A parallel computational algorithm that models three-dimensional elastic wave scattering in an infinite pipe is introduced. The algorithm combines two procedures: a Wave Function Expansion (WFE) and a Finite Element Discretization (FED). The WFE represents a flawless unbounded region while the FED idealizes a bounded region containing the defects. Unknown amplitudes in the WFE are determined by imposing continuity between the two regions; they are then used to calculate the reflection and transmission coefficients. The inversion of a large stiffness matrix resulting from the FED has been overcome in the current formulation by sub-structuring the finite element mesh. The algorithm is implemented in Fortran 90™ on a shared-memory, parallel computing platform using OpenMP™ directives. The algorithm is validated against available numerical and experimental results. Agreement with previous three-dimensional results for a radial crack in a steel pipe and a two-dimensional hybrid model of an axisymmetric cracked, welded steel pipe are shown to be excellent. New results are presented for an inclined crack in a steel pipe as well as for a non-axisymmetric cracked welded steel pipe.
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e-mail: umkotbam@cc.umanitoba.ca
e-mail: shah@cc.umanitoba.ca
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November 2004
Research Papers
Parallel Hybrid Algorithm for Three-Dimensional Elastic Wave Scattering in Steel Pipes
A. Mahmoud,
e-mail: umkotbam@cc.umanitoba.ca
A. Mahmoud
Mechanical and Industrial Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada
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A. H. Shah, Professor,
e-mail: shah@cc.umanitoba.ca
A. H. Shah, Professor
Civil Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada
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N. Popplewell
e-mail: npopple@cc.umanitoba.ca
N. Popplewell
Mechanical and Industrial Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada
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A. Mahmoud
Mechanical and Industrial Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada
e-mail: umkotbam@cc.umanitoba.ca
A. H. Shah, Professor
Civil Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada
e-mail: shah@cc.umanitoba.ca
N. Popplewell
Mechanical and Industrial Engineering Department, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada
e-mail: npopple@cc.umanitoba.ca
Contributed by the Pressure Vessels and Piping Division for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received by the PVP Division May 19, 2003; revision received November 20, 2003. Associate Editor: J. L. Rose.
J. Pressure Vessel Technol. Nov 2004, 126(4): 510-517 (8 pages)
Published Online: December 1, 2004
Article history
Received:
May 19, 2003
Revised:
November 20, 2003
Online:
December 1, 2004
Citation
Mahmoud, A., Shah, A. H., and Popplewell, N. (December 1, 2004). "Parallel Hybrid Algorithm for Three-Dimensional Elastic Wave Scattering in Steel Pipes ." ASME. J. Pressure Vessel Technol. November 2004; 126(4): 510–517. https://doi.org/10.1115/1.1762449
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