Technical Briefs

Optimum Shape of Constant Stress Toroidal Shells

[+] Author and Article Information
Vu Truong Vu

Faculty of Civil Engineering,
Ho Chi Minh City University of Transport,
No.2, D3 Street, Ward 25,
Binh Thanh District, HCMC, Viet Nam
e-mail: vutruongvu@gmail.com

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received January 30, 2012; final manuscript received May 10, 2012; published online March 18, 2013. Assoc. Editor: Haofeng Chen.

J. Pressure Vessel Technol 135(2), 024501 (Mar 18, 2013) (4 pages) Paper No: PVT-12-1012; doi: 10.1115/1.4007043 History: Received January 30, 2012; Revised May 10, 2012

The paper presents the optimization of toroidal shell cross-sections under internal pressure. The wall thickness distribution along a circular centerline is derived in an analytical form. In membrane solution, this cross-section gives a constant Mises stress all over the shell. Therefore, it leads to material saving and contained volume increase in comparison with the traditional cross-section of circular constant thickness. The optimum shapes are designed for two states of shell, one is elasticity and the other is up to destruction. The maximum material saving can reach 70% in some configurations of toroid. Results of the proposed method are as good as or better than those found in literature.

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Vu, V. T., and Blachut, J., 2009, “Plastic Instability Pressure of Toroidal Shells,” Trans. ASME J. Pressure Vessel Technol., 131(5), 051203. [CrossRef]
Steele, C. R., 1965, “Toroidal Pressure Vessels,” J. Spacecr. Rockets, 2, pp. 937–943. [CrossRef]
Bogomol'nyi, V. M., and Zhidyaev, N. A., 1992, “Optimization of the Geometric Parameters of Elbows,” Chem. Petrol. Eng., 28, pp. 418–420. [CrossRef]
Vu, V. T., 2010, “Minimum Weight Design for Toroidal Pressure Vessels Using Differential Evolution and Particle Swarm Optimization,” Struct. Multidiscip. Optim., 42(3), pp. 351–369. [CrossRef]
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Grahic Jump Location
Fig. 1

Geometry of toroidal shell

Grahic Jump Location
Fig. 2

3D-view of benchmark toroids with R/r = 1.25, 2.5, and 5

Grahic Jump Location
Fig. 3

Optimal cross-sections of constant Mises stress toroid



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