Evolutionary structural optimization (ESO) is a method for topology optimization developed by engineers in the early 1990s. Whilst there exists a great deal of engineering intuition about the algorithm, its mathematical foundation has repeatedly come into question.
This work seeks to explain the non-monotonic behaviour of the ESO algorithm by showing how the nonlinearities inherent in the underlying state equations leads to behaviour not predicted by the infinitesimal information used by the ESO algorithm.
Furthermore, we show how local h-refinement of the finite element mesh can show descent of the algorithm.