%0 Book Section %1 jensen_efficient_2006 %A Jensen, Jakob S. %B III European Conference on Computational Mechanics %D 2006 %E Motasoares, C. A. %E Martins, J. A. C. %E Rodrigues, H. C. %E Ambrósio, Jorge A. C. %E Pina, C. A. B. %E Motasoares, C. M. %E Pereira, E. B. R. %E Folgado, J. %I Springer Netherlands %K Design, Engineering Engineering, general %P 485--485 %T Efficient Optimization of Dynamic Systems using Padé Approximants %U http://link.springer.com/chapter/10.1007/1-4020-5370-3_485 %X A new efficient approach is proposed for optimization of the dynamic response of structures subjected to a time-harmonic load. Optimization of the dynamic response of large-scale systems is usually based on the modal approach, with only the lowest modes included in the expansion, see e.g. Tcherniak (2002). Especially if the response at more than a few frequencies is to be optimized, the direct approach in which the system equations are solved in the frequency domain will be computationally expensive. In Jensen & Sigmund (2005) it was demonstrated how the direct method can be used to optimize the response in a frequency range with reduced computational effort. Only a few target frequencies were considered, but these were repeatedly updated to match the most “critical” frequencies in the frequency range. The feasibility of this approach relies on the possibility for computing fast frequency response curves using Padé approximants (see e.g. Jin, 2002). In this work this approach is extended. Instead of using Padé approximants only to evaluate the frequency response to locate the critical frequencies, the response and the sensitivity analysis in the entire frequency domain of interest is now directly based on the Padé expansion.With this approach the direct system needs only be solved for a single frequency and the expansion to the entire frequency range is computed simply as a number of extra r.h.s.’s to the system equation and the solution of a few additional low-rank matrix equations. The new approach is exemplified by the design of a bi-material 2D elastic structure subjected to a time-harmonic load using topology optimization. The response of the structure is minimized in a finite frequency range based on a direct solution of the system equation for a single frequency only. %@ 978-1-4020-4994-1, 978-1-4020-5370-2

@incollection{jensen_efficient_2006, abstract = {A new efficient approach is proposed for optimization of the dynamic response of structures subjected to a time-harmonic load. Optimization of the dynamic response of large-scale systems is usually based on the modal approach, with only the lowest modes included in the expansion, see e.g. Tcherniak (2002). Especially if the response at more than a few frequencies is to be optimized, the direct approach in which the system equations are solved in the frequency domain will be computationally expensive. In Jensen \& Sigmund (2005) it was demonstrated how the direct method can be used to optimize the response in a frequency range with reduced computational effort. Only a few target frequencies were considered, but these were repeatedly updated to match the most “critical” frequencies in the frequency range. The feasibility of this approach relies on the possibility for computing fast frequency response curves using Padé approximants (see e.g. Jin, 2002). In this work this approach is extended. Instead of using Padé approximants only to evaluate the frequency response to locate the critical frequencies, the response and the sensitivity analysis in the entire frequency domain of interest is now directly based on the Padé {expansion.With} this approach the direct system needs only be solved for a single frequency and the expansion to the entire frequency range is computed simply as a number of extra r.h.s.’s to the system equation and the solution of a few additional low-rank matrix equations. The new approach is exemplified by the design of a bi-material {2D} elastic structure subjected to a time-harmonic load using topology optimization. The response of the structure is minimized in a finite frequency range based on a direct solution of the system equation for a single frequency only.}, added-at = {2013-01-26T11:35:39.000+0100}, author = {Jensen, Jakob S.}, biburl = {https://www.bibsonomy.org/bibtex/2ad0f010bda4cc23e4ce8628203bd4fc7/bhessen}, booktitle = {{III} European Conference on Computational Mechanics}, copyright = {©2006 Springer}, editor = {Motasoares, C. A. and Martins, J. A. C. and Rodrigues, H. C. and Ambrósio, Jorge A. C. and Pina, C. A. B. and Motasoares, C. M. and Pereira, E. B. R. and Folgado, J.}, file = {Snapshot:C:\Users\hessenauer\AppData\Roaming\Mozilla\Firefox\Profiles\1h9szxht.firefox4\zotero\storage\XDQZKSE3\10.html:text/html}, interhash = {d2d7076c2a801c236bc9c51af53a8db8}, intrahash = {ad0f010bda4cc23e4ce8628203bd4fc7}, isbn = {978-1-4020-4994-1, 978-1-4020-5370-2}, keywords = {Design, Engineering Engineering, general}, language = {en}, month = jan, pages = {485--485}, publisher = {Springer Netherlands}, timestamp = {2013-01-26T11:35:58.000+0100}, title = {Efficient Optimization of Dynamic Systems using Padé Approximants}, url = {http://link.springer.com/chapter/10.1007/1-4020-5370-3_485}, urldate = {2013-01-24}, year = 2006 }