Level Set Method
A new and improved topology optimization algorithm based on the level set method has been implemented in OptiStruct 2021.
Implemented in OptiStruct 12.0 - in the level set method, the boundary of the design is implicitly represented as the isosurface (the zero level set) of a function ϕ(x)ϕ(x) defined on the finite element mesh, as shown in Figure 1. In the level set model, the domain is defined based on the value of the level set function:
Where, D specifies the design domain; Ω represents the material region, ∂Ω stands for the boundary and D/Ω represents the region with no material. The dynamic motion of the boundary is governed by the so-called, level set equation:

Level-set based topology optimization can be considered as advanced shape optimization. It works like conventional shape optimization, where the design is changed by moving the boundary, while at the same time topological changes, such as boundary emerging and splitting can be handled naturally.