Symbolic Computation to Derive a Linear-Elastic Buckling Theory for Solids with Periodic Microstructure

A symbolic computation of a double scale asymptotic technique is used to derive a linearelastic buckling theory for solids with periodic microstructure. From the stationary potential energy, equations are obtained for the classic homogenization problem, and for its extension to the buckling problem at macro, micro and mixed scales. The limitation to #Y-periodic instability modes can be treated afterwards using a Floquet-Bloch theory. The symbolic procedure is worked out step-by-step and results are presented. The obtained equations present a theoretical framework for the topology optimization of structures and microstructures involving linear elastic buckling criteria.