二维连续体结构的拓扑和材料一体化设计

Integrative Design of Topology and Material of Two-dimensional Continuum Structures

通过基于Wolff法则的连续体拓扑优化方法所获得的连续体结构最优拓扑中的材料往往呈非均匀性.为了实现二维连续体结构的拓扑和材料的一体化设计,在获取结构的最优拓扑后,利用具有周期性微结构的二维网格结构比拟原正交各向异性非均匀连续体结构,使得两者在力学性能上等效,从而实现最优结构的材料设计.数值算例验证了比拟方法的正确性及材料设计的可行性.

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.