Topology optimization of a continuum structure with local volume constraints

Topology optimization of a continuum structure with volume constraint(s) on its subdomain(s) is investigated by a heuristic approach simulating the bone remodelling process. The essentials of the present approach are summarized as follows. Firstly, the structure is regarded as a piece of bone and the topology optimization process is equivalent to the bone remodelling process. Secondly, according to the dead zone in bone remodelling theory, global and local floating intervals of reference strain energy density (SED) are proposed and the update of the design variable of a material point is determined by the comparison between the local SED and the current interval of reference SED. Thirdly, to satisfy the global constraints in an optimization problem, the global reference interval changes in simulation. Finally, to satisfy the local volume constraints of subdomains in structure, the same amount of local reference intervals changes in simulation. Numerical example is employed to demonstrate the effects of the local volume constraint(s) on the optimal topologies of structures.