Determination of crack tip fields in linear elastostatics by the Meshless Local Petrov-Galerkin (MLPG) method

CMES - Computer Modeling in Engineering and Sciences

Volumn 2, Issue 2, 2001, Pages 273-289

  Ching, H K ^b   Batra, R C ^a  

^a Virginia Polytechnic Institute and State University   (United States)

^b NONE

Author keywords

Edge cracked plates; Edge notched plates; Mixed mode deformations; Singular fields; Stress intensity factors

Indexed keywords

EID: 0001848443     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Anderson, T. L. (1991): Fracture Mechanics: Fundamental and Applications (1st Ed.) CRC Press.
2. Atluri, S. N. (1997): Structural Integrity and Durability. Tech. Science Press, Forsyth, GA.
3. Atluri, S. N.; Zhu, T. (1998): A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, vol. 22, pp. 117-127.
4. Atluri, S. N.; Kim, H. G.; Cho, J. Y. (1999a): A critical assessment of the truly meshless local Petrov-Galerkin (MLPG) and local boundary integral equation (LBIE) methods. Computational Mechanics, vol 24, pp. 348-372.
5. Atluri, S. N.; Cho, J. Y.; Kim, H. G. (1999b): Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolants. Computational Mechanics, vol. 24, pp. 334-347.
6. Atluri, S. N.; Zhu, T. (2000): The Meshless Local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics. Computational Mechanics, vol. 25, pp. 169-179.
7. Batra, R. C.; Gummalla, R. R. (2000): Effect of material and geometric parameters on deformations near the notch tip of a dynamically loaded prenotched plate. International Journal of Fracture, vol. 101, pp. 99-140.
8. Batra, R. C.; Ravisankar, M. V. S. (2000): Three dimensional numerical simulation of the Kalthoff problem. International Journal of Fracture, vol. 105, pp. 161-186.
9. Belytschko, T.; Lu, Y. Y.; Gu, L. (1994): Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, vol. 37, pp. 229-256.
10. Belytschko, T.; Krongauz, Y.; Fleming, M.; Organ, D. J.; Liu, W.K. (1996): Smoothing and accelerated computations in the element free Galerkin method. Journal of Computational and Applied Mathematics, vol. 74, pp. 111-126.
11. Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P. (1996): Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering, vol. 139, pp. 3-47.
12. Chow, W.-T.; Beom, H. G.; Atluri, S. N. (1995): Calculation of stress intensity factors for an interfacial crack between dissimilar anisotropic media using a hybrid element method and the mutual integral. Computational Mechanics, vol. 15, pp. 546-557.
13. Eshelby, J. D. (1956): The continuum theory of lattice defects. Solid State Physics, vol. 3, pp. 79-141.
14. Fleming, M.; Chu, Y.; Moran, B.; Belytschko, T. (1997): Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering, vol. 40, pp. 1483-1504.
15. Gdoutos, E. E. (1993): Fracture Mechanics: an Introduction. Kluwer Academic Publishers.
16. Irwin, G. R. (1957): Analysis of stresses and strains near the end of a crack traversing a plate. Journal of Applied Mechanics, vol. 24, pp. 361-364.
17. Kalthoff, J. F.; Winkler, S. (1987): Failure mode transition at high strain rate of shear loading. In Chiem CY, Kunze HD, Meyer LW, editors, International Conference on Impact Loading and Dynamic Behavior of Materials, Vol. 1, pp. 185-195.
18. Kim, H. G.; Atluri, S. N. (2000): Arbitrary placement of secondary nodes, and error control in the meshless local Petrov-Galerkin (MLPG) method. Computer Modeling in Engineering and Sciences, vol. 1, pp. 11-32.
19. Krysl, P.; Belytschko, T. (1997): Element-free Galerkin: Convergence of the continuous and discontinuous shape functions. Computer Methods in Applied Mechanics and Engineering, vol. 148, pp. 257-277.
20. Lin, H; Atluri, S. N. (2000): Meshless local PetrovGalerkin (MLPG) method for convection-diffusion problems. Computer Modeling in Engineering and Sciences, vol. 1, pp. 45-60.
21. Lu, Y. Y.; Belytschko, T.; Gu, L. (1994): A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering, vol. 113, pp. 397-414.
22. Moran, B; Shih, C. F. (1987): Crack tip and associated domain integrals from momentum and energy balance. Engineering Fracture Mechanics, vol. 27(6), pp. 615-641.
23. Nikishkov, G. P.; Atluri, S. N. (1987): Calculation of fracture mechanics parameters for an arbitrary 3-D crack by the equivalent domain integral method. Int. J. Num. Method. Engg., vol. 24, pp. 1801-1822.
24. Organ, D. J.; Fleming, M.; Belytschko, T. (1996): Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Computational Mechanics, vol. 18, pp. 225-235.
25. Rao, B. N.; Rahman, S. (2000): An efficient meshless method for fracture analysis of cracks. Computational Mechanics, vol. 26, pp. 298-308.
26. Rice, J. R. (1968): A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, vol. 35, pp. 379-386.
27. Shih, C. F.; Asaro, R. J. (1988): Elastic-plastic analysis of cracks on bimaterial interfaces: Part I - small scale yielding. Journal of Applied Mechanics, vol. 55, pp. 299-316.
28. Yau, J. F.; Wang, S. S; Corten, H. T. (1980): A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics, vol. 47, pp. 335-341.