Analysis of a Plate Containing a Polygon-Shaped Inclusion With a Uniform Eigencurvature

[+] Author and Article Information
C. N. Duong, J. Yu

The Boeing Company, 2401 E. Wardlow Road, MC C078-0209, Long Beach, CA 90807-5309

J. Appl. Mech 70(3), 404-407 (Jun 11, 2003) (4 pages) doi:10.1115/1.1572898 History: Received July 03, 2000; Revised August 19, 2002; Online June 11, 2003
Copyright © 2003 by ASME
Topics: Tensors , Algorithms
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Beom,  H. G., and Earmme,  Y. Y., 1999, “The Elastic Field of an Elliptic Cylindrical Inclusion in a Laminate with Multiple Isotropic Layers,” ASME J. Appl. Mech., 66, pp. 165–171.
Mura, T., 1987, Mechanics of Defects in Solids, Martinus Nijhoff, Dordrecht.
Beom,  H. G., 1998, “Analysis of a Plate Containing an Elliptic Inclusions With Eigencurvatures,” Arch. Appl. Mech., 68, pp. 422–432.
Rodin,  G. J., 1996, “Eshelby’s Inclusion Problem for Polygons and Polyhedra,” J. Mech. Phys. Solids, 44, pp. 1977–1995.
Nozaki,  H., and Taya,  M., 1997, “Elastic Fields in a Polygon-Shaped Inclusion with Uniform Eigenstrains,” ASME J. Appl. Mech., 64, pp. 495–501.
Jones, R. M., 1975, Mechanics of Composite Materials, McGraw-Hill, New York.
Duong,  C. N., Wang,  J. J., and Yu,  J., 2000, “An Approximate Algorithmic Solution for the Elastic Fields in Bonded Patched Sheets,” Int. J. Solids Struct., 38, pp. 4685–4699.
Duong,  C. N., and Yu,  J., 2003, “Thermal Stresses in a One-Sided Bonded Repair by a Plate Inclusion Model,” J. Thermal Stresses, 26, pp. 457–466.


Grahic Jump Location
Two-dimensional construction of duplexes used in Rodin’s algorithm, 4. Part (a) shows the global structure and coordinate systems. Parts (b) and (c) show typical duplexes, with vertices shown as filled circles. In the (η,ζ) coordinate system, for duplex (b) add the simplex with vertices (0,0), (b,c), (b,0) to the simplex with vertices (0,0), (b,0), (b,c+), while for duplex (c) subtract the simplex with vertices (0,0), (b,0), (b,c) from the simplex with vertices (0,0), (b,0), (b,c+).
Grahic Jump Location
Geometrical parameters of the duplexes for evaluating the asymptotic form of the vertex singularity, 4
Grahic Jump Location
Regular polygon-shaped inclusions
Grahic Jump Location
Curvatures κ11 and κ22 in regular polygon-shaped inclusions along the x1-axis for an eigencurvature κij*=(1, 0, 0). (a) κ11, (b) κ22
Grahic Jump Location
Curvatures κ12 in regular polygon-shaped inclusions along x1-axis for an eigencurvature κij*=(0, 0, 1)




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