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TECHNICAL PAPERS

Novel Boundary Integral Equations for Two-Dimensional Isotropic Elasticity: An Application to Evaluation of the In-Boundary Stress

[+] Author and Article Information
V. Mantič, F. J. Calzado, F. París

Group Elasticity and Strength of Materials, School of Engineering, University of Seville, Camino de los Descubrimientos s/n, Seville, E-41092 Spain

J. Appl. Mech 70(6), 817-824 (Jan 05, 2004) (8 pages) doi:10.1115/1.1630813 History: Received September 18, 2002; Revised July 28, 2003; Online January 05, 2004
Copyright © 2003 by ASME
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References

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Rizzo,  F. J., and Shippy,  D. J., 1968, “A Formulation and Solution Procedure for the General Non-Homogeneous Elastic Inclusion Problem,” Int. J. Solids Struct., 4, pp. 1161–1179.
Cruse,  T., and Van Buren,  W., 1971, “Three-Dimensional Elastic Stress Analysis of a Fracture Specimen with an Edge Crack,” Int. J. Fract. Mech., 7, pp. 1–15.
Zhao,  Z. Y., 1996, “Interelement Stress Evaluation by Boundary Elements,” Int. J. Numer. Methods Eng., 39, pp. 2399–2415.
Mantič,  V., Graciani,  E., and Parı́s,  F., 1999, “A Simple Local Smoothing Scheme in Strongly Singular Boundary Integral Representation of Potential Gradient,” Comput. Methods Appl. Mech. Eng., 178, pp. 267–289.
Guiggiani,  M., Krishnasamy,  G., Rudolphi,  T. J., and Rizzo,  F. J., 1992, “A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations,” ASME J. Appl. Mech., 59, pp. 604–614.
Graciani,  E., Mantič,  V., Parı́s,  F., and Cañas,  J., 2000, “A Critical Study of Hypersingular and Strongly Singular Boundary Integral Representations of Potential Gradient,” Comput. Mech., 26, pp. 542–559.
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Avila, R., Mantič, V., and Parı́s, F., 1997, “Application of the Boundary Element Method to Elastic Orthotropic Materials in 2D: Numerical Aspects,” Proceedings, Boundary Elements XIX, M. Marchetti, C. A. Brebbia, and M. H. Aliabadi, eds., Computational Mechanics Publications, Southampton, pp. 55–64.
Niu,  Q., and Shepard,  M. S., 1993, “Superconvergent Extraction Techniques for Finite Element Analysis,” Int. J. Numer. Methods Eng., 36, pp. 811–836.
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Figures

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Simply supported beam subjected to a uniform load. Basic boundary element mesh.
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In-plane stress evaluated using boundary integral representation (14). Beam discretization by meshes of 12 and 36 linear elements.
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Normalized errors of the in-plane stress evaluated using boundary integral representation (14). Beam discretization by meshes of 36, 108, and 324 linear elements.
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Convergence of the normalized error of the in-plane stress evaluated using boundary integral representation (14). Beam discretization by meshes of 12, 36, 108, and 324 linear elements.
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An infinite plate with a circular hole subjected to uniaxial tension. Basic boundary element mesh.
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Hoop stress evaluated using boundary integral representation (14). Circumference discretization by meshes of 8 and 24 linear elements.
Grahic Jump Location
Normalized errors of the hoop stress evaluated using boundary integral representation (14). Circumference discretization by meshes of 24, 72, and 216 linear elements.
Grahic Jump Location
Convergence of the normalized error of the hoop stress evaluated using boundary integral representation (14). Circumference discretization by meshes of 8, 24, 72, and 216 linear elements.

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