Generation of surfaces via equilibrium of forces

This paper deals with the generation of minimal surfaces subject to a presc ribed volume constraint and surfaces with a given mean curvature. The gener ation of a surface with a desired curvature is related to finding the equil ibrium state of the surface under a uniform state of tension and under a pr escribed pressure. Assuming an initial configuration, the surface is discre tized 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 nod al forces. Thus, the equilibrium state of the surface is obtained iterative ly. The generation of a minimal surface subject to a prescribed volume cons traint is also considered and analyzed by a generalization of the method ou tlined. Numerical examples are given to illustrate the described approach. (C) 1999 Elsevier Science Ltd. All rights reserved.