2021). Small Symmetrical deformation of thin torus with circular cross-section. Thin-Walled Structures, 163, 107680. https://doi.org/10.1016/j.tws.2021.107680
Sutcliffe, W.J. (1971). Stress analysis of toroidal shells of elliptical cross-section. International Journal of Mechanical Sciences, 13(11), 951-958. https://doi.org/10.1016/0020-7403(71)90081-6
Galletly, G.D. (1998). Elastic buckling of complete toroidal shells of elliptical cross-section subjected to uniform internal pressure. Thin-Walled Structures, 30(1), 23-34. https://doi.org/10.1016/S0263-8231(97)00030-X
Zingoni, A., Enoma, N., & Govender, N. (2015). Equatorial bending of an elliptic toroidal shell. Thin-Walled Structures, 96, 286-294. https://doi.org/10.1016/j.tws.2015.08.017
Tangbanjongkij, C., Chucheepsakul, S., Pulngern, T., & Jiammeepreecha, W. (2022). Analytical and numerical approaches for stress and displacement components of pressurized elliptic toroidal vessels. International Journal of Pressure Vessels and Piping, 199, 104675. https://doi.org/10.1016/j.ijpvp.2022.104675
Tangbanjongkij, C., Chucheepsakul, S., Pulngern, T., & Jiammeepreecha, W. (2023). Axisymmetric buckling analysis of submerged hemi-elliptic toroidal shells. Thin-Walled Structures, 183, 110383. https://doi.org/10.1016/j.tws.2022.110383
Enoma, N., & Zingoni, A. (2020). Analytical formulation and numerical modelling for multi-shell toroidal pressure vessels. Computers and Structures, 232, 105811. https://doi.org/10.1016/j.compstruc.2017.07.013
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. (in Thai).
Jiammeepreecha, W., & Chucheepsakul, S. (2017). Nonlinear free vibration of internally pressurized axisymmetric spherical shell. KMUTT Research and Development Journal, 40(4), 509-532. (in Thai).
Langhaar, H.L. (1962). Energy methods in applied mechanics. John Wiley & Sons.
Jiammeepreecha, W., & Chucheepsakul, S. (2019). Nonlinear free vibration analysis of a toroidal pressure container under constrained volume condition. International Journal of Structural Stability and Dynamics, 19(10), 1950118. https://doi.org/10.1142/S0219455419501189
Mase, G.T., & Mase, G.E. (1999). Continuum mechanics for engineers, CRC Press.
Cook, R.D., Malkus, D.S., Plesha, M.E., & Witt, R.J. (2002). Concepts and applications of finite element analysis. John Wiley & Sons.
Langhaar, H.L. (1964). Foundations of practical shell analysis. University of Illinois at Urbana-Champaign.
Abaqus. (2016). ABAQUS Analysis User's Manual, Hibbitt, Karlsson and Sorensen, Pawtucket.