Theory for Topology Optimization
About the Density Model
Topology optimization with the density method is one of the oldest and most simple techniques. A domain control variable is discretized on nodes or elements, and a fictitious material is introduced to account for the material boundary in an implicit way. An interpolation is then constructed such that the physical governing equation is solved wherever the control variable is equal to one, while an equation associated with the fictitious material is solved where the control variable is equal to zero. The interpolation is specific to the physics, and it is constructed such that intermediate value of the control variable are suboptimal; see Ref. 1. Furthermore, the problem might be ill posed in the absence of a constraint on the design freedom. This constraint is often imposed implicitly by means of a filter that introduces a minimum length scale via its filter radius.