In view of the fact that the follow-up search for an optimal topology is affected by
deleting a large number of high-relative-density elements. When the typical density interpolation
approach, namely, solid isotropic microstructures with penalization (SIMP), is employed in the
continuum structural topology optimization, a new density interpolation approach based on the
logistic function is proposed in this paper. This method can weaken low-relative-density elements
while enhancing high-relative-density elements by polarization, and then rationally realize polar-
ization of the intermediate density elements. It can reduce the number of gray-scale elements as
much as possible to get the optimal topology with distinct boundaries in conjunction with the sen-
sitivity filtering method based on particle swarm optimization (PSO). Several typical numerical
examples are given to demonstrate this method.