3-D topology optimization based on nodal density of divided sub-elements for enhanced surface representation

The material distribution based on an element density is adequate for most of 2-D topology optimization problems. However, in 3-D topology optimization it is usually difficult to obtain a smooth topological configuration and a virtual connectivity phenomenon easily appears in a low-density domain. A 3-D structural topology optimization and novel surface-smoothing scheme based on SIMP (solid isotropic microstructure with penalization) and sub-element bilinear interpolation has been developed using node densities and a corresponding computer program was written in order to validate the proposed method. Compared to a common element density method, the proposed method resulted in more enhanced smooth surfaces of optimum topology designs. To show the usefulness of the method, three examples of 3-D structural topology optimizations were illustrated.