Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T12:40:25.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Study of Static Fracture Propagation by Element-Free Galerkin Method With Singular Weight Function at Crack Tip

Published online by Cambridge University Press:  05 May 2011

K.-J. Shen ,
J. P. Sheng  and
C.-Y. Wang
K.-J. Shen*
Affiliation:
Department of Civil Engineering, Vanung University, Chungli, Tao-Yuan, Taiwan 32046, R.O.C.
J. P. Sheng*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Tao-Yuan, Taiwan 32045, R.O.C.
C.-Y. Wang*
Affiliation:
Department of Civil Engineering, National Central University, Chungli, Tao-Yuan, Taiwan 32045, R.O.C.
*
*Associate Professor
*Associate Professor
**Professor
Get access

Abstract

Element-free Galerkin method (EFGM) based on moving least-square curve fitting concept is presented and applied to elastic fracture problems. Because no element connectivity data are needed, EFGM is very convenient and effective numerical method for crack growth analysis. This paper is intended as an investigation of crack trajectory for different notch locations under three-point bending test. The initial crack growth angles obtained by element-free Galerkin method in comparison with those obtained by lab test reveal that both results are very close. However, numerical results also show that the location of an original notch can stronger affect the variation of crack path for different increment. The stress intensity factors (SIF) of cracks under three-point bending test with different increment are also investigated by EFGM.

Keywords

Element-free methodCrack propagationFracture mechanics
Type
Technical Note
Information
Journal of Mechanics , Volume 21 , Issue 2 , June 2005 , pp. 125 - 129
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Nayroles, B., Touzot, G. and Villon, P., “Generalizing the Finite Element Method: Diffuse Approximation and Diffuse Elememts.” Computational Mechanics, 10, pp. 307–318 (1992).CrossRefGoogle Scholar
2.Belytschko, T., Lu, Y. Y. and Gu, L., “Element-Free Galerkin Method.” International Journal for Numerical Methods in Engineering, 37, pp. 2290–256 (1994).CrossRefGoogle Scholar
3.Lancaster, P. and Salkauskas, K., “Surfaces Generated by Moving Least Squares Method.” Mathematics of Computation, 37, pp. 141–158 (1981).CrossRefGoogle Scholar
4.Belytschko, T., Lu, Y. Y. and Gu, L., “Crack Propagation by Element Free Galerkin Method.” Engineering Fracture Mechanics, 51(2), pp. 295–315 (1995).CrossRefGoogle Scholar
5.Belytschko, T., Lu, Y. Y., Gu, L. and Tabbara, , “Element-Free Galerkin Methods for Static and Dynamic Fracture.” International Journal of Solids and Structures, 32(17/18), pp. 2547–2570 (1995).CrossRefGoogle Scholar
6.Fleming, M., Chu, Y. A., Moran, B. and Belytschko, T., “Enriched Element-Free Galerkin Methods for Crack Tip Fields.” International Journal for Numerical Methods in Engineering, 40, pp. 1483–1504 (1997).3.0.CO;2-6>CrossRefGoogle Scholar
7.Belytschko, T. and Fleming, M., “Smoothing, Enrichment and Contact in the Element-Free Galerkin Method.” Computers and Structures, 71, pp. 173–195 (1999).CrossRefGoogle Scholar
8.Belytschko, T., Organ, D. and Gerlach, C., “Element-Free Galerkin Methods for Dynamic Fracture in Concrete.” Comput. Methods Appl. Mech. Engrg., 187, pp. 385–399 (2000).CrossRefGoogle Scholar
9.Rao, B. N. and Rahman, S., “A Coupled Meshless-Finite Element Method for Fracture Analysis of Cracks,” International Journal of Pressure Vessels and Piping, 78, pp. 647–657 (2001).CrossRefGoogle Scholar
10.Lee, S. H. and Yoon, Y. C., “Numerical Prediction of Crack Propagation by an Enhanced Element-Free Galerkin Method.” Nuclear Engineering and Design, 227, pp. 257–271 (2004).CrossRefGoogle Scholar
11.Rice, J. R., “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks.” J. Appl. Mech., 35, pp. 379–386 (1968).CrossRefGoogle Scholar
12.Aoki, S., Kishimoto, K. and Sakata, M., “Crack-Tip Stress and Strain Singularity in Thermally Loaded Elastic-Plastic Material.” Journal of Applided Mechanics, 48, pp. 428–429 (1981).CrossRefGoogle Scholar
13.Herrmann, A. G. and Herrmann, G., “On Energy-Release Rates for a Plane Crack.” Journal of Basic Engineering, 48, pp. 525–528 (1981).Google Scholar
14.Erdogan, F. and Sih, S. C., “On the Crack Extension in Plates under Plane Loading and Transverse Shear.” ASME, Journal Basic Engineering, 85, pp. 519–525 (1963).CrossRefGoogle Scholar
15.Jang, Y. S. and Shah, S. P., “Mixed Mode Fracture of Concrete.” International Journal of Fracture, 38, pp. 123–142 (1988).Google Scholar