Phase field model for multi-material shape optimization of inextensible rods
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 $\Gamma$-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.
PDF AbstractCategories
Optimization and Control
Numerical Analysis
Mathematical Physics
Mathematical Physics
Numerical Analysis
35Q74, 41A60, 49J45, 49Q10, 74B20, 74P10
