Triller, J. ; Immel, R. ; Timmer, A. ; Harzheim, L. (2024)
The difference-based equivalent static load method: an improvement of the ESL method’s nonlinear approximation quality.
In: Structural and Multidisciplinary Optimization, 2021, 63 (6)
doi: 10.26083/tuprints-00023434
Artikel, Zweitveröffentlichung, Verlagsversion
 | Es ist eine neuere Version dieses Eintrags verfügbar. |
Kurzbeschreibung (Abstract)
Nonlinear dynamic structural optimization is a real challenge, in particular for problems that require the use of explicit solvers, e.g., crash. Here, the number of design variables is typically very limited. A way to overcome this drawback is to use linear auxiliary load cases which are derived from nonlinear dynamic analysis results in order to enable the application of linear static response optimization. The equivalent static load method (ESLM) provides a well-defined procedure to create such linear auxiliary load cases. The main idea here is that after the selection of a number of representative time steps, a set of equivalent static loads (ESLs) is computed for each time step such that the resulting displacement field in the linear static analysis is identical to the respective field in the nonlinear dynamic analysis. Each set of ESLs defines an auxiliary load case, which is used in the linear static response optimization. The crucial point is that the finite element (FE)-model for each auxiliary load case describes the undeformed initial geometry. This can lead to insufficient approximation quality in the linear static system for highly nonlinear problems. To overcome this drawback, a difference-based extension of the ESL method called DiESL has been developed for nonlinear dynamic response optimization problems. Here, the FE-model for each auxiliary load case describes the deformed nonlinear geometry at the respective time, and the corresponding ESLs create only the displacement field leading to the deformed state of the subsequent ESL time step. Consequently, responses in each linear auxiliary load case (corresponding to a time step) are computed as the accumulated sum of the previous linear auxiliary load cases. Furthermore, the linear static response optimization problem consists not only of one but of nT FE-models where nT is the number of selected time steps. Such a multi-model optimization (MMO) can be solved with commercial FE solvers. It turns out that the DiESL approach leads to a significant improvement of the nonlinear approximation quality and faster convergence to the optimum when compared to standard ESLM. This will be demonstrated and discussed based on selected test examples.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Triller, J. ; Immel, R. ; Timmer, A. ; Harzheim, L. |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | The difference-based equivalent static load method: an improvement of the ESL method’s nonlinear approximation quality |
| Sprache: | Englisch |
| Publikationsjahr: | 12 März 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | Juni 2021 |
| Ort der Erstveröffentlichung: | Berlin; Heidelberg; New York |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Structural and Multidisciplinary Optimization |
| Jahrgang/Volume einer Zeitschrift: | 63 |
| (Heft-)Nummer: | 6 |
| DOI: | 10.26083/tuprints-00023434 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/23434 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichung DeepGreen |
| Kurzbeschreibung (Abstract): | Nonlinear dynamic structural optimization is a real challenge, in particular for problems that require the use of explicit solvers, e.g., crash. Here, the number of design variables is typically very limited. A way to overcome this drawback is to use linear auxiliary load cases which are derived from nonlinear dynamic analysis results in order to enable the application of linear static response optimization. The equivalent static load method (ESLM) provides a well-defined procedure to create such linear auxiliary load cases. The main idea here is that after the selection of a number of representative time steps, a set of equivalent static loads (ESLs) is computed for each time step such that the resulting displacement field in the linear static analysis is identical to the respective field in the nonlinear dynamic analysis. Each set of ESLs defines an auxiliary load case, which is used in the linear static response optimization. The crucial point is that the finite element (FE)-model for each auxiliary load case describes the undeformed initial geometry. This can lead to insufficient approximation quality in the linear static system for highly nonlinear problems. To overcome this drawback, a difference-based extension of the ESL method called DiESL has been developed for nonlinear dynamic response optimization problems. Here, the FE-model for each auxiliary load case describes the deformed nonlinear geometry at the respective time, and the corresponding ESLs create only the displacement field leading to the deformed state of the subsequent ESL time step. Consequently, responses in each linear auxiliary load case (corresponding to a time step) are computed as the accumulated sum of the previous linear auxiliary load cases. Furthermore, the linear static response optimization problem consists not only of one but of nT FE-models where nT is the number of selected time steps. Such a multi-model optimization (MMO) can be solved with commercial FE solvers. It turns out that the DiESL approach leads to a significant improvement of the nonlinear approximation quality and faster convergence to the optimum when compared to standard ESLM. This will be demonstrated and discussed based on selected test examples. |
| Freie Schlagworte: | DiESL, Equivalent static load method, Multi-model optimization, Crashworthiness, Explicit solvers |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-234343 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet für Numerische Berechnungsverfahren im Maschinenbau (FNB) |
| Hinterlegungsdatum: | 12 Mär 2024 13:27 |
| Letzte Änderung: | 14 Mär 2024 06:24 |
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| Suche nach Titel in: | TUfind oder in Google |
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- The difference-based equivalent static load method: an improvement of the ESL method’s nonlinear approximation quality. (deposited 12 Mär 2024 13:27) [Gegenwärtig angezeigt]
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