Browse > Article
http://dx.doi.org/10.12989/sem.2018.66.5.649

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

Tian, Xinran (Department of Engineering Mechanics, Hohai University)
Du, Chengbin (Department of Engineering Mechanics, Hohai University)
Dai, Shangqiu (Department of Engineering Mechanics, Hohai University)
Chen, Denghong (College of Civil Engineering and Architecture, China Three Gorges University)
Publication Information
Structural Engineering and Mechanics / v.66, no.5, 2018 , pp. 649-663 More about this Journal
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.
Keywords
scaled boundary finite element method; stress intensity factors; T-stress; improved continued-fractions;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Wolf, J.P. and Song, C.M. (2000), "The scaled boundary finiteelement method-a primer: Derivations", Comput. Struct., 78(1-3), 191-210.   DOI
2 Xiao, Q.Z., Karihaloo, B.L. and Liu, X.Y. (2004), "Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element", Int. J. Fract., 125(3-4), 207-225.   DOI
3 Yang, Z.J. and Deeks, A.J. (2008), "Calculation of transient dynamic stress intensity factors at bimaterial interface cracks using a SBFEM-based frequency-domain approach", Sci. Chin. Ser. G: Phys. Mech. Astronom., 51(5), 519-531.   DOI
4 Yang, Z.J., Deeks, A.J. and Hao, H. (2007), "Transient dynamic fracture analysis using scaled boundary finite element method: A frequency-domain approach", Eng. Fract. Mech., 74(5), 669-687.   DOI
5 Yang, Z.J., Wang, X.F., Yin, D.S. and Zhang, C. (2015), "A nonmatching finite element-scaled boundary finite element coupled method for linear elastic crack propagation modelling", Comput. Struct., 153, 126-136.   DOI
6 Yau, J.F., Wang, S.S. and Corten, H.T. (1980), "A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity", J. Appl. Mech., 47(2), 335-347.   DOI
7 Portela, A., Aliabadi, M.H. and Rooke, D.P. (1993), "Dual boundary element incremental analysis of crack propagation", Comput. Struct., 46(2), 237-247.   DOI
8 Ooi, E.T., Man, H., Natarajan, S. and Song, C. (2015), "Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling", Eng. Fract. Mech., 144, 101-117.   DOI
9 Ooi, E.T., Shi, M., Song, C., Tin-Loi, F. and Yang, Z.J. (2013), "Dynamic crack propagation simulation with scaled boundary polygon elements and automatic remeshing technique", Eng. Fract. Mech., 106, 1-21.   DOI
10 Ooi, E.T. and Yang, Z.J. (2011), "Modelling dynamic crack propagation using the scaled boundary finite element method", Int. J. Numer. Meth. Eng., 88(4), 329-349.   DOI
11 Rethore, J., Gravouil, A. and Combescure, A. (2004), "A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing", Comput. Meth. Appl. Mech. Eng., 193(42), 4493-4510.   DOI
12 Rabczuk, T. and Belytschko, T. (2006), "Application of particle methods to static fracture of reinforced concrete structures", Int. J. Fract., 137(1-4), 19-49.   DOI
13 Chen, D., Birk, C., Song, C. and Du, C. (2014), "A high-order approach for modelling transient wave propagation problems using the scaled boundary finite element method", Int. J. Numer. Meth. Eng., 97(13), 937-959.   DOI
14 Barsoum, R.S. (1977), "Triangular quarter point elements elastic and perfectly plastic crack tip elements", Int. J. Numer. Meth. Eng., 11(1), 85-98.   DOI
15 Rabczuk, T., Gracie, R., Song, J. and Belytschko, T. (2009), "Immersed particle method for fluid-structure interaction", Int. J. Numer. Meth. Eng., 81(1), 48-71.   DOI
16 Rabczuk, T., Zi, G., Bordas, S. and Nguyen-Xuan, H. (2008), "A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures", Eng. Fract. Mech., 75(16), 4740-4758.   DOI
17 Rao, B.N. and Rahman, S. (2004), "An enriched meshless method for non-linear fracture mechanics", Int. J. Numer. Meth. Eng., 59(2), 197-223.   DOI
18 Rice, J.R. (1967), "A path independent integral and the approximate analysis of strain concentration by notches and cracks", J. Appl. Mech., 35(2), 379-386.   DOI
19 Belytschko, T., Chen, H., Xu, J. and Zi, G. (2003) "Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment", Int. J. Numer. Meth. Eng., 58(12), 1873-1905.   DOI
20 Chen, D. and Dai, S. (2017), "Dynamic fracture analysis of the soil-structure interaction system using the scaled boundary finite element method", Eng. Analy. Boundar. Elem., 77, 26-35.   DOI
21 Chen, Y.M. (1975), "Numerical computation of dynamic stress intensity factors by a Lagrangian finite-difference method", Eng. Fract. Mech., 7(4), 653-660.   DOI
22 Chidgzey, S.R. and Deeks, A.J. (2005), "Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method", Eng. Fract. Mech., 72(13), 2019-2036.   DOI
23 Chidgzey, S.R., Trevelyan, J. and Deeks, A.J. (2008), "Coupling of the boundary element method and the scaled boundary finite element method for computations in fracture mechanics", Comput. Struct., 86(11-12), 1198-1203.   DOI
24 Chiong, I., Ooi, E.T., Song, C. and Tin-Loi, F. (2014), "Scaled boundary polygons with application to fracture analysis of functionally graded materials", Int. J. Numer. Meth. Eng., 98(8), 562-589.   DOI
25 Dai, S., Augarde, C., Du, C. and Chen, D. (2014), "A fully automatic polygon scaled boundary finite element method for modelling crack propagation", Eng. Fract. Mech., 133, 163-178.
26 Fedelinski, P. (2010), "Computer modelling of dynamic fracture experiments", Key Eng. Mater., 454, 113-125.   DOI
27 Song, C. (2004a), "A matrix function solution for the scaled boundary finite-element equation in statics", Comput. Meth. Appl. Mech. Eng., 193(23-26), 2325-2356.   DOI
28 Saputra, A., Talebi, H., Tran, D., Birk, C. and Song, C. (2017), "Automatic image-based stress analysis by the scaled boundary finite element method", Int. J. Numer. Meth. Eng., 109(5), 697-738.   DOI
29 Simpson, R. and Trevelyan, J. (2011), "A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics", Comput. Meth. Appl. Mech. Eng., 200(1-4), 1-10.   DOI
30 Sladek, J., Sladek, V. and Fedelinski, P. (1999), "Computation of the second fracture parameter in elastodynamics by the boundary element method", Adv. Eng. Softw., 30(9-11), 725-734.   DOI
31 Song, C. (2004b), "A super-element for crack analysis in the time domain", Int. J. Numer. Meth. Eng., 61(8), 1332-1357.   DOI
32 Song, C. (2009), "The scaled boundary finite element method in structural dynamics", Int. J. Numer. Meth. Eng., 77(8), 1139-1171.   DOI
33 Legrain, G., Cartraud, P., Perreard, I. and Moes, N. (2011), "An XFEM and level set computational approach for imaebased modelling: Application to homogenization", Int. J. Numer. Meth. Eng., 86(7), 915-934.   DOI
34 Jiang, S., Du, C., Gu, C. and Chen, X. (2014), "XFEM analysis of the effects of voids, inclusions and other cracks on the dynamic stress intensity factor of a major crack", Atig. Fract. Eng. Mater. Struct., 37(8), 866-882.   DOI
35 Jiang, S., Du, C. and Gu, C. (2014), "An investigation into the effects of voids, inclusions and minor cracks on major crack propagation by using XFEM", Struct. Eng. Mech., 49(5), 597-618.   DOI
36 Jamal-Omidi, M., Falah, M. and Taherifar, D. (2014), "3-D fracture analysis of cracked aluminum plates repaired with single and double composite patches using XFEM", Struct. Eng. Mech., 50(4), 525-539.   DOI
37 Li, C., Ooi, E.T., Song, C. and Natarajan, S. (2015), "SBFEM for fracture analysis of piezoelectric composites under thermal load", Int. J. Sol. Struct., 52, 114-129.   DOI
38 Li, C. and Tong, L. (2015), "A mixed SBFEM for stress singularities in nearly incompressible multi-materials", Comput. Struct., 157, 19-30.   DOI
39 Murti, V. and Valliappan, S. (1986), "The use of quarter point element in dynamic crack analysis", Eng. Fract. Mech., 23(3), 585-614.   DOI
40 Natarajan, S. and Song, C. (2013), "Representation of singular fields without asymptotic enrichment in the extended finite element method", Int. J. Numer. Meth. Eng., 96(13), 813-841.   DOI
41 Natarajan, S., Song, C. and Belouettar, S. (2014), "Numerical evaluation of stress intensity factors and T-stress for interfacial cracks and cracks terminating at the interface without asymptotic enrichment", Comput. Meth. Appl. Mech. Eng., 279, 86-112.   DOI
42 Song, C. and Wolf, J.P. (1997), "The scaled boundary finiteelement method-alias consistent infinitesimal finite-element cell method-for elastodynamics", Comput. Meth. Appl. Mech. Eng., 147(3-4), 329-355.   DOI
43 Song, C., Tin-Loi, F. and Gao, W. (2010a), "A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges", Eng. Fract. Mech., 77(12), 2316-2336.   DOI
44 Song, C., Tin-Loi, F. and Gao, W. (2010b), "Transient dynamic analysis of interface cracks in anisotropic bimaterials by the scaled boundary finite-element method", Int. J. Sol. Struct., 47(7-8), 978-989.   DOI
45 Song, C. and Vrcelj, Z. (2008), "Evaluation of dynamic stress intensity factors and T-stress using the scaled boundary finiteelement method", Eng. Fract. Mech., 75(8), 1960-1980.   DOI
46 Song, S.H. and Paulino, G.H. (2006), "Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method", Int. J. Sol. Struct., 43(16), 4830-4866.   DOI
47 Ooi, E.T., Natarajan, S., Song, C. and Ooi, E.H. (2017), "Crack propagation modelling in concrete using the scaled boundary finite element method with hybrid polygon-quadtree meshes", Int. J. Fract. Jan., 203(1-2), 135-157.   DOI
48 Ooi, E.T., Song, C. and Natarajan, S. (2016), "Construction of high-order complete scaled boundary shape functions over arbitrary polygons with bubble functions", Int. J. Numer. Meth. Eng., 108(9), 1086-1120.   DOI
49 Song, C.M. and Wolf, J.P. (2000), "The scaled boundary finiteelement method-a primer: Solution procedures", Comput. Struct., 78(1-3), 211-225.   DOI
50 Song, C.M. and Wolf, J.P. (2002), "Semi-analytical representation of stress singularities as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method", Comput. Struct., 80(2), 183-197.   DOI
51 Wen, P.H., Aliabadi, M.H. and Rooke, D.P. (1997), "A contour integral method for dynamic stress intensity factors", Heoret. Appl. Fract. Mech., 27(1), 29-41.   DOI