One can impose a minimum length scale, Rmin, on a domain control variable, θc, using a Helmholtz filter (see Ref. 2):

where θf is the filtered material volume factor. The mesh element size is taken as the default filter radius, but the filter radius should not be smaller than mesh element size and one has to pick a fixed value to get mesh independent designs. The filtered material volume factor is continuous and discretized with linear polynomials. The filter can be turned off, in which case θf = θc holds. Figure 2-1 illustrates the filtering process, and it is taken from the model Topology Optimization of an MBB Beam in the Optimization Module Application Library.