A cost function involving the eigenvalues of an elastic structure is optimized using a phase-field approach, which allows for topology changes and multiple materials.We show continuity and differentiability of simple eigenvalues in the phase-field context. Existence of global minimizers can be shown, for which first order necessary optimality conditions can be obtained in generic situations. Furthermore, a combined eigenvalue and compliance optimization is discussed.

中文翻译：

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涉及弹性结构特征值的形状和拓扑优化：多相场方法

使用相场方法优化涉及弹性结构特征值的成本函数，该方法允许拓扑变化和多种材料。我们在相场上下文中展示了简单特征值的连续性和可微性。可以显示全局极小值的存在，为此可以在一般情况下获得一阶必要的最优条件。此外，还讨论了组合特征值和合规性优化。