A note on a jellyfish-like feasible domain in structural topology optimization

This paper extends recent studies on the fundamental properties of truss topology optimization to more general structural topology optimization problems. Some basic definitions such as topology design variables and their critical values, topology-dependent behaviour constraints which are directly associated with topology design variables and the limiting values of the constraint functions are introduced. Using grillage topology optimization problems as illustrations, it is demonstrated that the discontinuity of the topology-dependent behaviour constraint function at its critical values is the essential cause of the existence of a jellyfish-like feasible domain and a singular optimum. Jellyfish-like feasible domains may exist even in simple topology optimization problems subjected only to displacement constraints. Finally, the general conditions for the existence of jellyfish-like feasible domains and the classification of various structural topology optimization problems are discussed.