Interest in components with detailed structures increased with the progress in advanced manufacturing techniques in recent years. Parts with graded lattice elements can provide interesting mechanical, thermal, and acoustic properties compared to parts where only coarse features are included. One of these improvements is better global buckling resistance of the component. However, thin features are prone to local buckling. Normally, analyses with high computational effort are conducted on high-resolution finite element meshes to optimize parts with good global and local stability. Until recently, works focused only on either global or local buckling behavior. We use two-scale optimization based on asymptotic homogenization of elastic properties and local buckling behavior to reduce the effort of full-scale analyses. For this, we present an approach for concurrent local and global buckling optimization of parameterized graded lattice structures. It is based on a worst-case model for the homogenized buckling load factor, which acts as a safeguard against pure local buckling. Cross-modes residing on both scales are not detected. We support our theory with numerical examples and validations on dehomogenized designs, which show the capabilities of our method, and discuss the advantages and limitations of the worst-case model.

翻译：近年来，随着先进制造技术的进步，人们对具有精细结构的构件兴趣日益增加。与仅包含粗大特征的构件相比，具有分级点阵单元的构件可展现出更优的力学、热学和声学性能。其中一项改进在于构件整体抗屈曲能力的提升。然而，薄壁特征易发生局部屈曲。通常，需通过高计算量的高分辨率有限元网格分析来优化兼具良好全局与局部稳定性的构件。此前研究仅关注全局或局部屈曲行为中的单一维度。本文基于弹性性能与局部屈曲行为的渐进均匀化方法，采用双尺度优化以减少全尺度分析的计算负担。为此，我们提出一种针对参数化分级点阵结构进行全局与局部协同屈曲优化的方法。该方法基于均匀化屈曲载荷因子的最坏情况模型，该模型可作为防范纯局部屈曲的保障机制，但无法检测跨尺度交叉模态。我们通过数值算例及去均匀化设计验证支撑理论，展示了该方法的能力，并讨论了最坏情况模型的优势与局限性。