On equivalence between stress criterion and stiffness criterion in evolutionary structural optimisation

In a finite element analysis (FEA), the contours of element von Mises stress and stiffness sensitivity number are found to be very similar. This paper shows there to be an equivalence between the von Mises stress criterion and the stiffness criterion for element elimination or addition in evolutionary structural optimization. The examples presented demonstrate the same resulting topologies during the evolving process using the two "different" criteria. The effect of numerical errors on topology is also investigated. It is concluded that the optimized topologies of a structure using the fully stressed criterion and the minimum compliance or maximum stiffness criterion are equivalent.