A closed contour with no warping: A common feature in all confocally elliptical hollow sections

We show that for a confocally elliptical hollow section under Saint-Venant's torsion, there always exists a confocally elliptical closed contour inside the section that exhibits no warping. This property is generally true without any regard to the thickness or the aspect ratio of the hollow section, as long as the inner and the outer ellipses are confocal. This property allows us to apply Packham and Shail's (Packham, B. A, and Shail, R., 1978, "St. Venant Torsion of Composite Cylinders," J. Elast., 8, pp. 393-407) superposition method for the torsion solutions of a two-phase elliptical hollow section. Previously, this superposition method is only applicable to symmetric compound sections with respect to a straight line or a circular arc.