This article presents an approach to the minimum weight design for toroidal shells with strengthening component subject to internal pressure. The optimal shape is obtained by adjusting the geometry and wall thickness of the cross section associated with the thickness and position of the strengthening component. Constraints include first yield pressure, plastic pressures, plastic instability pressure, and internal volume of toroid. The weight saving can reach over 70% in some toroid configurations. The comparison of two optimization methods shows that differential evolution (DE) slightly outperforms particle swarm optimization (PSO) in the majority of investigated cases.
Issue Section:
Design and Analysis
References
1.
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
.2.
Steele
, C. R.
, 1965
, “Toroidal Pressure Vessels
,” J. Spacecr. Rockets
, 2
(6), pp. 937
–943
.3.
Marketos
, J. D.
, 1963
, “Optimum Toroidal Pressure Vessel Filament Wound Along Geodesic Lines
,” AIAA J.
, 1
(8
), pp. 1942
–1945
.4.
Mandel
, G.
, 1983
, “Torus-Shaped Pressure Vessel
,” UK Patent No. GB
2,110,566A.5.
Li
, S.
, and Cook
, J.
, 2002
, “An Analysis of Filament Overwound Toroidal Pressure Vessels and Optimum Design of Such Structures
,” ASME J. Pressure Vessel Technol.
, 124
(2
), pp. 215
–222
.6.
Vu
, V. T.
, 2013
, “Optimum Shape of Constant Stress Toroidal Shells
,” ASME J. Pressure Vessel Technol.
, 135
(2
), p. 024501
.7.
Blachut
, J.
, 1995
, “Plastic Loads for Internally Pressurised Torispheres
,” Int. J. Pressure Vessels Piping
, 64
(2
), pp. 91
–100
.8.
Storn
, R.
, and Price
, K.
, 1997
, “Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces
,” J. Global Optim.
, 11
(4
), pp. 341
–359
.9.
Kennedy
, J.
, and Eberhart
, R.
, 1995
, “Particle Swarm Optimization
,” IEEE International Conference on Neural Networks
(ICNN
), Perth, WA, Nov. 27–Dec. 1, pp. 1942
–1948
.10.
Clerc
, M.
, and Kennedy
, J.
, 2002
, “The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space
,” IEEE Trans. Evol. Comput.
, 6
(1
), pp. 58
–73
.Copyright © 2016 by ASME
You do not currently have access to this content.