  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.
