Minimal elastic networks
Anna Dall'Acqua, Matteo Novaga, Alessandra Pluda
TL;DR
This paper studies minimal elastic networks composed of three curves meeting at junctions with equal angles, proving existence, regularity, and properties of the optimal configurations.
Contribution
It establishes the existence and regularity of minimizers for elastic networks with specific junction conditions, a novel analysis in this context.
Findings
Existence of minimizers is proven.
Regularity properties of the minimal networks are established.
Properties of the minimal configurations are characterized.
Abstract
We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some properties of the minimal configurations.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Point processes and geometric inequalities · Structural Analysis and Optimization