Use of structural analogy in generation of smooth surfaces for engineering purposes
The use of the minimization of surface integrals of functions of the mean and Gaussian curvature to obtain smooth surfaces that satisfy given boundary and other conditions is discussed. A structural analogy based on the bending theory of shells is introduced to enable the designer to predict the effect of changing parameters in the integrals to be minimized. Surfaces of zero mean curvature (minimal or soap film surfaces), surfaces of constant mean curvature (inflated soap films, including the sphere) and the elastica (in two dimensions) are all special cases of the theory.
scientific article; zbMATH DE number 4070157