Topology Optimization Design Of Extremal Composite Microstructure Based On Homogenization Method

In order to make the most of material, reduce material consumption and ensure its best performance, homogenization method combined with optimality criteria is applied to topology optimization design of micro-structure of extremal composite in two and three dimensions and multi-functional extremal composite in three dimensions.Topology optimization of micro-structure of two-phase extremal composite is carried out in this paper. Firstly, the predictions of effective elastic properties and effective thermal conductivities of composite with periodicity are done based on homogenization method by ANSYS and MATLAB. A loading approach to determine periodic boundary condition on ANSYS is proposed when it comes to predicting effective thermal conductivity. Then,topology optimization model of two-phase composite is built with FEM and homogenization method. In this model, relative density of each element is defined as design variables and volume fraction of solid material as the optimization constraints.Sensitivity filter method which can smooth the distribution of element sensitivity is used to eliminate numerical instabilities during the optimization process. The problem is solved by optimality criteria and optimal micro-structures which have extremal elastic properties and extremal thermal conductivities in two dimensions and three dimensions are obtained. The layouts of optimal micro-structure under different volume fraction are discussed and the resulted optimal shear moduli are compared with Hashin-Shtrikman upper limit values.Numerical results show that homogenization method combined with the optimality criteria method can effectively realize topology optimization design of micro-structure with extremal properties. For this reason, homogenization method combined with optimality criteria is used to topological design of composites micro-structure of large-scale wind turbine blade in three dimensions to achieve its lightweight properties and extemal performance.In addition, topological design of micro-structure of multi-functional extremal composites in three dimensions is studied to meet the application on engineering more properly. Weighted sum of effective elastic modulus and effective thermal conductivity are defined as objectives. Micro-structures with extremal elastic properties and extremal thermal conductivities are realized.The results obtained in this paper offer some guidelines for topology optimization design of micro-structures of composite materials in a certain extent.