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TECHNICAL PAPERS

On Displacement Fields in Orthotropic Laminates Containing an Elliptical Hole

[+] Author and Article Information
S. M. Chern

Civil Engineering Department, Chung-Cheng Institute of Technology, Tahsi, Taoyuan 33509, Taiwan

M. E. Tuttle

Mechanical Engineering Department, University of Washington MS 352600, Seattle, WA 98195

J. Appl. Mech 67(3), 527-539 (Apr 26, 2000) (13 pages) doi:10.1115/1.1309545 History: Received January 25, 1999; Revised April 26, 2000
Copyright © 2000 by ASME
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References

Green,  A. E., and Taylor,  G. I., 1945, “Stress Systems in Aeolotropic Plates III,” Proc. R. Soc. London, Ser. A, 184, pp. 181–195; pp. 218–219.
Bonora,  N., Costanzi,  M., and Marchetti,  M., 1993, “On Closed Form Solution for the Elastic Stress Field Around Holes in Orthotropic Composite Plates Under in-Plane Stress Conditions,” Composite Structures,25, pp. 139–156.
Sampath,  S. G., and Hulbert,  L. E., 1975, “Analysis of Multiholed Orthotropic Laminated Plates by the Boundary-Point-Squares Methods,” ASME J. Pressure Vessel Technol., 75, pp. 118–122.
Hayashi, T., 1986, “Stress Analysis of the Anisotropic Plate With a Hole Under the Uniaxial Loading,” Composite ’86: Recent Advances in Japan and the United States, Proc. Japan-U.S. CCM-III, K. Kawata, S. Umekawa, and A. Kobayashi, eds., Japan Society of Composite Materials, Tokyo, pp. 197–204.
Kaltakci,  M. Y., 1996, “Stress Concentrations and Failure Criteria in Anisotropic Plates With Circular Holes Subjected to Tension or Compression,” Comput. Struct., 61, pp. 67–78.
Daniel, I. M., Rowlands, R. E., and Whiteside, J. B., 1973, “Deformation and Failure of Boron-Epoxy Plate With Circular Hole,” Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP 521, American Society for Testing and Materials, Philadelphia, PA, pp. 143–164.
Rowlands,  R. E., Daniel,  I. M., and Whiteside,  J. B., 1973, “Stress and Failure Analysis of a Glass-Epoxy Composite Plate With a Circular Hole,” Exp. Mech., 13, No. 1, pp. 31–37.
Sneddon, I. N., 1975, “Integral Transform Methods for the Solution of Mixed Boundary Value Problems in the Classical Theory of Elastostatics,” Application of Integral Transforms in the Theory of Elasticity (CISM Courses and Lectures No. 220), I. N Sneddon, ed., Springer-Verlag, New York.
Gilbert,  R. P., and Schneider,  M., 1987, “The Boundary Integral Method for Two-Dimensional Orthotropic Materials,” J. Elast., 18, pp. 61–82.
Ladopoulas,  E. G., 1989, “Singular Integral Operators Method for Two-Dimensional Plasticity Problems,” Comput. Struct., 33, pp. 859–865.
Ting, T. C. T., 1996, Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York.
Savin, G. N., 1961, Stress Concentration Around Holes, Pergamon Press, New York.
Lekhnitskii, S. G., 1963, Theory of Elasticity of an Anisotropic Body, Holden-Day, San Francisco.
Bonora,  N., Costanzi,  M., and Marchetti,  M., 1994, “A Computational Procedure to Calculate Stress-Strain Field Around Simple Shape Holes in Composite Laminates,” Comput. Struct., 53, No. 5, pp. 1167–1179.
Ukadgaonker,  V. G., and Rao,  D. K. N., 1999, “Stress Distribution Around Triangular Holes in Anisotropic Plates,” Comput. Struct., 45, No. 1, pp. 171–183.
Jen,  M.-H. R., Kau,  Y. S., and Hsu,  J. M., 1993, “Interlaminar Stresses in a Centrally Notched Composite Laminate,” Int. J. Solids Struct., 30, No. 21, pp. 2911–2928.
Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity: Fundamental Equations, Plane Theory of Elasticity, Torsion, and Bending, P. Noordhoff, Groningen (translated from the Russian by J. R. M. Radok).
Kobayashi, Albert S., ed., 1993, Handbook on Experimental Mechanics, 2nd Ed., Society for Experimental Mechanics, Bethel, CT.

Figures

Grahic Jump Location
Schematic of infinite orthotropic plate with elliptical hole
Grahic Jump Location
(a) Measured v-displacement fringe pattern induced in a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy∞=93 MPa (6). (b) v-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=93 MPa, predicted according to the original Savin solution. (c) v-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=93 MPa, predicted according to the revised solution. (d) v-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=93 MPa, predicted by a finite element method (ANSYS) analysis.
Grahic Jump Location
(a) Measured u-displacement fringe pattern induced in a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=93 MPa (6). (b) u-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=93 MPa, predicted according to the original Savin solution. (c) u-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=93 MPa, predicted according to the revised solution. (d) u-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=93 MPa, predicted by the finite element method (ANSYS) analysis.
Grahic Jump Location
(a) v-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the original Savin solution. (b) v-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the revised solution. (c) v-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted by the finite element method (ANSYS) analysis.
Grahic Jump Location
(a) u-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the original Savin solution. (b) u-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the revised solution. (c) u-displacement fringe pattern for a [0/±45/90]s boron-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted by the finite element method (ANSYS) analysis.
Grahic Jump Location
(a) Measured v-displacement fringe pattern induced in a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=198 MPa (7). (b) v-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=198 MPa, predicted according to the original Savin solution (resolution reduced to 50.8 μm). (c) v-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=198 MPa, predicted according to the revised solution. (d) v-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=198 MPa, predicted by the finite element method (ANSYS) analysis.
Grahic Jump Location
(a) u-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=198 MPa, predicted according to the original Savin solution (resolution reduced to 50.8 μm). (b) u-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=198 MPa, predicted according to the revised solution. (c) u-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to σy=198 MPa, predicted by the finite element method (ANSYS) analysis.
Grahic Jump Location
(a) v-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the original Savin solution (resolution=2.76 μm). (b) v-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the revised solution (resolution=1.38 μm). (c) v-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted by the finite element method (ANSYS) analysis (resolution=1.38 μm).
Grahic Jump Location
(a) u-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the original Savin solution (resolution=2.76 μm). (b) u-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted according to the revised solution (resolution=1.38 μm). (c) v-displacement fringe pattern for a [0/±45/90]s glass-epoxy panel containing a 25.4-mm-dia circular hole, subjected to τxy=17.2 MPa, predicted by the finite element method (ANSYS) analysis (resolution=1.38 μm).

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