A global damping factor for a non‐invasive form finding algorithm. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Landkammer, Philipp; Steinmann, Paul
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 327
• Page End: 328
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510154
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Inverse form finding based on the finite element method (FEM) aims in determining the optimal material (undeformed) configuration when knowing the target spatial (deformed) configuration in a discretized setting. The strategy is to iteratively update the material coordinates and recompute the spatial configuration by a FEM simulation until the computed spatial nodal positions are close enough to a priori given spatial nodal positions. A form finding algorithm is utilized, which is purely based on geometrical considerations and can be coupled with arbitrary external FEM software via subroutines in a non‐invasive fashion. At large deformations degenerated elements can occur when updating the material coordinates. Evaluating the mesh quality of the updated material configuration and adjusting a global damping factor before recomputing the next spatial configuration helps to avoid mesh distortions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)