The primary focus of traditional topological optimization in continuum structures is addressing stress, compliance, and other relevant factors associated with single-phase materials. However, the optimal design of structural buckling performance has gained increasing attention due to its significant economic loss and safety risk. Furthermore, the versatility, lightweight nature, and adjustability of composite multiple-phase materials offer significant potential for application in various fields. Therefore, this paper presents a novel methodology for optimizing multi-phase materials’ design by concurrently incorporating structural buckling criteria and compliance design. Linear buckling analysis is utilized to determine the critical buckling load of the structure, and a buckling constraint is incorporated into the topology optimization model to regulate its buckling performance. A refined material interpolation model scheme is introduced to enhance the algorithm’s robustness and eliminate pseudo-eigenmode in buckling analysis. The numerical results demonstrate that the final topology optimization design exhibits distinct and discernible boundaries for the topological configurations of multiple-phase materials. Moreover, it is possible to effectively regulate the buckling property while minimizing any compromise on stiffness.

连续体结构中传统拓扑优化的主要焦点是解决与单相材料相关的应力、柔度和其他相关因素。然而结构屈曲性能优化设计因其巨大的经济损失和安全风险而日益受到关注。此外，复合多相材料的多功能性、轻质性和可调节性为各个领域的应用提供了巨大的潜力。因此，本文提出了一种通过同时结合结构屈曲标准和柔度设计来优化多相材料设计的新颖方法。利用线性屈曲分析确定结构的临界屈曲载荷，并将屈曲约束纳入拓扑优化模型中以调节其屈曲性能。引入了一种精细的材料插值模型方案，以增强算法的鲁棒性并消除屈曲分析中的伪本征模。数值结果表明，最终的拓扑优化设计对于多相材料的拓扑结构表现出明显且可辨别的边界。此外，可以有效地调节屈曲特性，同时最大限度地减少对刚度的影响。