Submitted Paper

Inserted: 10 sep 2022
Last Updated: 7 aug 2023

Year: 2023

Abstract:

We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both rigidities as objectives. We then formulate a phase field approximation of the optimization problem and show the convergence to the aforementioned sharp interface model via Γ-convergence. In the final part of this work we numerically approximate minimizers of the phase field problem by using a steepest descent approach and relate the resulting optimal shapes to the development of the morphology of plant stems.

Keywords: shape optimization, numerical simulations, steepest descent, Γ-convergence, bending and torsional rigidity, sharp interface, phase field problems, diffuse interface, optimality conditions, plant morphology