Symmetry preserving in Topological Mapping for tension structures

Abstract

When using Topological Mapping (TM) together with the Force Density Method (FDM) in order to find a first form of equilibrium for a tension structure whose fixed nodes coincide in plan view with the vertices of a regular polygon, it has been observed that the symmetry may be lost. The problem is related to the mapping procedure that is introduced in the process. However, if some rules are followed in constructing the topology for the mesh, the symmetry can be preserved. With a symmetric mesh, the later cutting pattern generation process becomes simpler, easier, and cheaper. This paper will provide one simple algorithm that has been proved to work effectively in preserving the symmetry in the cited type of tension structures. Several examples are presented in order to better illustrate the applicability of these easy prescriptions.