Textile models are often assumed to have homogenous and well defined cross-sections. For these models, the use of a power elliptical cross-sectional shape has been found to be beneficial as different shapes can be created, e.g. lenticular, elliptical or rectangular, with a single function. The cross-sectional area of a power ellipse is usually determined numerically as the analytical determination of the cross-sectional area is not straightforward. This short communication presents an analytical solution for this shape.
Gommer, F., Brown, L. P., & Wedgwood, K. C. A. (2016). Analytical method using gamma functions for determining areas of power elliptical shapes for use in geometrical textile models. Composites Part A: Applied Science and Manufacturing, 81, 222–224. https://doi.org/10.1016/j.compositesa.2015.11.031