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APPLICATION OF BOUNDARY ELEMENT METHOD FOR 3D WAVE SCATTERING IN CYLINDERS

Department of Mechanical Engineering, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, Canada, P7B 5E1, Canada

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and

A. H. SHAH

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

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https://doi.org/10.1142/S0219876211002332Cited by:2 (Source: Crossref)

Abstract

A boundary element method (BEM) is presented to study 3D wave scattering by cracks in a cylinder. Green's functions needed in the kernel of boundary integral equations in BEM are derived with the help of guided wave functions. Guided wave modes in the cylinder are obtained by a semi-analytical finite element (SAFE) method. Green's functions are constructed numerically by superposition of guided wave modes. In this method, the cylinder is discretized in the radial direction into several coaxial circular cylinders (sub-cylinders) and the radial dependence of the displacement in each sub-cylinder is approximated by quadratic interpolation polynomials. A numerical procedure is used here to accurately calculate the Cauchy's principal value (CPV) and weakly singular integrals. The multi-domain technique is employed here to model the crack surface. Numerical results are presented to show the effectiveness of the proposed solution.

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