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