In classical level set based topology optimization theory, a typical function like the signed distance function is chosen as the level set function whose zero level set represents the boundary of solid domain. The boundary is updated along the steepest descent direction achieved from sensitivity analysis, which gradually generates the optimal structure  .
Based on the classical level set method, my research tries to develop a more advanced level set theory. More specifically, I’m trying to set up a new set of numerical algorithms with higher computational efficiency, which leads to the optimal structure with better performance. In addition, the new algorithm will be employed to guide the optimal design for functional materials and cellular structures.
For example, Fig. 1 and Fig. 2 plot the optimal structure for the initial cantilever beam and simply supported beam, respectively.
Figure 1 The optimal structure for the initial cantilever beam
Figure 2 The optimal structure for the initial simply supported beam