论文标题
相位场模型，用于对不可延迟杆的多物质形状优化
Phase field model for multi-material shape optimization of inextensible rods
论文作者
论文摘要
我们得出了一个模型，以优化非均匀弹性杆的弯曲和扭转刚度。这是通过研究尖锐的界面形状优化问题和周长惩罚来实现的，这将两个刚性视为目标。然后，我们制定了优化问题的相位场近似，并通过$γ$ -Convergence显示了上述尖锐接口模型的收敛。在这项工作的最后一部分中，我们通过使用最陡峭的下降方法来数值近似相位场问题的最小化，并将所得的最佳形状与植物茎形态的发展相关联。
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.
