Implication of Using Large Value of Penalty Factor

Question - With regards to the Topology Optimizer Penalty Factor, what is the implication of using a very large number (>>10) for this property?

Answer - Penalty factor is penalizing the stiffness matrix with this equation penalized stiffness = ( pseudo density)^penalty factor × stiffness. The higher the penalty factor, the lower the grey region in the final design. The grey region is the region which contains the intermediate density in the design ( the pseudo density between 0.4 to 0.6). The less the grey region, the better is the design. So once users have selected a final design, they can deploy Penalty Factor to reduce the grey region.

The implication of using too high a penalty factor is that it creates the potential for a huge gradient between different elements, making the solution unstable. The stiffness might not be too high because the pseudo density is always between 0 and 1. But it can create a huge gradient of how stiffness is varying in the design.