“Tracing” the Equilibrium — Recent Advances in Numerical Form Finding

Abstract

This paper explains the numerically and physically caused problems encountered in a computational form finding process of prestressed membrane structures and proposes effective stabilization techniques for the respective cases. The updated reference strategy (URS) is used to stabilize the problem of “floating meshes”, which is caused by the inverse nature of the discretized problem. The convergence of the resulting iterative solution can be effectively monitored with the help of a new error norm, which has been recently developed. It allows measuring the actual stress deviations by a simple to be used, scalar, dimensionless quantity which is proposed for practical usage. Additionally, a simplified stress adaptation scheme is presented, which automatically adapts the prescribed stresses during the iterative form finding procedure, if a physically incompatible stress state is detected. This is especially important, as most of the form finding tasks in reality (e.g. prescribed constant anisotropic) show a slight incompatibility in their original problem formulation, which necessitates an automatic modification of the input parameters. Success is demonstrated by typical, challenging test cases. Further reference to practically relevant implementations of the proposed techniques is made.