Topology optimization of multiscale structures considering local and global buckling response

Much work has been done in topology optimization of multiscale structures for maximum stiffness or minimum compliance design. Such approaches date back to the original homogenization-based by Bends{\o}e and Kikuchi from 1988, which lately revived due advances manufacturing methods like additive manufacturing. Orthotropic microstructures locally oriented principal stress directions provide highly efficient optimal designs, whereas pure objective, porous isotropic are sub-optimal hence not useful. It has, however, postulated exemplified that (infill) may enhance structural buckling stability but this yet be directly proven optimized. In work, we optimize with infill. To do this, establish local density dependent Willam-Warnke yield surfaces based on estimates Bloch-Floquet-based cell analysis predict instability homogenized materials. These buckling-based constraints combined a global criterion obtain optimized designs take both into account. De-homogenized small large sizes confirm validity approach demonstrate huge gains as well time savings compared standard singlescale approaches.