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

The calculation of moments area is one the most fundamental aspects engineering mechanics for calculating properties beams or determination invariants in different kind geometries. While a variety shapes, such as circles, rectangles, ellipses, their combinations, can be described symbolically, symbolic expressions are missing freeform cross-sections. In particular, periodic B-spline cross-sections suitable an alternative beam cross-section, e.g., representation topology optimization results. this work, therefore, description various parametric representations B-splines computed. found then compared with computational methods and checked validity. resulting equations show simple method that used fast conceptual computation B-splines.