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A global damping factor for a non‐invasive form finding algorithm
Author(s) -
Landkammer Philipp,
Steinmann Paul
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510154
Subject(s) - finite element method , subroutine , discretization , a priori and a posteriori , algorithm , computer science , inverse , element (criminal law) , mathematics , geometry , structural engineering , mathematical analysis , engineering , philosophy , epistemology , operating system , law , political science
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)