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      Calculation of dynamic stress intensity factors and T-stress using an improved SBFEM

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      https://www.riss.kr/link?id=A105367555

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      다국어 초록 (Multilingual Abstract)

      The scaled boundary finite element method is extended to evaluate the dynamic stress intensity factors and T-stress with a numerical procedure based on the improved continued-fraction. The improved continued-fraction approach for the dynamic stiffness matrix is introduced to represent the inertial effect at high frequencies, which leads to numerically better conditioned matrices. After separating the singular stress term from other high order terms, the internal displacements can be obtained by numerical integration and no mesh refinement is needed around the crack tip. The condition numbers of coefficient matrix of the improved method are much smaller than that of the original method, which shows that the improved algorithm can obtain well-conditioned coefficient matrices, and the efficiency of the solution process and its stability can be significantly improved. Several numerical examples are presented to demonstrate the increased robustness and efficiency of the proposed method in both homogeneous and bimaterial crack problems.
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      The scaled boundary finite element method is extended to evaluate the dynamic stress intensity factors and T-stress with a numerical procedure based on the improved continued-fraction. The improved continued-fraction approach for the dynamic stiffness...

      The scaled boundary finite element method is extended to evaluate the dynamic stress intensity factors and T-stress with a numerical procedure based on the improved continued-fraction. The improved continued-fraction approach for the dynamic stiffness matrix is introduced to represent the inertial effect at high frequencies, which leads to numerically better conditioned matrices. After separating the singular stress term from other high order terms, the internal displacements can be obtained by numerical integration and no mesh refinement is needed around the crack tip. The condition numbers of coefficient matrix of the improved method are much smaller than that of the original method, which shows that the improved algorithm can obtain well-conditioned coefficient matrices, and the efficiency of the solution process and its stability can be significantly improved. Several numerical examples are presented to demonstrate the increased robustness and efficiency of the proposed method in both homogeneous and bimaterial crack problems.

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      참고문헌 (Reference)

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      9 Song, C., "The scaled boundary finite element method in structural dynamics" 77 (77): 1139-1171, 2009

      10 Song, C.M., "Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method" 80 (80): 183-197, 2002

      1 Jiang, S., "XFEM analysis of the effects of voids, inclusions and other cracks on the dynamic stress intensity factor of a major crack" 37 (37): 866-882, 2014

      2 Barsoum, R.S., "Triangular quarter point elements elastic and perfectly plastic crack tip elements" 11 (11): 85-98, 1977

      3 Yang, Z.J., "Transient dynamic fracture analysis using scaled boundary finite element method: A frequency-domain approach" 74 (74): 669-687, 2007

      4 Song, C., "Transient dynamic analysis of interface cracks in anisotropic bimaterials by the scaled boundary finite-element method" 47 (47): 978-989, 2010

      5 Murti, V., "The use of quarter point element in dynamic crack analysis" 23 (23): 585-614, 1986

      6 Song, C., "The scaled boundary finiteelement method-alias consistent infinitesimal finite-element cell method-for elastodynamics" 147 (147): 329-355, 1997

      7 Song, C.M., "The scaled boundary finiteelement method-a primer: Solution procedures" 78 (78): 211-225, 2000

      8 Wolf, J.P., "The scaled boundary finiteelement method-a primer: Derivations" 78 (78): 191-210, 2000

      9 Song, C., "The scaled boundary finite element method in structural dynamics" 77 (77): 1139-1171, 2009

      10 Song, C.M., "Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method" 80 (80): 183-197, 2002

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      20 Chen, D., "Dynamic fracture analysis of the soil-structure interaction system using the scaled boundary finite element method" 77 : 26-35, 2017

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      26 Ooi, E.T., "Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon-quadtree meshes" 203 (203): 135-157, 2017

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      28 Ooi, E.T., "Construction of high-order complete scaled boundary shape functions over arbitrary polygons with bubble functions" 108 (108): 1086-1120, 2016

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      31 Yang, Z.J., "Calculation of transient dynamic stress intensity factors at bimaterial interface cracks using a SBFEM-based frequency-domain approach" 51 (51): 519-531, 2008

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      33 Rabczuk, T., "Application of particle methods to static fracture of reinforced concrete structures" 137 (137): 19-49, 2006

      34 Shouyan Jiang, "An investigation into the effects of voids, inclusions and minor cracks on major crack propagation by using XFEM" 국제구조공학회 49 (49): 597-618, 2014

      35 Rao, B.N., "An enriched meshless method for non-linear fracture mechanics" 59 (59): 197-223, 2004

      36 Legrain, G., "An XFEM and level set computational approach for imaebased modelling: Application to homogenization" 86 (86): 915-934, 2011

      37 Ooi, E.T., "Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling" 144 : 101-117, 2015

      38 Song, C., "A super-element for crack analysis in the time domain" 61 (61): 1332-1357, 2004

      39 Rethore, J., "A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing" 193 (193): 4493-4510, 2004

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      43 Yau, J.F., "A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity" 47 (47): 335-347, 1980

      44 Li, C., "A mixed SBFEM for stress singularities in nearly incompressible multi-materials" 157 : 19-30, 2015

      45 Song, C., "A matrix function solution for the scaled boundary finite-element equation in statics" 193 (193): 2325-2356, 2004

      46 Chen, D., "A high-order approach for modelling transient wave propagation problems using the scaled boundary finite element method" 97 (97): 937-959, 2014

      47 Rabczuk, T., "A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures" 75 (75): 4740-4758, 2008

      48 Dai, S., "A fully automatic polygon scaled boundary finite element method for modelling crack propagation" 133 : 163-178, 2014

      49 Song, C., "A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges" 77 (77): 2316-2336, 2010

      50 Wen, P.H., "A contour integral method for dynamic stress intensity factors" 27 (27): 29-41, 1997

      51 Majid Jamal-Omidi, "3-D fracture analysis of cracked aluminum plates repaired with single and double composite patches using XFEM" 국제구조공학회 50 (50): 525-539, 2014

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      2016 1.12 0.62 0.94
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