Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2017-4pp.452-456

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 52, Issue 4 / 2017 | Next article >>
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
<< Previous article | Volume 52, Issue 4 / 2017 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100