论文标题
涉及弹性结构特征值的形状和拓扑优化：多相视野方法
Shape and Topology Optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach
论文作者
论文摘要
优化了涉及弹性结构特征值的成本功能，该成本功能是由多阶段方程描述的。这使我们能够处理拓扑变化和多种材料。我们证明了特征值的连续性和不同性，并确定了全球最小化的优化问题。我们进一步得出了局部最小化器的一阶最佳条件。此外，还讨论了结合特征值和合规性优化的优化问题。
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and differentiability of the eigenvalues and we establish the existence of a global minimizer to our optimization problem. We further derive first-order necessary optimality conditions for local minimizers. Moreover, an optimization problem combining eigenvalue and compliance optimization is also discussed.
