  An optimization method for the design of multi-lattice structures satisfying
local buckling constraints is proposed in this paper. First, the concept of
free material optimization is introduced to find an optimal elastic tensor
distribution among all feasible elastic continua. By approximating the elastic
tensor under the buckling-containing constraint, a matching lattice structure
is embedded in each macro element. The stresses in local cells are especially
introduced to obtain a better structure. Finally, the present method obtains a
lattice structure with excellent overall stiffness and local buckling
resistance, which enhances the structural mechanical properties.
