Lei and I will be working on developing the appropriate relations and numerical methods for topological optimization of  2D ideal structures.  In this constraint-based optimization study we will try to determine the density distribution which minimizes the strain energy for a fixed volume of material.  This problem is a subset of the so-called "G-closure" problem in topological optimization where we have restricted our possible configurations to certain ideal geometries.   

If time permits, it may also be interesting to consider solving the equivalent "homogenized" problem and to pursue the idea of trying to introduce explicit dependence of the homogenized stiffness on the length scale of the microstructure.  With this approach, the density can be treated as a "slowly varying" function of macroscopic length scale and an optimal continuous distribution of density can be determined through simple optimization studies. 

Andrew Seagraves