A substructured FE/XFE method for stress intensity factors computation in an industrial structure
DOI:
https://doi.org/10.13052/REMN%20%2016/2007Keywords:
X-FEM, level set, FETI, substructuring method, domain decompositionAbstract
The introduction of the eXtended Finite Element Method (X-FEM) into a commercial Finite Element (FE) software was achieved through a substructuring method. For fracture mechanics problems, the domain is decomposed into cracked and safe subdomains which are solved by the XFE-code and the FE-software, respectively. The interface problem is solved using a FETI solver. The new approach is compared with a classical FE-approach in the case of a planar crack in a compressor drum of a turbofan engine.
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References
Bordas S., Moran B., « Enriched Finite Elements and Level Sets for Damage Tolerance Assessment
of Complex Structures », Engineering Fracture Mechanics, 2006. in press.
Farhat C., Roux F. X., « A Method of Finite Element Tearing and Interconnecting and its Parallel
Solution Algorithm », International Journal for Numerical Methods in Engineering, vol.
, p. 1205-1227, 1991.
Farhat C., Roux F. X., « Implicit Parallel Processing in Structural Mechanics », Computational
Mechanical Advance, vol. 2, n 1, p. 1-124, 1994. North-Holland.
Hughes T., « Consider a Spherical Cow- Conservation of Geometry in Analysis: Implications
for Computational Methods in Engineering », IMA Workshop: Compatible Spatial Discretizations
for Partial Differential Equations, 2004.
Lesoinne M., Pierson K., « An efficient FETI implementation on distributed shared memory
machine with independent numbers of subdomains and processors », Contemporary Mathematics,
Melenk J. M., Babuška I., « The Partition of Unity Finite Element Method: Basic Theory
and Applications », Computer Methods in Applied Mechanics and Engineering, vol. 139,
p. 289-314, 1996.
Moës N., Dolbow J., Belytschko T., « A finite element method for crack growth without remeshing
», International Journal for Numerical Methods in Engineering, vol. 46, p. 131-150,
Moran B., Shih C. F., « Crack Tip and Associated Domain Integrals from Momentum and
Energy Balance », Engineering Fracture Mechanics, vol. 27, n 6, p. 615-641, 1987.
Saad Y., Iterative methods for sparse linear systems, 2nd edn, SIAM, 2000.
SAMCEF, General purpose finite element analysis package, Technical report,
http://www.samcef.com, 2006.
Sethian J. A., Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational
Geometry, Fluid Mechanics, Computer Vision, and Material Science, Cambridge
University Press, Cambridge, 1996.
Stolarska M., Chopp D. L., Moës N., Belytschko T., « Modelling Crack Growth by Level Sets
in the Extended Finite Element Method », International Journal for Numerical Methods in
Engineering, vol. 51, p. 943-960, 2001.
Wyart E., Duflot M., Coulon D., Martiny P., Pardoen T., Remacle J.-F., Lani F., « Substructuring
FE-XFE approaches applied to three dimensional crack propagation », Submitted to the
Journal of Computational and Theoretical Applied Mathematics, 2006.
Yau J. F.,Wang S. S., Corten H. T., « A Mixed-Mode Crack Analysis of Isotropic Solids Using
Conservation Laws of Elasticity », Journal of Applied Mechanics, vol. 47, p. 335-341, 1980.