Level set-based heterogeneous object modeling and optimization

This paper presents a level set-based heterogeneous object (HO) modeling and optimization method. This HO model employs multiple level set functions to build the geometry, utilizes zero-value level set contours as material source profiles, and realizes functionally graded material blending with a signed distance-based blending function. More importantly, this HO model supports the concurrent structure and material optimization because of the unified level set framework for both structure and material composition representation. Beyond macro HO, heterogeneous meta-material optimization will be addressed as well. This new model remedies the shortage of traditional HO models that focus more on modeling but less on optimization. About the numerical optimization, design update with the sensitivity result will be carefully discussed, since there includes infeasible terms (in domain integration format). Two strategies will be explored to address this issue: ignoring the infeasible part of the sensitivity, or transforming the sensitivity result into a purely boundary integration-based expression. A few numerical examples will be studied to prove the effectiveness of the proposed HO modeling and optimization method.