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V.V. Mokryakov, "Strength Analysis of an Elastic Plane Containing a Square Lattice of Circular Holes under Mechanical Loading," Mech. Solids. 49 (5), 568-577 (2014)
Year 2014 Volume 49 Number 5 Pages 568-577
DOI 10.3103/S0025654414050082
Title Strength Analysis of an Elastic Plane Containing a Square Lattice of Circular Holes under Mechanical Loading
Author(s) V.V. Mokryakov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, vmokryakov@mail.ru, mokr@ipmnet.ru)
Abstract The strength characteristics of an elastic plane weakened by a square lattice of circular holes are considered. The stress concentrations in three distinct lattices under the conditions of uniaxial tension/compression in various directions are studied. The minimum and maximum values of the stress concentrations are calculated, and the stress fields in various lattices are considered.

We show that under the compression conditions fracture can occur inside the material rather than on the hole boundaries. It is demonstrated that in dense lattices the stress concentrations exhibit power-law dependence on the structure parameter equal to the ratio of the length of the interval between the holes to the hole radius.
Keywords elasticity, hole, strength, stress concentration, extension, compression, anisotropy
References
1.  F. A. Mumpton, "La Roca Magica: Uses of Natural Zeolites in Agriculture and Industry," Paper Colloq. Nat. Acad. Sci. (House Dellgates Biogr., Maryland) 96, 3463-3470 (1999).
2.  C. Baerlocher, L. B. McCusker, and D. H. Olson, Atlas of Zeolite Framework Types (Elsevier B.V., Amsterdam, 2007).
3.  J. M. Newsam and M. M. J. Treacy, "ZeoFile: A Stack of Zeolite Structure Types," Zeolites 13, 183-186 (1993).
4.  L. T. Canham, "Silicon Quantum Wire Array Fabrication by Elecrochemical and Chemical Dissolution of Wafers," Appl. Phys. Lett. 57, 1046-1048 (1990).
5.  K. Krishan, "Invited Review Article Ordering of Voids and Gas Bubbles in Radiation environments," Radiat. Effects 66 (3-4), 121-155 (1982).
6.  J. H. Evans, "Observations of a Regular Void Array in High Purity Molybdenum and T.Z.M. Irradiated at High Temperatures with 2MeV Nitrogen Ions," Radiat. Effects 10 (1-2), 55-60 (1971).
7.  E. I. Grigolyuk and L. A. Filshtinskii, Perforated Plates and Shells (Nauka, Moscow, 1970) [in Russian].
8.  G. N. Savin, Stress Distribution near Holes (Naukova Dumka, Kiev, 1968) [in Russian].
9.  M. P. Savruk, Two-Dimensional Problems of Elasticity for Bodies with Cracks (Naukova Dumka, Kiev, 1981) [in Russian].
10.  A. M. Lin'kov, Complex Method of Boundary Integral Equations in Elasticity (Nauka, St. Petersburg, 1999) [in Russian].
11.  R. E. Peterson, Stress-Concentration Design Factors (Wiley, New York, 1953).
12.  G. A. Van Fo Fy, "One of Solutions of Plane Two-Periodic Problem of Elasticity," Dokl. Akad. Nauk Ukr. SSR, No. 9, 1152-1155 (1965).
13.  G. Horvay, "The Plain-Strain Problem of Perforated Plates," J. Appl. Mech. 19 (3), 355-360 (1952).
14.  R. Bailey and R. Hicks, "Behavior of Perforated Plates under Plane Stress," J. Mech. Engng Sci. 2 (2), 143-161 (1960).
15.  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).
16.  K. Ting, K. T. Chen, and W. S. Yang, "Stress Analysis of Multiple Circular Holes with the Rhombic Array Using Alternating Method," Int. J. Pressure Vessels Piping 76 (8), 503-514 (1999).
17.  J. Helsing and A. Jonsson, "Complex Variable Boundary Integral Equations for Perforated Infinite Planes," Engng Anal. Bound. Elem. 25, 191-202 (2001).
18.  S. Vigdergauz, "The Effective Properties of a Perforated Elastic Plate: Numerical Optimization by Genetic Algorithm," Int. J. Solid Struct. 38 (48-49), 8593-8616 (2001).
19.  I. V. Andrianov, V. V. Danishevs'kyy, and A. L. Kalamkarov, "Asymptotic Analysis of Perforated Plates and Membranes. P. 1: Static Problems for Small Holes," Int. J. Solid Struct. 49 (2), 298-310 (2012).
20.  I. V. Andrianov, V. V. Danishevs'kyy, and A. L. Kalamkarov, "Asymptotic Analysis of Perforated Plates and Membranes. P. 2: Static and Dynamic Problems for Large Holes," Int. J. Solid Struct. 49 (2), 311-317 (2012).
21.  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).
22.  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).
23.  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)].
24.  N. I. Muskhelishvili, Several Fundamental Problems of Mathematical Theory of Elasticity (Nauka, Moscow, 1966) [in Russian].
25.  C. Rocco, G. V. Guineae, J. Planas, and M. Elices, "Size Effect and Boundary Conditions in the Brazilian Test: Theoretical Analysis," Mat. Struct. 32, 437-444 (1999).
26.  X. Markenscoff, "Stress Amplification in Small Geometries," Comp. Mech. 19, 77-83 (1996).
27.  X. Markenscoff, "Stress Amplification in the Neighborhood of an Eccentric Large Hole in a Strip in Tension," ZAMP 51 (4), 550-554 (2000).
28.  R. V. Goldstein and P. S. Shushpannikov, "Application of the Method of Multipole Expansions in the 3D-Elasticity Problem for a Medium with Ordered System of Spherical Pores," ZAMP 89 (6), 504-510 (2009).
Received 25 October 2012
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