Premium
Efficient crack growth analyzes by combining fast methods for BEM
Author(s) -
Weber W.,
Kolk K.,
Kuhn G.
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610082
Subject(s) - boundary element method , stress intensity factor , computation , extrapolation , discontinuity (linguistics) , substructure , stress field , matrix (chemical analysis) , nonlinear system , paris' law , mathematics , computer science , structural engineering , algorithm , finite element method , mathematical analysis , fracture mechanics , materials science , engineering , crack closure , physics , composite material , quantum mechanics
Abstract The combination of fast methods for the boundary element method (BEM) for efficient crack growth analyzes is presented. Due to the nonlinearity of fatigue crack growth an incremental procedure has to be applied. Within each increment a stress analysis is needed. Based on the asymptotic stress field the stress intensity factors (SIFs) are calculated by an extrapolation method. Then, a new crack front is determined by a reliable 3D crack growth criterion. Finally, the numerical model has to be updated for the next increment. The time dominant factor in each increment is the computation of the stress field. Due to the stress concentration problem the BEM is utilized. To speed‐up the calculation several independent fast methods are exploited. An algebraic technique is the adaptive cross approximation (ACA) method which is acting on the system matrix itself. The application of the substructure technique leads to a blockwise band matrix and therefore to reduced memory requirements. Further savings in memory and computation time are reached by modelling cracks with the dual discontinuity method (DDM) and using the ACA method in each substructure. The efficiency of the combined methods is shown by a complex industrial example. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)