Stiffness design of heterogeneous periodic beam by topology optimization with integration of commercial software

• Microstructure topology design method of periodic beam structure is developed.
• Implementation of optimization is generalized integrating commercial software.
• The sensitivity information is calculated with the element mutual strain energy.
• The method can be extended to periodic truss beam structures directly.

A topology optimization method is developed for microstructure design of heterogeneous periodic beam structure aiming at its extreme or specified effective stiffness. The effective stiffness is calculated using a FEM formulation of asymptotic homogenization method for heterogeneous periodic beam. Sensitivity of stiffness to the density design variable is derived analytically based on the solution of unit cell problems under corresponding generalized strain fields. Implementation of optimization procedure is generalized to take full advantage of commercial FEM software capabilities, with several examples presented to demonstrate its effectiveness. It is shown here the proposed method is extendible to periodic truss beam design.