Denk M, Jäger M, Wartzack S (2023)
Publication Language: English
Publication Status: Published
Publication Type: Journal article
Future Publication Type: Journal article
Publication year: 2023
Original Authors: Martin Denk, Michael Jäger, Sandro Wartzack
Book Volume: 4
Pages Range: 476-492
Journal Issue: 2
URI: https://www.mdpi.com/2673-3161/4/2/27
Open Access Link: https://www.mdpi.com/2673-3161/4/2/27
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.
APA:
Denk, M., Jäger, M., & Wartzack, S. (2023). Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections. Applied Mechanics, 4(2), 476-492. https://dx.doi.org/10.3390/applmech4020027
MLA:
Denk, Martin, Michael Jäger, and Sandro Wartzack. "Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections." Applied Mechanics 4.2 (2023): 476-492.
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