Topology Optimization of Continuum Structures with Many Subdomains

The topology optimization of a structure with many subdomains is solved by a bionics approach, called as floating interval of reference strain energy density (SED). In practical engineering, a structure to be optimized may have many subdomains and each one is filled with a type of solid material as an initial design. To solve such kind of structural topology optimization, we present a heuristic approach according to bone remodelling theory. The main ideas of the method are as follows. First, the structure to be optimized is considered as a piece of bone and the optimization process of structure is equivalent to the bone remodelling process, in which the distribution of local material in a bone tissue varies when the deformation of tissue goes beyond a so-called dead zone. Second, based on the concept of dead zone, a SED interval is adopted to control the update of local material in structure. Third, to satisfy the constraint(s) of the optimization problem, the reference interval changes in optimization. Particularly, the update of the reference interval is determined by the active constraint of optimization problem. A numerical example is given to show the significance of this kind of optimization problem, finally.