 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
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| << Previous article | Volume 51, Issue 4 / 2016 | Next article >> |
| V.V. Mokryakov, "Stress Concentration Localization in Doubly Periodic Square Systems of Circular Holes in Uniaxial Compression," Mech. Solids. 51 (4), 424-435 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
4 |
Pages |
424-435 |
| DOI |
10.3103/S0025654416040063 |
| Title |
Stress Concentration Localization in Doubly Periodic Square Systems of Circular Holes in Uniaxial Compression |
| Author(s) |
V.V. Mokryakov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, mokr@ipmnet.ru) |
| Abstract |
We consider the stress concentration points in infinite elastic doubly periodic perforated plates (lattices) under the conditions of external uniaxial compression. Special attention is paid to the internal localization of stress concentrations (i.e., to the case of stress concentration origination inside the material rather than on the boundaries of the holes). We consider a parametric domain (depending on the angle of application of the external load and the structure parameter of the lattice) and calculate the domain dimensions (the extreme values of the parameters). We discover a point in the parametric domain at which the following three cases of fracture initiation are possible: two cases on the hole contour and one case inside the material. |
| Keywords |
elasticity, doubly periodic lattice, circular holes, strength, stress concentration, compression, fracture initiation |
| References |
| 1. | V. Ya. Natanson,
"On Stresses in an Extended Plate Weakened by Equal Holes in Chessboard Arrangement,"
Mat. Sb.
42 (5), 616-636 (1935). |
| 2. | R. C. J. Howland,
"Stress in a Plate Containing an Infinite Row of Holes,"
Proc. Roy. Soc. London. Ser. A
148, 471-491 (1935). |
| 3. | G. Horvay,
"The Plain Strain Problem of Perforated Plates,"
J. Appl. Mech.
19, 355-360 (1952). |
| 4. | R. Bailey and R. Hicks,
"Behavior of Perforated Plates under Plane Stress,"
J. Mech. Engng Sci.
2 (2), 143-165 (1960). |
| 5. | G. A. Van Fo Fi,
"On a Solution of a Plane Doubly Periodic Problem of Elasticity,"
Dokl. Akad. Nauk UkrSSR,
No. 9, 1152-1155 (1965). |
| 6. | G. N. Savin,
Stress Distribution near Holes
(Naukova Dumka, Kiev, 1968)
[in Russian]. |
| 7. | A. Rekik, M. Bornert, and F. Auslender,
"A Critical Evaluation of Local Field Statistics Predicted by Various Linearization Schemes
in Nonlinear Mean-Filed Homogenization,"
Mech. Mat.
54, 1-17 (2012). |
| 8. | S. L. Parvanova, P. S. Dineva, and G. D. Manolis,
"Dynamic Behavior of a Finite-Sized Elastic Solid with Multiple Cavities and Inclusions Using
BIEM,"
Acta Mech.
224, 597-618 (2013). |
| 9. | H. Saito,
"Stress in a Plate Containing Infinite Parallel Rows of Holes,"
ZAMM
37 (3-4), 111-115 (1957). |
| 10. | H. Martikka and E. Taitokari,
"Design of Perforated Shell Drying Drums,"
Mech. Engng Res.
2 (2), 31-44 (2012). |
| 11. | M. Isida and H. Igawa,
"Analysis of a Zig-Zag Array of Circular Holes in an Infinite Solid under Uniaxial Tension,"
Int. J. Solids Struct.
27 (7), 849-864 (1991). |
| 12. | K. Ting, K. T. Chen, and W. S. Yang,
"Stress Analysis of the Multiple Circular Holes with the Rhombic Array Using Alternating Method,"
Int. J. Pressure Vessels Piping
76, 503-514 (1999). |
| 13. | S. G. Mogilevskaya, S. L. Crouch, and J. Wang,
"A Complex Boundary Integral Method for Multiple Circular Holes in an Infinite Plane,"
Engng Anal. Bound. Elem.
27, 789-802 (2003). |
| 14. | W. J. O'Donnell and B. F. Langer,
"Design of Perforated Plates,"
J. Engng Ind.
84, 1-13 (1962). |
| 15. | J. E. Goldberg and K. N. Jabbour,
"Stresses and Displacements in Perforated Plates,"
Nuclear Struct. Engng
2, 360-381 (1965). |
| 16. | Su Shu-lan, Rao Qiu-hua, and He Yue-hui,
"Theoretical Prediction of Effective Elastic Constants for New Intermetallic Compound Porous
Material,"
Trans. Nonferrous Met. Soc. China
23, 1090-1097 (2013). |
| 17. | E. I. Grigolyuk and L. A. Fil'shtinskii,
Perforated Plates and Shells
(Nauka, Moscow, 1970)
[in Russian]. |
| 18. | N. I. Muskhelishvili,
Several Fundamental Problems of Mathematical Theory of Elasticity
(Nauka, Moscow, 1966)
[in Russian]. |
| 19. | M. P. Savruk,
Two-Dimensional Elasticity Problems for Bodies with Cracks
(Naukova Dumka, Kiev, 1981)
[in Russian]. |
| 20. | A. M. Lin'kov,
Complex Method Of Boundary Integral Equations in Elasticity
(Nauka, St. Petersburg, 1999)
[in Russian]. |
| 21. | V. V. Mokryakov,
Study of Strength of an Elastic Plane with an Infinite Quadratic Lattice of Circular Holes under Mechanical Loading,
Preprint No. 1023 (IPMekh RAN, Moscow, 2012)
[in Russian]. |
| 22. | V. V. Mokryakov,
"Application of the Multipole Method to the Problem on Two Close Holes,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 129-145 (2007)
[Mech. Solids (Engl. Transl.)
42 (5), 771-785 (2007)]. |
| 23. | V. V. Mokryakov,
"Study of the Dependence of Effective Compliancies of a Plane with an Array of Circular Holes
on Array Parameters,"
Vych. Mekh. Sploshn. Sred
3 (3), 90-101 (2010). |
| 24. | V. V. Mokryakov,
"Application of the Multipole Expansion Method for Calculating the Stress State
in an Infinite Elastic Plane with Several Circular Holes,"
Vych. Mekh. Sploshn. Sred
5 (2), 168-177 (2012). |
| 25. | R. V. Goldstein, V. V. Mokryakov, N. M. Osipenko, and P. S. Shushpannikov,
"Application of the Multipole Expansion Method for Solving 2D- and 3D-Elasticity
and Fracture Mechanics Problems for the Medium with Pores,"
in Proc. 5th Biot Conf. on Poromechanics (BIOT-5). July 10-12, 2013, Vienna, Austria,
p. 131 (paper on CD: pp. 2297-2306). |
| 26. | V. L. Kolmogorov,
Stress. Deformations. Fracture
(Metallurgiya, Moscow, 1970)
[in Russian]. |
| 27. | R. V. Goldstein and P. S. Shushpannikov,
"Application of the Method of Multiple Expansions in the 3D-Elasticity Problem
for a Medium with Ordered System of Spherical Pores,"
ZAMM
89 (6), 504-510 (2009). |
|
| Received |
20 January 2014 |
| Link to Fulltext |
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