Denk, M.; Jäger, M.; Wartzack, S. Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections. Appl. Mech.2023, 4, 476-492.
Denk, M.; Jäger, M.; Wartzack, S. Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections. Appl. Mech. 2023, 4, 476-492.
Denk, M.; Jäger, M.; Wartzack, S. Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections. Appl. Mech.2023, 4, 476-492.
Denk, M.; Jäger, M.; Wartzack, S. Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections. Appl. Mech. 2023, 4, 476-492.
Abstract
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 way for fast conceptual computation of such moments of area of periodic B-splines.
Keywords
B-spline; cross-section; beam; moments of area; parametric; symbolic; moments; area
Subject
Engineering, Mechanical Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
