Connecting Microstructures for Multiscale Topology Optimization With Connectivity Index Constraints
2018
With the rapid developments of advanced manufacturing and its ability to manufacture
microscale features, architected materials are receiving ever increasing attention in
many physics fields. Such a design problem can be treated in topology optimization as
architected material with repeated unit cells using the homogenization theory with the
periodic boundary condition. When multiple architected materials with spatial variations
in a structure are considered, a challenge arises in topological solutions, which may not
be connected between adjacent material architecture. This paper introduces a new measure,
connectivity index (CI), to quantify the topological connectivity, and adds it as a
constraint in multiscale topology optimization to achieve connected architected materials.
Numerical investigations reveal that the additional constraints lead to microstructural
topologies, which are well connected and do not substantially compromise their
optimalities
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