Reanalysis of the Extended Finite Element Method for Crack Initiation and Propagation
作者： Matthew Pais , Nam-Ho Kim , Timothy Davis
DOI: 10.2514/6.2010-2536
关键词:
摘要: The extended finite element method allows one to represent strong (cracks) and weak (holes, material interfaces) discontinuities independent of the mesh through partition unity. This avoid costly remeshing which occurs in vicinity crack tip traditional framework when modeling growth. However, fatigue growth simulation has been computationally challenging due large number simulations needed model failure. Reanalysis techniques are well developed areas design optimization for modification stiffness matrix account addition/modification degrees freedom as a result change. In this paper, it is observed that quasi-static involves addition system equations. Therefore, new reanalysis algorithm based on an incremental Cholesky factorization introduced method. also used predict angle initiation using algorithm. examples contained within show 30-48% reduction total computational time achievable approach solving problems or It shown assembly insensitive elements proposed
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sci-hub.se 参考文章(27)
Steven C. Chapra, Raymond Canale, Numerical Methods for Engineers ,(1986)
M. L. Williams, On the Stress Distribution at the Base of a Stationary Crack American Society Mechanical Engineers. ,(1956)
Keisuke Tanaka, Fatigue crack propagation from a crack inclined to the cyclic tensile axis Engineering Fracture Mechanics. ,vol. 6, pp. 493- 507 ,(1974) , 10.1016/0013-7944(74)90007-1
T. Belytschko, N. Mo�s, S. Usui, C. Parimi, Arbitrary discontinuities in finite elements International Journal for Numerical Methods in Engineering. ,vol. 50, pp. 993- 1013 ,(2001) , 10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M
Stanley Osher, James A Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations Journal of Computational Physics. ,vol. 79, pp. 12- 49 ,(1988) , 10.1016/0021-9991(88)90002-2
Stanley Osher, Ronald P. Fedkiw, Level set methods: an overview and some recent results Journal of Computational Physics. ,vol. 169, pp. 463- 502 ,(2001) , 10.1006/JCPH.2000.6636
A. Gravouil, N. Moës, T. Belytschko, NON-PLANAR 3D CRACK GROWTH BY THE EXTENDED FINITE ELEMENT AND LEVEL SETS- PART II: LEVEL SET UPDATE International Journal for Numerical Methods in Engineering. ,vol. 53, pp. 2569- 2586 ,(2002) , 10.1002/NME.430
B.S Wu, C.W Lim, Z.G Li, A finite element algorithm for reanalysis of structures with added degrees of freedom Finite Elements in Analysis and Design. ,vol. 40, pp. 1791- 1801 ,(2004) , 10.1016/J.FINEL.2004.01.004
I. BABUŠKA, J. M. MELENK, The Partition of Unity Method International Journal for Numerical Methods in Engineering. ,vol. 40, pp. 727- 758 ,(1997) , 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
C. F. Shih, R. J. Asaro, Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I—Small Scale Yielding Journal of Applied Mechanics. ,vol. 55, pp. 299- 316 ,(1988) , 10.1115/1.3173676