Penalty factor in topology optimization
What is use of penalty factor in topology optimization?
Best Answer

akhemka Forum Coordinator
Hi @skadam ,
Penalty factor is used to scale the structural stiffness matrix of each element depending on the topology density (which is calculated during solution as between 0 and 1). The higher the Penalty Factor, the more the stiffness matrix is weighted towards elements with a density close to 1  i.e. less ambiguity in portions to keep/discard. This factor is penalizing the stiffness matrix with this equation penalized stiffness = ( pseudo density)^penalty factor × stiffness. The higher the penalty factor, it reduces the grey region in the final design. The less the grey region, the better is the design. So the users once have selected the design can deploy this to reduce the grey regions in the design. The penalty factor cannot be very high value because it creates a huge gradient between different elements and make the solution unstable. The stiffness will not be high because the pseudo density is always between 0 and 1. But it creates a huge gradient of how stiffness is varying in the design.
Regards,
Ashish Khemka
Answers
Hi @skadam ,
Penalty factor is used to scale the structural stiffness matrix of each element depending on the topology density (which is calculated during solution as between 0 and 1). The higher the Penalty Factor, the more the stiffness matrix is weighted towards elements with a density close to 1  i.e. less ambiguity in portions to keep/discard. This factor is penalizing the stiffness matrix with this equation penalized stiffness = ( pseudo density)^penalty factor × stiffness. The higher the penalty factor, it reduces the grey region in the final design. The less the grey region, the better is the design. So the users once have selected the design can deploy this to reduce the grey regions in the design. The penalty factor cannot be very high value because it creates a huge gradient between different elements and make the solution unstable. The stiffness will not be high because the pseudo density is always between 0 and 1. But it creates a huge gradient of how stiffness is varying in the design.
Regards,
Ashish Khemka