Updated weight method: an optimisation-based form-finding method of tensile membrane structures

Tensile membrane structures (TMS) are gaining wide acceptance in spanning large open areas and are popular for their unique aesthetics. For a given boundary condition, the shape of a TMS subjected only to initial prestress is not known beforehand. The process of finding this shape, or 'form-finding', presents various numerical issues and challenges related to its practical implementation. This paper proposes a novel optimisation-based form-finding technique, titled 'updated weight method' (UWM), for frame- and cable-supported, minimal and non-minimal TMS. In this, the objective function is defined as a weighted function of the geometrical shape. UWM has the advantage of relating these weights to the desired membrane prestress (and cable tensions) in the equilibrium shape. Issues related to convergence and mesh distortion are also efficiently handled in this method. A wide variety of simple and complex problems are used to test the proposed methodology, and overall, an efficient and accurate form-finding solution is demonstrated for all problems. UWM is adequately generic to incorporate different constraints and to allow the use of any (numerical) optimisation tool of choice.