Generating Smooth Curves in 3 Dimensions by Minimizing Higher Order Strain Energy Measures
Sigrid Adriaenssens, Samar Malek, Masaaki Miki, Chris J K Williams · International Journal of Space Structures · 2013
Elastic beams or rods in two and three dimensions produce smooth curves by minimizing the strain energy due to classical Euler-Bernoulli bending and Saint-Venant torsion subject to constraints on the arc length and end positions and orientations. However it is possible to postulate other strain energy measures. In this paper we describe a strain energy measure which is the sum of the square of the rate of change of curvature and the square of the product of the curvature and the Frenet torsion.