A General Finite Element Approach to the form Finding of Tensile Structures by the Updated Reference Strategy

Abstract

Starting from a rigorous mechanical formulation, a numerical procedure is developed for the form finding of minimal surfaces and pre-stressed membrane structures. The method is based on an iteratively adapted regularisation of the stiffness matrix which gives the method its name: the updated reference strategy. The method can be applied to any finite element discretization of cable and membrane structures subjected to pre-stress as well as lateral pressure or other external loading. It is very robust and reliable as is shown by many illustrative examples. Further analysis states that the well known force density method is the special case of applying the updated reference strategy to cable nets.