Structural Engineering and Mechanics

  • 제66권5호
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  • Pages.649-663
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  • 2018
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2017.10.28
  • 심사 : 2018.03.11
  • 발행 : 2018.06.10
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Barsoum, R.S. (1977), "Triangular quarter point elements elastic and perfectly plastic crack tip elements", Int. J. Numer. Meth. Eng., 11(1), 85-98. https://doi.org/10.1002/nme.1620110109
  2. 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. https://doi.org/10.1002/nme.941
  3. 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. https://doi.org/10.1016/j.enganabound.2017.01.002
  4. 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. https://doi.org/10.1002/nme.4613
  5. Chen, Y.M. (1975), "Numerical computation of dynamic stress intensity factors by a Lagrangian finite-difference method", Eng. Fract. Mech., 7(4), 653-660. https://doi.org/10.1016/0013-7944(75)90021-1
  6. 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. https://doi.org/10.1016/j.engfracmech.2004.07.010
  7. 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. https://doi.org/10.1016/j.compstruc.2007.11.007
  8. 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. https://doi.org/10.1002/nme.4645
  9. 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.
  10. Fedelinski, P. (2010), "Computer modelling of dynamic fracture experiments", Key Eng. Mater., 454, 113-125. https://doi.org/10.4028/www.scientific.net/KEM.454.113
  11. 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. https://doi.org/10.1111/ffe.12150
  12. 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. https://doi.org/10.12989/sem.2014.49.5.597
  13. 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. https://doi.org/10.12989/sem.2014.50.4.525
  14. 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. https://doi.org/10.1002/nme.3085
  15. 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. https://doi.org/10.1016/j.ijsolstr.2014.09.020
  16. Li, C. and Tong, L. (2015), "A mixed SBFEM for stress singularities in nearly incompressible multi-materials", Comput. Struct., 157, 19-30. https://doi.org/10.1016/j.compstruc.2015.05.011
  17. Murti, V. and Valliappan, S. (1986), "The use of quarter point element in dynamic crack analysis", Eng. Fract. Mech., 23(3), 585-614. https://doi.org/10.1016/0013-7944(86)90164-5
  18. 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. https://doi.org/10.1002/nme.4557
  19. 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. https://doi.org/10.1016/j.cma.2014.06.024
  20. 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. https://doi.org/10.1007/s10704-016-0136-4
  21. 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. https://doi.org/10.1002/nme.5259
  22. 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. https://doi.org/10.1016/j.engfracmech.2015.06.083
  23. 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. https://doi.org/10.1016/j.engfracmech.2013.02.002
  24. 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. https://doi.org/10.1002/nme.3177
  25. Portela, A., Aliabadi, M.H. and Rooke, D.P. (1993), "Dual boundary element incremental analysis of crack propagation", Comput. Struct., 46(2), 237-247. https://doi.org/10.1016/0045-7949(93)90189-K
  26. 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. https://doi.org/10.1016/j.cma.2004.03.005
  27. 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. https://doi.org/10.1007/s10704-005-3075-z
  28. 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. https://doi.org/10.1002/nme.2670
  29. 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. https://doi.org/10.1016/j.engfracmech.2008.06.019
  30. 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. https://doi.org/10.1002/nme.868
  31. 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. https://doi.org/10.1115/1.3601206
  32. 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. https://doi.org/10.1002/nme.5304
  33. 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. https://doi.org/10.1016/j.cma.2010.06.015
  34. 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. https://doi.org/10.1016/S0965-9978(99)00019-8
  35. 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. https://doi.org/10.1016/j.cma.2004.01.017
  36. Song, C. (2004b), "A super-element for crack analysis in the time domain", Int. J. Numer. Meth. Eng., 61(8), 1332-1357. https://doi.org/10.1002/nme.1117
  37. Song, C. (2009), "The scaled boundary finite element method in structural dynamics", Int. J. Numer. Meth. Eng., 77(8), 1139-1171. https://doi.org/10.1002/nme.2454
  38. 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. https://doi.org/10.1016/j.engfracmech.2010.04.032
  39. 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. https://doi.org/10.1016/j.ijsolstr.2009.12.015
  40. 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. https://doi.org/10.1016/j.engfracmech.2007.11.009
  41. 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. https://doi.org/10.1016/S0045-7825(97)00021-2
  42. Song, C.M. and Wolf, J.P. (2000), "The scaled boundary finiteelement method-a primer: Solution procedures", Comput. Struct., 78(1-3), 211-225. https://doi.org/10.1016/S0045-7949(00)00100-0
  43. 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. https://doi.org/10.1016/S0045-7949(01)00167-5
  44. 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. https://doi.org/10.1016/j.ijsolstr.2005.06.102
  45. 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. https://doi.org/10.1016/S0167-8442(97)00005-0
  46. Wolf, J.P. and Song, C.M. (2000), "The scaled boundary finiteelement method-a primer: Derivations", Comput. Struct., 78(1-3), 191-210. https://doi.org/10.1016/S0045-7949(00)00099-7
  47. 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. https://doi.org/10.1023/B:FRAC.0000022229.54422.13
  48. 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. https://doi.org/10.1007/s11433-008-0057-y
  49. 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. https://doi.org/10.1016/j.engfracmech.2006.06.018
  50. 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. https://doi.org/10.1016/j.compstruc.2015.02.034
  51. 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. https://doi.org/10.1115/1.3153665

피인용 문헌

  1. Stochastic Fracture Analysis Using Scaled Boundary Finite Element Methods Accelerated by Proper Orthogonal Decomposition and Radial Basis Functions vol.2021, pp.None, 2021, https://doi.org/10.1155/2021/9181415