Users:Form Finding/Form-finding with the eXtended URS

The main challenge in numerical form-finding ist the singular stiffness matrix due to the possible in-plane movements of the nodes, corresponding to the floating in a soap bubble. Any form-finding method is based on finding a stabilization for that problem.

Dieringer ^[1] introduced the eXtended URS (xURS) as an extension to the Updated Reference Strategy with the following reasoning:

• The instability is only due to the possible motions in the curved plane, hence in-plane stabilization is required. In URS this is introduced to the stabilization term by the formulation in the reference configuration.
• Out-of-plane equilibrium would best be described by the original problem in the current configuration.
• Therefore a split of the problem along the current surface normal n is performed: out-of-plane the force and stiffness in the current configuration are taken, in-plane the stabilized terms are used.

A priori the outcome should be higher accurate results with less form-finding steps. However, the number of equilibrium iterations now might increase since the problem is more non-linear than it used to be without xURS. See ^[1] for a complete description of the method and application examples.

Benchmark examples

• form-finding of a catenoid with xURS: ..\examples\benchmark_examples\analyses\cbm_formfinding_xURS_Membrane1\cbm_formfinding_xURS_Membrane1.dat

References

1. ↑ ^{1.0 1.1} Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Lehrstuhl für Statik, Technische Universität München, 2014