Effects of Local Volume Constraints on Optimal Topologies of Continuums

Optimal stiffness design of a structure with local volume constraints on its subdomains is investigated. In practical engineering, a structure may have many sub domains with local volume constraints to meet the multi-function of structure. A new heuristic approach simulating the bone remodelling process is presented to solve such problem. The essentials of the present approach are summarized as follows. Firstly, the topology optimization of structure is equivalent to bone remodelling process. Corresponding to the dead zone in bone remodelling theory, a floating interval of reference strain energy density (SED) is proposed. Secondly, the update of the design variable, i.e. the relative density of a material point, is determined by 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 sub domains in structure, the same amount of local reference intervals are adopted to modify the update rule of local materials. Numerical examples are employed to demonstrate the effects of the local volume constraints on the optimal topologies of structures.