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Article

An Investigaton of Minimum-Weight Dual-Material Symmetrically Loaded Wheels and Torsion Arms

[+] Author and Article Information
Peter Dewhurst, Sriruk Srithongchai

Department of Industrial and Manufacturing Engineering, University of Rhode Island, Kingston, RI 02881

J. Appl. Mech 72(2), 196-202 (Mar 15, 2005) (7 pages) doi:10.1115/1.1831295 History: Received May 14, 2003; Revised July 21, 2004; Online March 15, 2005
Copyright © 2005 by ASME
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References

Michell,  A. G. M., 1904, “Limits of Economy of Material in Frame-Structures,” Philos. Mag., 6, pp. 589–597.
Hemp, W. S., 1958, “The Theory of Structural Design,” Report No. 115, College of Aeronautics, Cranfield, UK.
Chan, H. S. L., 1960, “The Design of Michell Optimum Structures,” Report No. 142, Cranfield College of Aeronautics, UK.
Chan, H. S. Y., 1963, “Optimum Michell Frameworks for Three Parallel Forces,” Report No. 167, Cranfield College of Aeronautics, UK.
Hemp, W. S., 1973, Optimum Structures, Clarendon Press, Oxford.
Rozvany,  G. I. N., 1996, “Some Shortcomings in Michell’s Truss Theory,” Struct. Optim., 12, pp. 244–250.
Prager, W., 1958, “A Problem of Optimal Design,” Proceedings of the Union of Theoretical and Applied Mechanics, Warsaw.
Srithongchai,  S., and Dewhurst,  P., 2003, “Comparisons of Optimality Criteria for Minimum-Weight Dual Material Structures,” Int. J. Mech. Sci., 45, pp. 1781–1797.
Hill, R., 1950, The Mathematical Theory of Plasticity, Clarendon Press, Oxford.
Johnson,  W., 1961, “An Analogy Between Upper-Bound Solutions for Plane-Strain Metal Working and Minimum-Weight Two-Dimensional Frames,” Int. J. Mech. Sci., 3, pp. 239–246.
Green,  A. P., 1954, “On the Use of Hodographs in Problems of Plane Plastic Strain,” J. Mech. Phys. Solids, 16, pp. 267–276.
Johnson,  W., Chitkara,  N. R., Reid,  S. R., and Collins,  I. F., 1971, “The Displacement Field and Its Significance for Certain Minimum Weight Two-Dimensional Frames Using the Analogy With Perfectly Plastic Flow in Metal Working,” Int. J. Mech. Sci., 13, pp. 547–561.
Dewhurst,  P., 2001, “Analytical Solutions and Numerical Procedures for Minimum-Weight Michell Structures,” J. Mech. Phys. Solids, 49, pp. 445–467.
Srithongchai,  S., Demircubuk,  M., and Dewhurst,  P., 2003, “A Theoretical and Experimental Investigation of a Family of Minimum-Volume Simply-Supported Beams,” Int. J. Mech. Sci., 45, pp. 37–55.
Prager,  W., 1978, “Optimal Layout of Trusses With a Finite Number of Joints,” J. Mech. Phys. Solids, 26, pp. 241–250.
Rozvany,  X., Bendsoe,  X., and Kirsch,  X., 1995, “Layout Optimization of Structures,” Appl. Mech. Rev., 48, pp. 41–118.
Prager, W., and Rozvany, G. I. N., 1977, “Optimization of Structural Geometry,” in Dynamical Systems, edited by Bednarek, A. R. and Cesari, L., Academic Press, New York.
Dewhurst, P., 2004, “A General Optimality Criterion for Strength and Stiffness of Dual Material-Property Structures,” Int. J. Mech. Sci., in press.

Figures

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Prototype pure torsion wheel manufactured by free-form laser sintering
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Elemental truss members adjacent to boundary
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Field of orthogonal logarithmic spirals
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(a) Selected layout curves for a general logarithmic spiral wheel structure, (b) associated force diagram
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Quadrant of truss wheel structure
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Truss approximation of Prager torsion arm
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Truss approximation of Michell torsion arm

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