A new form-finding method based on mean curvature flow of surfaces

Abstract

In this paper, we present a new form-nding method for freeform shell structures. For a given boundary curve, we design a construction that is an approximation of the corresponding minimal surface. The surface is represented by a triangular network of curves and its initial shape can be an arbitrary smooth surface with the given boundary. In order to satisfy the minimal surface condition, we apply the mean curvature  ow model to the given initial shape and we let it evolve until it reaches the equilibrium. Since it is desirable in practice to have the structure as uniform as possible, we propose a method for tangential redistribution of nodes on the individual curves. The mathematical model is discretized by a  owing control volume scheme and the paper also provides the details of the discretization technique.