The role of sensitivity in optimality criteria based structural topology optimization algorithms

Optimality criteria (OC) methods are often used in structural optimization due to their efficiency and simplicity. This class of algorithms are comprised of two complimentary ingredients: the optimality criteria and the resizing algorithm. This manuscript discusses why common criteria used to solve classical minimum compliance problems cannot be directly extended to optimization problems considering stress measures. We demonstrate that sensitivity of the compliance is a local quantity, i.e., it depends only on the relative density at a given point. However, stress-based sensitivity is not a local quantity, as it depends on the relative density of a given region. For this reason, stress-based optimization algorithms must consider some kind of global update rule, nonetheless, the sensitivity of a given point must also consider the influence of other points. This discussion is, then, used to infer about the Proportional Topology Optimization method (PTO) and its derivatives and explains why PTO works for compliance minimization problems but fails to be effective for stress-based problems. The objective here is not to disregard any formulation presented in the literature, but to present conceptual results that may be useful for the development of new topology optimization algorithms in the future.