Integrative design of topology and material of two-dimensional continuum structures

An integrative design approach for two-dimensional (2D) continuum structures is introduced. Four steps are contained in the design process. Firstly, the optimal topology of a 2D structure is obtained by using a bionics optimization method, which is based on Wolff's law in bone mechanics, i.e., the optimization process of the 2D structure is considered as the remodelling process a piece of bone with the same loading conditions and the optimal material distribution of structure is obtained when the bone is in the remodelling equilibrium state. Commonly, the material in the optimal topology of the structure shows heterogeneous, e.g. porous and anisotropic. Therefore, in the second step of the approach, the point is to mesh the whole optimal structure with finite sub-domains. In each sub-domain, the material properties are considered as homogeneous. Thirdly, the material in each sub-domain is substituted for a lattice structure with periodic quadrilateral unit cells. The poles in the unit cell of a lattice structure are determined by the local material elastic properties, i.e., the lattice structure and the material in the same sub-domain have the same elastic properties. The approach to find the size of the poles in an unit cell is called as pseudo-membrane (PM) method. Firstly, the sub-domains are glued to form a whole structure. To verify the validity of the integrative design approach, a numerical example is given to show the detail design process.