Parametrization of Cross-Sections by CNN Classification and Moments of Area Regression for Frame Structures

Denk, Martin; Rother, Klemens; Neuhäusler, Josef; Petroll, Christoph; Paetzold, Kristin

doi:10.1007/978-3-662-65216-9_9

Cited by 1 publication

(1 citation statement)

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“…The parametric representation of various shapes and topologies has been discussed in various articles for simple polygons as common cross-section types [16,17] and also for more complex topologies consisting of multiple polygons such as hexagonal networks [18,19]. The knot positions of these for one or several polygons can be considered as control points for tensor product splines.…”

Section: State Of the Artmentioning

confidence: 99%

Symbolic Parametric Representation of the Area and the Second Moments of Area of Periodic B-Spline Cross-Sections

2023

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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.

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