Concurrent optimization of structure topology and infill properties with a cardinal-function-based parametric level set method

In this paper, a parametric level-set-based topology optimization framework is proposed, to concurrently optimize structural topology at the macroscale as well as the infill material properties at the mesoscale. With the parametric level set framework, both the boundary evolution and the material property optimization during the optimization process are driven by the Method of Moving Asymptotes (MMA) optimizer, which is more efficient than the PDE-driven level set approach when handling nonlinear problems with multiple constraints. Rather than using a radial basis function (RBF) for the level set parameterization, a new type of cardinal basis function (CBF) was constructed as the kernel function for the proposed parametric level set approach. With this CBF kernel function, the bounds of the design variables can be defined explicitly, which is a great advantage compared with the RBF-based level set method. A variational approach was conducted to regulate the level set function to be a distance-regularized shape for a better material property interpolation accuracy and higher design robustness. With the embedded distance information from the level set model, boundary layer and the infill can be naturally discriminated.