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Keywords: domain decomposition methods, nonlinear structural analysis, post-buckling, nonlinear re-localization.

Summary

The study was focused on the primal [2,3] and mixed [4] domain decomposition methods, showing that the mixed method is the best choice, because it can reduced the number of global iterations increasing the load step size, and as a consequence of these, reducing also the number of total local iterations.

Another important point is the capability, when choosing the appropriate Robin parameter, of passing critical points much more easily than for the primal version. Different options are presented for choosing the Robin parameter, in this work the Schur complement of the neighbouring substructures was used. An analysis of the influence of this parameter was carried out. In order to describe the complete behaviour of the structure an "arc-length" method was implemented [5] at the global level.

The method was tested over a wing-box type structure made of triangular plate elements, the final configuration shows some parts of the structure buckling.

Finally the method is parallelized; a BDDC method was implemented [6], solved by a GMRES algorithm, because of the non-symmetry of the operator as a result of the corotationnal formulation used [7].

References

1: P. Cresta, O. Allix, C. Rey, S. Guinard, "Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses", Computer Methods in Applied Mechanics and Engineering, 196, 1436-1446, 2007. doi:10.1016/j.cma.2006.03.013
2: P. Le Tallec, Y.H.D. Roeck, M. Vidrascu, "Domain decomposition methods for large linearly elliptic three-dimensional problems", Journal of Computational and Applied Mathematics, 34(1), 93-117, 1991. doi:10.1016/0377-0427(91)90150-I
3: J. Mandel, "Balancing Domain Decomposition", Communication in Applied Numerical Methods, 9, 233-241, 1993. doi:10.1002/cnm.1640090307
4: P. Ladevèze, "Sur une famille d'algorithmes en mécanique des structures", Compte rendu de l'académie de Sciences, 300(2), 41-44, 1985.
5: M.A. Crisfield, "A fast incremental/iterative solution procedure that handles 'snap-through"', Computers and Structures, 13, 55-62, 1981. doi:10.1016/0045-7949(81)90108-5
6: C.R. Dohrmann, "A Preconditioner for Substructuring Based on Constrained Energy Minimization", SIAM Journal on Scientific Computing, 25(1), 246-258, 2003. doi:10.1137/S1064827502412887
7: C.A. Felippa, B. Haugen, "A unified formulation of small-strain corotational finite elements: I. Theory", Computer Methods in Applied Mechanics and Engineering, 194(21-24), 2285-2335, 2005. doi:10.1016/j.cma.2004.07.035

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 95 PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by: Paper 6 Newton-Krylov-Schur Method with a Nonlinear Localization: Parallel Implementation for Post-Buckling Analysis of Large Structures J. Hinojosa¹, O. Allix¹, P.-A. Guidault¹ and Ph. Cresta² ¹Laboratoire de Mécanique et Technologie, École Normale Supérieure de Cachan, France ²EADS Innovation Works, Campus Engineering, Blagnac, France doi:10.4203/ccp.95.6 purchase the full-text of this paper Full Bibliographic Reference for this paper J. Hinojosa, O. Allix, P.-A. Guidault, Ph. Cresta, "Newton-Krylov-Schur Method with a Nonlinear Localization: Parallel Implementation for Post-Buckling Analysis of Large Structures", in , (Editors), "Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 6, 2011. doi:10.4203/ccp.95.6 Keywords: domain decomposition methods, nonlinear structural analysis, post-buckling, nonlinear re-localization. Summary The study was focused on the primal [2,3] and mixed [4] domain decomposition methods, showing that the mixed method is the best choice, because it can reduced the number of global iterations increasing the load step size, and as a consequence of these, reducing also the number of total local iterations. Another important point is the capability, when choosing the appropriate Robin parameter, of passing critical points much more easily than for the primal version. Different options are presented for choosing the Robin parameter, in this work the Schur complement of the neighbouring substructures was used. An analysis of the influence of this parameter was carried out. In order to describe the complete behaviour of the structure an "arc-length" method was implemented [5] at the global level. The method was tested over a wing-box type structure made of triangular plate elements, the final configuration shows some parts of the structure buckling. Finally the method is parallelized; a BDDC method was implemented [6], solved by a GMRES algorithm, because of the non-symmetry of the operator as a result of the corotationnal formulation used [7]. References 1 P. Cresta, O. Allix, C. Rey, S. Guinard, "Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses", Computer Methods in Applied Mechanics and Engineering, 196, 1436-1446, 2007. doi:10.1016/j.cma.2006.03.013 2 P. Le Tallec, Y.H.D. Roeck, M. Vidrascu, "Domain decomposition methods for large linearly elliptic three-dimensional problems", Journal of Computational and Applied Mathematics, 34(1), 93-117, 1991. doi:10.1016/0377-0427(91)90150-I 3 J. Mandel, "Balancing Domain Decomposition", Communication in Applied Numerical Methods, 9, 233-241, 1993. doi:10.1002/cnm.1640090307 4 P. Ladevèze, "Sur une famille d'algorithmes en mécanique des structures", Compte rendu de l'académie de Sciences, 300(2), 41-44, 1985. 5 M.A. Crisfield, "A fast incremental/iterative solution procedure that handles 'snap-through"', Computers and Structures, 13, 55-62, 1981. doi:10.1016/0045-7949(81)90108-5 6 C.R. Dohrmann, "A Preconditioner for Substructuring Based on Constrained Energy Minimization", SIAM Journal on Scientific Computing, 25(1), 246-258, 2003. doi:10.1137/S1064827502412887 7 C.A. Felippa, B. Haugen, "A unified formulation of small-strain corotational finite elements: I. Theory", Computer Methods in Applied Mechanics and Engineering, 194(21-24), 2285-2335, 2005. doi:10.1016/j.cma.2004.07.035 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £85 +P&P)
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