We present a 250-line Matlab code for topology optimization for linearized buckling criteria. The code is conceived to handle stiffness, volume and buckling load factors (BLFs) either as the objective function or as constraints. We use the Kreisselmeier-Steinhauser aggregation function in order to reduce multiple objectives (viz. constraints) to a single, differentiable one. Then, the problem is sequentially approximated by using MMA-like expansions and an OC-like scheme is tailored to update the variables. The inspection of the stress stiffness matrix leads to a vectorized implementation for its efficient construction and for the sensitivity analysis of the BLFs. This, coupled with the efficiency improvements already presented by Ferrari and Sigmund (Struct Multidiscip Optim 62:2211–2228, 2020a), cuts all the computational bottlenecks associated with setting up the buckling analysis and allows buckling topology optimization problems of an interesting size to be solved on a laptop. The efficiency and flexibility of the code are demonstrated over a few structural design examples and some ideas are given for possible extensions.

我们提出了一个 250 行的 Matlab 代码，用于线性屈曲标准的拓扑优化。该代码旨在将刚度、体积和屈曲载荷因子 (BLF) 作为目标函数或约束进行处理。我们使用 Kreisselmeier-Steinhauser 聚合函数将多个目标（即约束）减少到一个单一的、可微的目标。然后，通过使用类似 MMA 的扩展顺序逼近问题，并定制类似 OC 的方案来更新变量。应力刚度矩阵的检查导致其有效构造和 BLF 灵敏度分析的矢量化实施。这一点，再加上法拉利和 Sigmund 已经提出的效率改进（Struct Multidiscip Optim62:2211–2228, 2020a)，消除了与设置屈曲分析相关的所有计算瓶颈，并允许在笔记本电脑上解决有趣大小的屈曲拓扑优化问题。代码的效率和灵活性通过几个结构设计示例得到了证明，并给出了一些可能的扩展的想法。