Analytical formfinding

Abstract

In this article, formfinding theories for different structures are considered. The beginning of analytical formfinding theories coincides with the analysis of the Olympic Roof in Munich (1972). Therefore, this article starts with the derivation of the force-density method with respect to cable net calculations as those procedures were used for the cable net calculation of the Munich stadium. Later on, the formfinding theories were adapted to textile membranes and foils, so the constitutive equations are extended by crimp- and shear-stiffness. The crimp-stiffness produces a correlation between warp- and weft-stiffness in textile membranes. The shear-stiffness causes shear-stresses because of angle-deformations. Pneumatic structures such as air-halls, air-domes, and ethylene tetrafluoroethylene cushions are widely used. The formfinding calculation of those pneumatically stressed membranes is also demonstrated. An important formfinding input value for those structures is the size of the volume itself. Therefore, an additional constraint in the volume formfinding strategy is the so-called volume equation, which is related to the internal pressure. Minimal surfaces such as soap films (and pneumatically stressed bubbles) have a very specific material behavior which is extensively described. The analytical formfinding theories were always developed due to physical modeling procedures. Mixed formfinding tools combine stiff elements with soft surface materials, as is often done in physical models when, for example, a stiff timber bar is used together with a soft nylon mesh.