Transient analysis of the dynamic stress intensity factors using SGBEM for frequency-domain elastodynamics |
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| Authors: | A-V Phan LJ Gray A Salvadori |
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| Affiliation: | 1. Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei, 010014 Bucharest, Romania;2. Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, 010141 Bucharest, Romania;3. Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus;4. Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK;1. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, Jiangxi 330013, PR China;2. Department of Computational Science and Statistics, Nantong University, Nantong, Jiangsu 226019, PR China;3. School of Mechanical Engineering, Xiangtan University, Xiangtan, Hunan 411105, PR China;4. Engineering Research Center of Complex Tracks Processing Technology and Equipment of Ministry of Education, Xiangtan University, Xiangtan 411105, PR China;5. Key Laboratory of Welding Robot and Application Technology of Hunan Province, Xiangtan University, Xiangtan 411105, PR China;6. School of Civil Engineering and Urban Construction, Jiujiang University, Jiujiang, Jiangxi 332005, PR China |
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| Abstract: | In this paper, a two-dimensional symmetric-Galerkin boundary integral formulation for elastodynamic fracture analysis in the frequency domain is described. The numerical implementation is carried out with quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the first part is identical to that for elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs can be obtained in a post-processing step by applying the standard fast Fourier transform (FFT) and algorithm to the frequency responses of these DSIFs. Several test examples are presented for the calculation of the DSIFs due to two types of impact loading: Heaviside step loading and blast loading. The results suggest that the combination of the symmetric-Galerkin boundary element method and standard FFT algorithms in determining transient responses of the DSIFs is a robust and effective technique. |
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