Topology Optimization with linearized buckling criteria in 250 lines of Matlab

Abstract: 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 2020, 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 is demonstrated over a few structural design examples and some ideas are given for possible extensions.