Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 364, Issue -, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2020.112922
Keywords
Slender elastic structure; Developable surface; Curvature-based elements; Constraint-based nonlinear optimization
Funding
- ERC grant GEM [StG-2014-639139]
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We propose a robust and efficient numerical model to compute stable equilibrium configurations of clamped elastic ribbons featuring arbitrarily curved natural shapes. Our spatial discretization scheme relies on elements characterized by a linear normal curvature and a quadratic geodesic torsion with respect to arc length. Such a high-order discretization allows for a great diversity of kinematic representations, while guaranteeing the surface of the ribbon to remain perfectly inextensible. Stable equilibria are calculated by minimizing the sum of the gravitational and elastic energies of the ribbon, under a developability constraint. Our algorithm compares favorably to standard shooting and collocation methods, as well as to experiments. It furthermore shows significant differences in behavior compared to numerical models for thin elastic rods, while yielding a substantial speed-up compared to a more general thin elastic shell simulator. These results confirm the benefit of designing a special numerical model dedicated to ribbons. (C) 2020 Elsevier B.V. All rights reserved.
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