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RESEARCH PAPERS: Optimal, Vibration, and Approximate Solutions

Optimal Jump Nonhomogeneity of Prismatic Bars in Torsion

[+] Author and Article Information
M. G. Faulkner, A. Mioduchowski, D. P. Hong

Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G ZG8

J. Vib., Acoust., Stress, and Reliab 106(4), 547-553 (Oct 01, 1984) (7 pages) doi:10.1115/1.3269235 History: Received March 01, 1981; Online November 23, 2009

Abstract

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.

Copyright © 1984 by ASME
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