The problem of optimal nonhomogeneity of a bar subjected to Saint-Venant torsion is formulated as a variational problem so that the necessary conditions for optimality may be derived. In this formulation, the shear modulus function G(x,y) which varies in a jumplike manner is to be optimized with the specified composition of two different elastic materials. It is shown in this paper that a prismatic, nonhomogeneous bar can, in fact, be optimized, and the maximum torsional rigidity is achieved by performing the proposed iterative procedure based on the derived necessary conditions. As a numerical example, the optimal solutions for prismatic bars with cross-sectional shapes of a square and an equilateral triangle are obtained by the computer program which uses the Finite Element Method formulated on the basis of the hybrid stress approach.
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October 1984
This article was originally published in
Journal of Vibration, Acoustics, Stress, and Reliability in Design
Research Papers
Optimal Jump Nonhomogeneity of Prismatic Bars in Torsion
M. G. Faulkner,
M. G. Faulkner
Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G ZG8
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A. Mioduchowski,
A. Mioduchowski
Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G ZG8
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D. P. Hong
D. P. Hong
Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G ZG8
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M. G. Faulkner
Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G ZG8
A. Mioduchowski
Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G ZG8
D. P. Hong
Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G ZG8
J. Vib., Acoust., Stress, and Reliab. Oct 1984, 106(4): 547-553 (7 pages)
Published Online: October 1, 1984
Article history
Received:
March 1, 1981
Online:
November 23, 2009
Citation
Faulkner, M. G., Mioduchowski, A., and Hong, D. P. (October 1, 1984). "Optimal Jump Nonhomogeneity of Prismatic Bars in Torsion." ASME. J. Vib., Acoust., Stress, and Reliab. October 1984; 106(4): 547–553. https://doi.org/10.1115/1.3269235
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