Hi, I am working on topology optimization of a beam for a project and I have a problem. I am supposed to optimizate this beam so that its stiffness is highest for most of its mass removed. However when looking at the results for diffrent percentages of mass removed I realized that stiffness increases as mass decreases. How is this possible, I am looking at the stiffness value in a wrong way? I have attached the initial beam, and 10% and 90% of mass removed for example.
What are the units for that stiffness value (silly they don't show the units)? It should be a distance of deflection divided by force. Probably they don't count the weight of the beam as part of the force, so they show a number for some sort of effective stiffness, while calculating the actual total force. Removing mass will reduce the actual total force, so deflection may be reduced, so what they show is an improved effective stiffness.
Typically, first natural mode of vibration is used to indicate stiffness, fn=sqrt(K/M).
By the way, your case is a good example for comparing between solid material part and structure material (or weldment) part.
Looks good! That's what you want.
The stiffness is not proportional to the mass.