Generation of surfaces via equilibrium of forces

摘要

This paper deals with the generation of minimal surfaces subject to a prescribed volume constraint and surfaces with a given mean curvature. The generation of a surface with a desired curvature is related to finding the equilibrium state of the surface under a uniform state of tension and under a prescribed pressure. Assuming an initial configuration, the surface is discretized into nodes and elements, and its final equilibrating configuration is found in a stepwise manner. In each step, the nodal forces are calculated and the surface is allowed to undergo displacements proportional to the nodal forces. Thus, the equilibrium state of the surface is obtained iteratively. The generation of a minimal surface subject to a prescribed volume constraint is also considered and analyzed by a generalization of the method outlined. Numerical examples are given to illustrate the described approach.