A global damping factor for a non‐invasive form finding algorithm

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.