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A modified fourier series method for the torsion analysis of bars with multiply connected cross sections

โœ Scribed by Yoon Young Kim; Min Su Yoon

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
880 KB
Volume
34
Category
Article
ISSN
0020-7683

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โœฆ Synopsis

A modified Fourier series method is proposed for the torsion analysis of prismatic bars with multiply connected cross sections. The key feature in the present approach is the combined use of polynomials and Fourier series solutions unlike in the existing approaches which use the Fourier series only. The replacement of the zeroth harmonic terms in the Fourier series solutions by carefully selected polynomials resolves the major problem of functional dependence which the direct Fourier series method may pose. The polynomials and Fourier series solutions are selected to satisfy the governing equation exactly so that the numerical calculation is minimal. The effectiveness and generality of the present method is verified through numerical examples.

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An asymptotic solution is obtained for the problem of maximizing the torsional rigidity of elastic, multiply-connected cylindrical bars for a given area of cross-section. The shapes of the inner contours of the multiply-connected cross-section are specified while the outer contour is determined as a