On feasible domain in topology optimization of trusses

摘要

Some definitions, such as κ dimensional feasible sub-domain, neighbor feasible sub-domain, κ dimensional connected feasible sub-domain and κ dimensional singular feasible sub-domain, are advanced. Based on these definitions, the definition of singular optima in topology optimization of structure, which was given by Rozvany, is revised. Furthermore, the feasible domain in topology optimization of trusses is researched in this paper. The sufficient and necessary condition for the connection of sub-domain is given, and it is proved that the sub-domains of different topologies in design space are always connected for the topology optimization of trusses with stress constraints, zero sectional area lower limit constraints and without the upper limit constraints of sectional area. Simultaneously, some examples with non-connected sub-domains are given, which are the topology optimizations of trusses with the lower bound constraints, local buckling constraints.