A new approach to produce optimal porous mesostructures and at the same time optimizing the macro structure subject to a compliance cost functional is presented. It is based on a phase-field formulation of topology optimization and uses a local volume constraint (LVC). The main novelty is that the radius of the LVC may depend both on space and a local stress measure. This allows for creating optimal topologies with heterogeneous mesostructures enforcing any desired spatial grading and accommodating stress concentrations by stress dependent pore size. The resulting optimal control problem is analysed mathematically, numerical results show its versatility in creating optimal macroscopic designs with tailored mesostructures.

提出了一种产生最佳多孔介孔结构的新方法，同时根据合规成本函数优化宏观结构。它基于拓扑优化的相场公式，并使用局部体积约束 (LVC)。主要的新颖之处在于 LVC 的半径可能取决于空间和局部应力测量。这允许创建具有异质介观结构的最佳拓扑结构，以执行任何所需的空间分级并通过应力相关的孔径来适应应力集中。对产生的最优控制问题进行数学分析，数值结果显示其在创建具有定制细观结构的最优宏观设计方面的多功能性。