Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections
The calculation of moments of area is one of the most fundamental aspects of engineering mechanics for calculating the properties of beams or for the determination of invariants in different kind of geometries. While a variety of shapes, such as circles, rectangles, ellipses, or their combinations,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Applied Mechanics |
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| Online Access: | https://www.mdpi.com/2673-3161/4/2/27 |
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| author | Martin Denk Michael Jäger Sandro Wartzack |
| author_facet | Martin Denk Michael Jäger Sandro Wartzack |
| author_sort | Martin Denk |
| collection | DOAJ |
| description | The calculation of moments of area is one of the most fundamental aspects of engineering mechanics for calculating the properties of beams or for the determination of invariants in different kind of geometries. While a variety of shapes, such as circles, rectangles, ellipses, or their combinations, can be described symbolically, such symbolic expressions are missing for freeform cross-sections. In particular, periodic B-spline cross-sections are suitable for an alternative beam cross-section, e.g., for the representation of topology optimization results. In this work, therefore, a symbolic description of the moments of area of various parametric representations of such B-splines is computed. The expressions found are then compared with alternative computational methods and checked for validity. The resulting equations show a simple method that can be used for the fast conceptual computation of such moments of area of periodic B-splines. |
| first_indexed | 2024-03-11T02:49:30Z |
| format | Article |
| id | doaj.art-383f681124ea48c7b4f3643c0cc92d4a |
| institution | Directory Open Access Journal |
| issn | 2673-3161 |
| language | English |
| last_indexed | 2024-03-11T02:49:30Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Mechanics |
| spelling | doaj.art-383f681124ea48c7b4f3643c0cc92d4a2023-11-18T09:04:59ZengMDPI AGApplied Mechanics2673-31612023-04-014247649210.3390/applmech4020027Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-SectionsMartin Denk0Michael Jäger1Sandro Wartzack2Engineering Design, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, GermanyEngineering Design, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, GermanyEngineering Design, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, GermanyThe calculation of moments of area is one of the most fundamental aspects of engineering mechanics for calculating the properties of beams or for the determination of invariants in different kind of geometries. While a variety of shapes, such as circles, rectangles, ellipses, or their combinations, can be described symbolically, such symbolic expressions are missing for freeform cross-sections. In particular, periodic B-spline cross-sections are suitable for an alternative beam cross-section, e.g., for the representation of topology optimization results. In this work, therefore, a symbolic description of the moments of area of various parametric representations of such B-splines is computed. The expressions found are then compared with alternative computational methods and checked for validity. The resulting equations show a simple method that can be used for the fast conceptual computation of such moments of area of periodic B-splines.https://www.mdpi.com/2673-3161/4/2/27B-splinecross-sectionbeammoments of areaparametricsymbolic |
| spellingShingle | Martin Denk Michael Jäger Sandro Wartzack Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections Applied Mechanics B-spline cross-section beam moments of area parametric symbolic |
| title | Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections |
| title_full | Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections |
| title_fullStr | Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections |
| title_full_unstemmed | Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections |
| title_short | Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections |
| title_sort | symbolic parametric representation of the area and the second moments of area of periodic b spline cross sections |
| topic | B-spline cross-section beam moments of area parametric symbolic |
| url | https://www.mdpi.com/2673-3161/4/2/27 |
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