Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time Integration
In this paper, the direct differentiation of generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula>...
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| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/12/2/128 |
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| author | Erich Wehrle Veit Gufler |
| author_facet | Erich Wehrle Veit Gufler |
| author_sort | Erich Wehrle |
| collection | DOAJ |
| description | In this paper, the direct differentiation of generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> time integration is derived, equations are introduced and results are shown. Although generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> time integration has found usage, the derivation and the resulting equations for the analytical sensitivity analysis via direct differentiation are missing. Thus, here, the sensitivity equations of generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> time integration via direct differentiation are provided. Results with generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> are compared with Newmark-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">β</mi></semantics></math></inline-formula> time integration and their sensitivities with numerical sensitivities via forward finite differencing in terms of accuracy and performance. An example is shown for each linear structural dynamics and flexible multibody dynamics. |
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| format | Article |
| id | doaj.art-267e4b57ccd6416a873f18c3aa684833 |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-07T22:23:32Z |
| publishDate | 2024-02-01 |
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| series | Machines |
| spelling | doaj.art-267e4b57ccd6416a873f18c3aa6848332024-02-23T15:25:05ZengMDPI AGMachines2075-17022024-02-0112212810.3390/machines12020128Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time IntegrationErich Wehrle0Veit Gufler1Collins Aerospace, Applied Research and Technology, Multidisciplinary Design Optimization Research Group, 80805 Munich, GermanyFaculty of Engineering, Free University of Bozen-Bolzano, Universitätsplatz 1, 39100 Bozen, South Tyrol, ItalyIn this paper, the direct differentiation of generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> time integration is derived, equations are introduced and results are shown. Although generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> time integration has found usage, the derivation and the resulting equations for the analytical sensitivity analysis via direct differentiation are missing. Thus, here, the sensitivity equations of generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> time integration via direct differentiation are provided. Results with generalized-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">α</mi></semantics></math></inline-formula> are compared with Newmark-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">β</mi></semantics></math></inline-formula> time integration and their sensitivities with numerical sensitivities via forward finite differencing in terms of accuracy and performance. An example is shown for each linear structural dynamics and flexible multibody dynamics.https://www.mdpi.com/2075-1702/12/2/128sensitivity analysistime integrationstructural dynamicsflexible multibody dynamics |
| spellingShingle | Erich Wehrle Veit Gufler Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time Integration Machines sensitivity analysis time integration structural dynamics flexible multibody dynamics |
| title | Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time Integration |
| title_full | Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time Integration |
| title_fullStr | Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time Integration |
| title_full_unstemmed | Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time Integration |
| title_short | Analytical Sensitivity Analysis of Dynamic Problems with Direct Differentiation of Generalized-<i>α</i> Time Integration |
| title_sort | analytical sensitivity analysis of dynamic problems with direct differentiation of generalized i α i time integration |
| topic | sensitivity analysis time integration structural dynamics flexible multibody dynamics |
| url | https://www.mdpi.com/2075-1702/12/2/128 |
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