Topological Mapping for Tension Structures

The "form finding" methods for tension structures may be classified into two different groups: the linear and nonlinear methods. One of the linear methods is the force density method (FDM). In this paper advantage is taken of an important property of the FDM by which knowledge of the initial position of the nonfixed nodes of the structure is not needed, only the connectivity of the nodes is necessary for the solution of the problem. Accordingly, a new mapping method is presented that is based on topology, in contrast to the mapping methods used so far that are based exclusively on geometry. The most important contribution of this new approach is that due to mapping in topology, an initial guess of the equilibrium position is not needed as part of the solution process. The ease of implementation is also shown in this paper, along with future research that may improve this new idea. Several examples are presented that illustrate the applicability of this new method.