 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| A.M. Lin'kov, E. Rejwer, and L. Rybarska-Rusinek, "Torsional Rigidity of a Bar with Multiple Fibers," Mech. Solids. 52 (4), 452-456 (2017) |
| Year |
2017 |
Volume |
52 |
Number |
4 |
Pages |
452-456 |
| DOI |
10.3103/S0025654417040124 |
| Title |
Torsional Rigidity of a Bar with Multiple Fibers |
| Author(s) |
A.M. Lin'kov (Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia; Rzeszów University of Technology, al. Powstanców Warszawy 12, Rzeszów, 35-959 Poland, voknilal@hotmail.com)
E. Rejwer (Rzeszów University of Technology, al. Powstanców Warszawy 12, Rzeszów, 35-959 Poland)
L. Rybarska-Rusinek (Rzeszów University of Technology, al. Powstanców Warszawy 12, Rzeszów, 35-959 Poland) |
| Abstract |
The classical problem of torsion is newly considered with the complex fast multipole method used to determine the torsional rigidity of a bar with multiple fibers. New analytical formulas are given for the rigidity in the case of circular contours of the fibers and the bar. It is shown that the method ensures the results which, up to three significant digits, agree well with the solutions obtained by series expansions. For a fixed concentration of a great many (up to 540) thin fibers whose shear modulus is significantly (30 times) greater than the shear modulus of the matrix, the torsional rigidity weakly depends on the diameter and the distance between the fibers. The torsional rigidity G becomes 2.5 times larger as the fiber concentration c increases from 0 to 0.16 for a very small concentration interval (0≤c≤0.03), where the dependence G(c) is linear. The inverse quantity 1/G (torsional compliance) varies linearly in a much wider range of concentrations (0≤c≤0.16). |
| Keywords |
torsion, complex variables, boundary elements, fast multipole method |
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|
| Received |
02 May 2017 |
| Link to Fulltext |
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