Zero density lower bounds in topology optimization

In topology optimization, the notion of topology is introduced into the analysis by assigning density design variables to positions throughout the design domain. The standard practice is to set the lower bound values of the density design variables so that they are small but nonzero values. The intent of the nonvanishing lower bound has been to ensure that the (tangent) stiffness matrix of the finite element analysis remains nonsingular, and the lower bound values are selected so that the low density elements are structurally insignificant to the extent that the structural analysis can be performed. However, from a pragmatic point of view, we should desire that void material be represented by regions of zero density elements. Here, a simple algorithm that does not requiring remeshing and accommodates the zero density design variable values is presented, and the ramifications of the zero density lower bounds on the topology optimization are discussed.