Frontiers of Mechanical Engineering >
A family of non-conforming crack front elements of quadrilateral and triangular types for 3D crack problems using the boundary element method
Received date: 03 Feb 2019
Accepted date: 30 Mar 2019
Published date: 15 Sep 2019
Copyright
This study focuses on establishing non- conforming crack front elements of quadrilateral and triangular types for 3D crack problems when the dual boundary element method is applied. The asymptotic behavior of the physical variables in the area near the crack front is fully considered in the construction of the shape function. In the developed quadrilateral and triangular crack front elements, the asymptotic term, which captures the asymptotic behavior of the physical variable, is multiplied directly by the conventional Lagrange shape function to form a new crack front shape function. Several benchmark numerical examples that consider penny-shaped cracks and straight-edge crack problems are presented to illustrate the validity and efficiency of the developed crack front elements.
Guizhong XIE , Fenglin ZHOU , Hao LI , Xiaoyu WEN , Fannian MENG . A family of non-conforming crack front elements of quadrilateral and triangular types for 3D crack problems using the boundary element method[J]. Frontiers of Mechanical Engineering, 2019 , 14(3) : 332 -341 . DOI: 10.1007/s11465-019-0540-3
1 |
Zhang D H, Li Y Q, Xie G Z,
|
2 |
Zhang D H, Li Y Q, Liu J X,
|
3 |
Zhang D H, Xie G Z, Li Y Q,
|
4 |
Zhang D H, Bai D P, Liu J B,
|
5 |
Mi Y, Aliabadi M H. Dual boundary element method for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements, 1992, 10(2): 161–171
|
6 |
Sladek V, Sladek J, Tanaka M. Nonsingular BEM formulations for thin-walled structures and elastostatic crack problems. Acta Mechanica, 1993, 99(1–4): 173–190
|
7 |
Zhang Y M, Gu Y, Chen J T. Boundary element analysis of the thermal behaviour in thin-coated cutting tools. Engineering Analysis with Boundary Elements, 2010, 34(9): 775–784
|
8 |
Yao Z H, Wang H T. Some benchmark problems and basic ideas on the accuracy of boundary element analysis. Engineering Analysis with Boundary Elements, 2013, 37(12): 1674–1692
|
9 |
Zhang J M, Lin W C, Dong Y,
|
10 |
Feng S Z, Han X, Wang G. An efficient on-line algorithm for the optimal design of multi-material structures under thermal loads. International Journal of Thermal Sciences, 2018, 132: 567–577
|
11 |
Feng S Z, Cheng Y H. An element decomposition method for heat transfer analysis. International Journal of Heat and Mass Transfer, 2018, 123: 437–444
|
12 |
Feng S Z, Bordas S P A, Han X,
|
13 |
Cheng C, Niu Z, Recho N. Analysis of the stress singularity for a bi-material V-notch by the boundary element method. Applied Mathematical Modelling, 2013, 37(22): 9398–9408
|
14 |
Cheng C, Ge S, Yao S, et al. Thermal stress singularity analysis for V-notches by natural boundary element method. Applied Mathematical Modelling, 2016, 40(19–20): 8552–8563
|
15 |
Zhu B J, Qin T Y. Application of hypersingular integral equation method to three-dimensional crack in electromagnetothermoelastic multiphase composites. International Journal of Solids and Structures, 2007, 44(18–19): 5994–6012
|
16 |
Henshell R D, Shaw K G. Crack tip finite elements are unnecessary. International Journal for Numerical Methods in Engineering, 1975, 9(3): 495–507
|
17 |
Lv J H, Jiao Y Y, Wriggers P,
|
18 |
Sáez A, Gallego R, Dominguez J. Hypersingular quarter-point boundary elements for crack problems. International Journal for Numerical Methods in Engineering, 1995, 38(10): 1681–1701
|
19 |
Hong H K, Chen J T. Derivations of integral equations of elasticity. Journal of Engineering Mechanics, 1988, 114(6): 1028–1044
|
20 |
Mi Y, Aliabadi M H. Discontinuous crack-tip elements: Application to 3D boundary element method. International Journal of Fracture, 1994, 67(3): R67–R71
|
21 |
Pan E, Yuan F G. Boundary element analysis of three-dimensional cracks in anisotropic solids. International Journal for Numerical Methods in Engineering, 2000, 48(2): 211–237
|
22 |
Xie G Z, Zhang J, Huang C,
|
23 |
Li J, Feng W Z, Gao X W. A dual boundary integral equation method based on direct evaluation of higher order singular integral for crack problems. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2): 387–398 (in Chinese)
|
24 |
Xie G Z, Zhang D, Meng F,
|
25 |
Ariza M P, Saez A, Dominguez J. A singular element for three-dimensional fracture mechanics analysis. Engineering Analysis with Boundary Elements, 1997, 20(4): 275–285
|
26 |
Ariza M P, Dominguez J. Boundary element formulation for 3D transversely isotropic cracked bodies. International Journal for Numerical Methods in Engineering, 2004, 60(4): 719–753
|
27 |
Aliabadi M H, Rooke D P. Numerical Fracture Mechanics. Boston: Kluwer Academic Publishers, 1991
|
28 |
Shah R C, Kobayashi A S. Stress intensity factor for an elliptical crack under arbitrary normal loading. Engineering Fracture Mechanics, 1971, 3(1): 71–96
|
29 |
Chen L S, Kuang J H. A displacement extrapolation method for determining the stress intensity factors along flaw border. International Journal of Fracture, 1992, 57(4): R51–R58
|
30 |
Liu Y. On the displacement discontinuity method and the boundary element method for solving 3-D crack problems. Engineering Fracture Mechanics, 2016, 164: 35–45
|
31 |
Tada H, Paris P C, Irwin G R. The Stress Analysis of Cracks Handbook. Vol. 130. New York: ASME, 2000
|
32 |
Murakami Y, Keer L M. Stress intensity factors handbook, Vol. 3. Journal of Applied Mechanics, 1993, 60(4): 1063
|
33 |
Raju I S, Newman J C Jr. Three Dimensional Finite-Element Analysis of Finite-Thickness Fracture Specimens. NASA Technical Note, NASA TN D-8414. 1977
|
/
〈 | 〉 |