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Vol. 37 (1996) No. 3 December n. 122


Application of formian and dynamic relaxation to the form-finding of minimal surfaces

< Table of Contents for Vol. 37 (1996) No. 3 December n. 122
  • Journal Name: Journal of the International Association for Shell and Spatial Structures (J. IASS)
  • ISSN: (Electronic Version) 1996-9015
  • ISSN: (Print Version) 1028-365X
  • Issue: Vol. 37 (1996) No. 3 December n. 122
  • Title: Application of formian and dynamic relaxation to the form-finding of minimal surfaces
  • Author(s): W. J. Lewis, T. S. Lewis
  • Keywords: form-finding, numerical methods
Abstract
This paper documents a computational approach adopted for the form-finding of lightweight tension structures comprising prestressed cable nets and fabric membranes. The approach utilises the principle of minimum potential energy of surface tension for finding optimum shapes of tension membranes. The same principle governs the formation of soap-films, which are considered as ideal lightweight tension structures. The main properties of soap-films are: a constant surface stress, zero mean curvature at every point on the surface, and a minimum surface area which is in stable equilibrium. For this reason, soap-film surfaces are described in the technical literature as stable minimal surfaces. The numerical algorithm presented for modelling stable minimal surfaces uses a novel approach of utilising two independent computational techniques: Formian, for the generation of the initial surface topology and post-processing of data, and Dynamic Relaxation as a solver of the resulting non-linear system of equilibrium equations. Numerous examples of stable minimal surface membranes generated by this integrated approach are presented. Some of the examples are used to illustrate potential problems associated with numerical modelling of the minimum energy forms of tension structures.

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