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RESEARCH PAPER

Parallel Hybrid Algorithm for Three-Dimensional Elastic Wave Scattering in Steel Pipes

[+] Author and Article Information
A. Mahmoud, N. Popplewell

Mechanical and Industrial Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada

A. H. Shah

Civil Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada

J. Pressure Vessel Technol 126(4), 510-517 (Dec 01, 2004) (8 pages) doi:10.1115/1.1762449 History: Received May 19, 2003; Revised November 20, 2003; Online December 01, 2004
Copyright © 2004 by ASME
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References

Rose, J. L., and Quarry, M. J., 1999, “Feasibility of Ultrasonic Guided Waves for Nondestructive Evaluation of Gas Pipelines,” Topical Report GRI-99/0076, Gas Research Institute.
Mahmoud, A., 2002, “Hybrid Formulation of Wave Scattering in a Cracked Circular Pipe,” M.Sc. thesis, University of Manitoba, Canada.
Zhu,  W., 2002, “An FEM Simulation for Guided Elastic Wave Generation and Reflection in Hollow Pipes With Corrosion Defects,” ASME J. Pressure Vessel Technol., 124, pp. 108–117.
Zhaung,  W., Shah,  A. H., and Datta,  S. K., 1997, “Axisymmetric Guided Wave Scattering by Cracks in Welded Steel Pipes,” ASME J. Pressure Vessel Technol., 119, pp. 401–406.
Bai, H., 2002, “Elastic Wave Scattering in Cracked Pipes,” Ph.D. dissertation, University of Manitoba, Canada.
Bai,  H., Shah,  A. H., Popplewell,  N., and Datta,  S. K., 2001, “Scattering of Guided Waves by Circumferential Cracks in Steel Pipes,” ASME J. Appl. Mech., 68, pp. 619–631.
Bathe, K. J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ.
Karunasena,  W. M., Shah,  A. H., and Datta,  S. K., 1991, “Plane-Strain-Wave Scattering by Cracks in Laminated Composite Plates,” J. Eng. Mech. Div., 117(8), pp. 1738–1753.
Westlake, J. R., 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations, Robert E. Krieger, New York.
Leopold, C., 2001, Parallel and Distributed Computing: A Survey of Models, Paradigms, and Performance, John Wiley & Sons, New York.
Chandra, R., Kohr, D., Menon, R., Dagum, L., Maydan, D., and McDonald, J., 2001, Parallel Programming in OpenMP, Morgan Kaufmann, San Francisco, CA.
Alleyne,  D. N., Lowe,  M. J. S., and Cawley,  P., 1998, “The Reflection of Guided Waves From Circumferential Notches in Pipes,” ASME J. Appl. Mech., 65, pp. 635–641.
Desai, C. S., and Abel, J. F., 1972, Introduction to the Finite Element Method: A Numerical Method for Engineering Analysis, Von Nostrand Reinhold Company, New York.

Figures

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(a) Lateral section of a cylinder having an inclined, surface breaking, symmetrical crack, and (b) cross section through the crack
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Illustrating the mesh scheme for the condensation procedure: (a) Arrangement of nodes in a plane; and (b) arrangement of planes.
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An 8-processor (P1[[ellipsis]]P8) having a (a) shared-memory and (b) distributed memory architecture
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Structure of a parallel region in an OpenMP program
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Reflection coefficients for three vertical cracks (ϕ=0) having different lengths
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Reflection coefficients versus normalized frequency for various axisymmetric cracks in a welded steel pipe. H/Rm=0.1, ν=0.29, W=0.1875, and B=0.09375.
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Reflection coefficients versus normalized frequency for variously sized, nonaxisymmetric inclined (ϕ=20 deg) cracks in a steel pipe. D=0.3,H/Rm=0.135, ν=0.287, and W=0.4.
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Reflection coefficients versus normalized frequency for variously sized, nonaxisymmetric vertical (ϕ=0) circumferential cracks in a welded steel pipe. H/Rm=0.1, ν=0.29, W=0.1875, and B=0.09375.
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Normalized reflection and transmission coefficients in a welded steel pipe as a function of the crack length. f=190 kHz,H/Rm=0.1, ν=0.29, D=0.5, ϕ=0, W=0.1875, and B=0.09375. (a) Reflection coefficients, and (b) transmission coefficients.

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