- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 715613, 16 pages
Combined Visibility and Surrounding Triangles Method for Simulation of Crack Discontinuities in Meshless Methods
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
Received 25 July 2012; Accepted 27 September 2012
Academic Editor: Khalida I. Noor
Copyright © 2012 H. Pirali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. R. Liu, Mesh Free Methods, CRC Press, Boca Raton, Fla, USA, 1st edition, 2003.
- T. N. Bittencourt, P. A. Wawrzynek, A. R. Ingraffea, and J. L. Sousa, “Quasi-automatic simulation of crack propagation for 2D lefm problems,” Engineering Fracture Mechanics, vol. 55, no. 2, pp. 321–334, 1996.
- P. O. Bouchard, F. Bay, and Y. Chastel, “Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria,” Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 35-36, pp. 3887–3908, 2003.
- S. R. Beissel, G. R. Johnson, and C. H. Popelar, “An element-failure algorithm for dynamic crack propagation in general directions,” Engineering Fracture Mechanics, vol. 61, no. 3-4, pp. 407–425, 1998.
- F. R. Biglari, A. T. Kermani, M. H. Parsa, K. M. Nikbin, and N. P. O'Dowd, “Comparison of fine and conventional blanking based on ductile fracture criteria,” in Proceedings of the 7th Biennial Conference on Engineering Systems Design and Analysis, pp. 265–270, Manchester, UK, July 2004.
- Y. T. Gu and L. C. Zhang, “Coupling of the meshfree and finite element methods for determination of the crack tip fields,” Engineering Fracture Mechanics, vol. 75, no. 5, pp. 986–1004, 2008.
- T. Rabczuk, S. Bordas, and G. Zi, “On three-dimensional modelling of crack growth using partition of unity methods,” Computers and Structures, vol. 88, no. 23-24, pp. 1391–1411, 2010.
- S. E. Mousavi and N. Sukumar, “Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method,” Computer Methods in Applied Mechanics and Engineering, vol. 199, no. 49-52, pp. 3237–3249, 2010.
- I. V. Singh, B. K. Mishra, S. Bhattacharya, and R. U. Patil, “The numerical simulation of fatigue crack growth using extended finite element method,” International Journal of Fatigue, vol. 36, no. 1, pp. 109–119, 2012.
- P. H. Wen and M. H. Aliabadi, “A variational approach for evaluation of stress intensity factors using the element free Galerkin method,” International Journal of Solids and Structures, vol. 48, no. 7-8, pp. 1171–1179, 2011.
- T. P. Fries and H. G. Matthies, Classification and Overview of Meshfree Methods, Informatikbericht 2003-3, Technical University Braunschweig, Brunswick, Germany, 2003.
- V. P. Nguyen, T. Rabczuk, S. Bordas, and M. Duflot, “Meshless methods: a review and computer implementation aspects,” Mathematics and Computers in Simulation, vol. 79, no. 3, pp. 763–813, 2008.
- T. Belytschko, Y. Krongauz, M. Fleming, D. Organ, and W. K. S. Liu, “Smoothing and accelerated computations in the element free Galerkin method,” Journal of Computational and Applied Mathematics, vol. 74, no. 1-2, pp. 111–126, 1996.
- Y. Krongauz and T. Belytschko, “EFG approximation with discontinuous derivatives,” International Journal for Numerical Methods in Engineering, vol. 41, no. 7, pp. 1215–1233, 1998.
- D. Organ, M. Fleming, T. Terry, and T. Belytschko, “Continuous meshless approximations for nonconvex bodies by diffraction and transparency,” Computational Mechanics, vol. 18, no. 3, pp. 225–235, 1996.
- B. Muravin and E. Turkel, Advance Diffraction Method as a Tool for Solution of Complex Non-Convex Boundary Problems in Meshfree Methods for Partial Differential Equations, vol. 26, Springer, Berlin, Germany, 2002, Edited by M. Griebel, M. A. Schweitzer.
- M. Fleming, Y. A. Chu, B. Moran, and T. Belytschko, “Enriched element-free Galerkin methods for crack tip fields,” International Journal for Numerical Methods in Engineering, vol. 40, no. 8, pp. 1483–1504, 1997.
- G. Ventura, J. X. Xu, and T. Belytschko, “A vector level set method and new discontinuity approximations for crack growth by EFG,” International Journal for Numerical Methods in Engineering, vol. 54, no. 6, pp. 923–944, 2002.
- T. Rabczuk and T. Belytschko, “Cracking particles: a simplified meshfree method for arbitrary evolving cracks,” International Journal for Numerical Methods in Engineering, vol. 61, no. 13, pp. 2316–2343, 2004.
- T. Rabczuk, P. M. A. Areias, and T. Belytschko, “A simplified mesh-free method for shear bands with cohesive surfaces,” International Journal for Numerical Methods in Engineering, vol. 69, no. 5, pp. 993–1021, 2007.
- A. Carpinteri, “Post-peak and post-bifurcation analysis of cohesive crack propagation,” Engineering Fracture Mechanics, vol. 32, no. 2, pp. 265–278, 1989.
- A. Carpinteri, “A scale-invariant cohesive crack model for quasi-brittle materials,” Engineering Fracture Mechanics, vol. 69, no. 2, pp. 207–217, 2001.
- H. Tada, P. C. Paris, and G. R. Irwin, The Stress Analysis of Cracks Handbook, Del Research, Hellrtown, Pa, USA, 1975.
- S. Hagihara, M. Tsunori, T. Ikeda, and N. Miyazaki, “Application of meshfree method to elastic-plastic fracture mechanics parameter analysis,” Computer Modeling in Engineering and Sciences, vol. 17, no. 2, pp. 63–72, 2007.
- T. Belytschko, Y. Y. Lu, and L. Gu, “Element-free Galerkin methods,” International Journal for Numerical Methods in Engineering, vol. 37, no. 2, pp. 229–256, 1994.
- P. Krysl and T. Belytschko, “Element-free Galerkin method: convergence of the continuous and discontinuous shape functions,” Computer Methods in Applied Mechanics and Engineering, vol. 148, no. 3-4, pp. 257–277, 1997.
- T. L. Anderson, Fracture Mechanics, Fundamentals and Applications, 2nd edition, 1995.
- A. Saxena, Nonlinear Fracture Mechanics for Engineers, 1998.