 | | 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 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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 |
| References |
| 1. | L. Greengard and V. A. Rokhlin,
"A Fast Algorithm for Particle Simulation,"
J. Comput. Phys.
73, 325-348 (1987). |
| 2. | L. Greengard,
The Rapid Evaluation of Potential Fields in Particle Systems
(MIT Press, Massachusetts, 1988). |
| 3. | Y. J. Liu,
Fast Multipole Boundary Element Methods: Theory and Applications in Engineering
(Cambridge Univ. Press, New York, 2009). |
| 4. | L. Ying, G. Biros, and D. Zorin,
"A Kernel-Independent Adaptive Fast Multipole Algorithm in Two and Three Dimensions,"
J. Comput. Phys.
196, 591-626 (2004). |
| 5. | N. I. Muskhelishvili,
Some Basic Problems of the Mathematical Theory of Elasticity
(Nauka, Moscow, 1966; Groningen, Noordhoff, 1963). |
| 6. | Y. M. Kuo and H. D. Conway,
"The Torsion of Composite Tubes and Cylinders,"
Int. J. Solids Struct.
9 (2), 1553-1565 (1973). |
| 7. | Y. M. Kuo and H. D. Conway,
"Torsion of Cylinders with Multiple Reinforcement,"
J. Engng Mech. Div.
100, 221-233 (1974). |
| 8. | J. T. Chen and Y. T. Lee,
"Torsional Rigidity of a Circular Bar with Multiple Circular Inclusions
Using the Null-Field Integral Approach,"
Comput. Mech.
44, 221-232 (2009). |
| 9. | S. P. Timoshenko and J. N. Goodiear,
Theory of Elasticity
(Nauka, Moscow, 1975; McGraw-Hill, New York, 1987). |
| 10. | A. A. Dobroskok and A. M. Lin'kov,
"Complex Variable Equations and the Numerical Solution of Harmonic
Problems for Piecewise-Homogeneous Media,"
Prikl. Mat. Mekh.
73 (3), 439-458 (2009)
[J. Appl. Math. Mech. (Engl. Transl.)
73 (3), 313-325 (2009)]. |
| 11. | E. Rejwer, L. Rybarska-Rusinek, and A. M. Linkov,
"The Complex Variable Fast Multipole Boundary Element Method for the Analysis of Strongly Inhomogeneous Media,"
Engng Anal. Bound. Elem.
43, 105-116 (2014). |
| 12. | Y. Saad and M. N. Schultz,
"GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems,"
SIAM J. Sci. Stat. Comput.
7 (3), 856-869 (1986). |
| 13. | T. F. Ford,
"Viscosity Concentration and Fluidity Concentration Relationship
for Suspensions of Spherical Particles in Newtonian Liquids,"
J. Phys. Chem.
64, 1168-1174 (1960). |
| 14. | B. Abedian and M. L. Kachanov,
"On the Effective Viscosity of Suspensions,"
Int. J. Engng Sci.
48, 962-965 (2010) |
| 15. | V. A. Kuz'kin, A. M. Krivtsov, and A. M. Lin'kov,
"Computer Simulation of Effective Viscosity of the Proppant-Liquid Mixture
Used in the Hydraulic Fracturing,"
Fiz.-Tekhn. Probl. Razrab. Polez. Iskopaemykh,
No. 1, 3-12 (2014). |
|
| Received |
02 May 2017 |
| Link to Fulltext |
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