Microstructure interpolation for macroscopic design

We present a method for multiple length scale structural optimisation. We first optimise isotropic microstructures for maximum bulk modulus at five solid fractions. Shape interpolation between these optimised microstructures produces a continuous set that smoothly varies in both geometry and mechanical properties. This smooth set is used for macroscopic optimisation via the material distribution method. The approach is computationally efficient and the geometric smoothness makes it clear how the microstructures can be transitioned between neighbouring elements. Performance comparisons are made to traditional structural optimisation for some example compliance optimisation problems. The interpolated microstructure designs are most advantageous for two dimensional problems involving multiple loading cases. In these cases, intermediate densities are utilised to more effectively distribute the load. In three dimensions, the method would be useful for a number of applications where specific microstructural requirements, such as a connected pore space, are needed within a multiple-scale design.