Concurrent Analysis and Design of Structure and Its Periodic Materials

The specific good properties of cellular materials and composite materials, such as low density and high permeability, make the optimal design of such materials necessary and attractive. However, the given materials for the structures may not be optimal or suitable since the boundary condition and applied loads vary in practical applications; hence the macro-structure and its material micro-structure should be considered simultaneously. Although abundant studies have been reported on the structural and material optimization at each level, very few of them considered the mutual coordination on both scales. In this paper, two FE models are built for the macro-structure and the micro-structure, respectively; and the effective elastic properties of the periodic micro-structure are blended into the analysis of macro-structure by the homogenization theory. Here, a topological optimum is obtained by gradually re-distributing the constituents within the micro-structure and updating the topological shape at the macro-structure until converges are achieved on both scales. The mutual coordination between the roles of micro-scale and macro-scale is considered. Some numerical examples are presented, which illustrate that the proposed optimization algorithm is effective and highly efficient for the micro-structure design and macro-structure optimization. For the composite design, one can see reasonable effects of the stiffness of base materials on the resultant topologies.