Multi-material model and shape optimization for bending and torsion of inextensible rods

09/09/2022

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by   Patrick Dondl, et al.

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We derive a model for the optimization of bending and torsional rigidity of non-homogeneous elastic rods, by studying a sharp interface shape optimization problem with perimeter penalization for the rod cross section, that treats the resulting torsional and bending rigidities as objectives. We then formulate a phase field approximation to the optimization problem and show Γ-convergence to the aforementioned sharp interface model. This also implies existence of minimizers for the sharp interface optimization problem. Finally, we numerically find minimizers of the phase field problem using a steepest descent approach and relate the resulting optimal shapes to the development of plant morphology.