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A coupled finite element – element-free Galerkin method.(English)Zbl 0840.73058

Summary: A procedure is developed for coupling meshless methods such as the element-free Galerkin method with finite element methods. The coupling is developed so that continuity and consistency are preserved on the interface elements. Results are presented for both elastostatic and elastodynamic problems, including a problem with crack growth.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74R99 Fracture and damage

Cite

References:

[1]Belytschko, T.; Chang, H. S.; Lu, Y. Y. 1989: A variationally coupled finite element-boundary element method. Computers and Structures 33 (1), 17-20 ·Zbl 0697.73063 ·doi:10.1016/0045-7949(89)90124-7
[2]Belytschko, T.; Lu, Y. Y.; Gu, L. 1994: Element-free Galerkin methods. International Journal of Numerical Methods in Engineering 37: 229-256 ·Zbl 0796.73077 ·doi:10.1002/nme.1620370205
[3]Belytschko, T.; Lu, Y. Y.; Gu, L.; Tabbara, M. (1995). Element-free Galerkin methods for static and dynamic fracture. International Journal of Solids and Structures, Volume 32, # 17, pp 2547-2570 ·Zbl 0918.73268 ·doi:10.1016/0020-7683(94)00282-2
[4]Belytschko, T.; Tabbara M. (to appear): Dynamic fracture using element-free Galerkin methods. International Journal of Numerical Methods in Engineering
[5]Decker, R. F. (Ed.) 1979: Source Book on Maraging Steels. American Society for Metals
[6]Hughes, T. J. R. 1987: The Finite Element Method. Englewood Cliffs, New Jersey: Prentice-Hall ·Zbl 0634.73056
[7]Kalthoff, J. F.; Winkler, S. 1987: Failure mode transition at high rates of shear loading. In C. Y. Chiem, H. D. Kunze, and L. W. Meyer (Eds.), International Conference on Impact Loading and Dynamic Behavior of Materials, Volume 1, pp. 185-195
[8]Lancaster, P.; Salkauskas, K. 1981: Surfaces generated by moving least squares methods. Mathematics of Computation 37: 141-158 ·Zbl 0469.41005 ·doi:10.1090/S0025-5718-1981-0616367-1
[9]Lancaster, P.; Salkauskas, K. 1986: Curve and Surface Fitting. Academic Press ·Zbl 0649.65012
[10]Li, F. Z.; Shih, C. F.; Needleman, A. 1985: A comparison of methods for calculating energy release rates. Engineering Fracture Mechanics 21 (2): 405-421 ·doi:10.1016/0013-7944(85)90029-3
[11]Liu, W. K.; Jun, S.; Li, S.; Adee, J.; Belytschko, T. 1995: Reproducing kernel particle methods for structural dynamics. International Journal for Numerical Methods in Engineering 38: 1655-1679 ·Zbl 0840.73078 ·doi:10.1002/nme.1620381005
[12]Lu, Y. Y.; Belytschko, T.; Gu, L. 1994. A new implementation of the element free Galerkin method. Computer Methods in Applied Mechanics and Engineering 113: 397-414 ·Zbl 0847.73064 ·doi:10.1016/0045-7825(94)90056-6
[13]Lu, Y. Y.; Belytschko, T.; Liu, W. K. 1991: A variationally coupled FE-BE method for elasticity and fracture mechanics. Computer Methods in Applied Mechanics and Engineering 85: 21-37 ·Zbl 0764.73085 ·doi:10.1016/0045-7825(91)90120-U
[14]Lu, Y. Y.; Belytschko, T.; Tabbara, M. (to appear): Element-free Galerkin methods for wave propagation and dynamic fracture. Computer Methods in Applied Mechanics and Engineering ·Zbl 1067.74599
[15]Moran, B.; Shih, C. F. 1987: Crack tip and associated domain integrals from momentum and energy balance. Engineering Fracture Mechanics 27 (6): 615-641 ·doi:10.1016/0013-7944(87)90155-X
[16]Nayroles, B.; Touzot, G.; Villon, P. 1992: Generalizing the finite element method: diffuse approximation and diffuse elements. Computational Mechanics 10: 307-318 ·Zbl 0764.65068 ·doi:10.1007/BF00364252
[17]Nishioka, T.; Atluri, S. N. 1983: A numerical study of the use of path independent integrals in elasto-dynamic crack propagation. Engineering Fracture Mechanics 18 (1): 23-33 ·doi:10.1016/0013-7944(83)90092-9
[18]Nishioka, T.; Atluri, S. N. 1984: On the computation of mixed mode K-factors for a dynamical propagating crack, using path-indpendent integrals J infk ? . Engineering Fracture Mechanics 20 (2): 193-208 ·doi:10.1016/0013-7944(84)90128-0
[19]Nishioka, T.; Atluri, S. N. 1986: Computational methods in dynamic fracture. In S. N. Atluri, (Ed.), Computational Method in the Mechanics of Fracture, Chapter 10, pp. 336-383. Elsevier
[20]Timoshenko, S. P.; Goodier, J. N. 1970: Theory of Elasticity (Third ed.). New York: McGraw Hill ·Zbl 0266.73008
[21]Williams, J. R.; Amaratunga, K. 1994: Introduction to wavelets in engineering. International Journal for Numerical Methods in Engineering 37: 2365-2388 ·Zbl 0812.65144 ·doi:10.1002/nme.1620371403
[22]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 47: 335-341 ·Zbl 0463.73103 ·doi:10.1115/1.3153665
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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