Parametric Optimum Design For Material Properties Based-on Homogenization Method

Composite materials have been widely used in Hi-tech fields because of their special properties of mechanics and physics. The homogenization method, which has solid mathematical foundation, has been widely employed to estimate equivalent properties of composite materials with the rapid development of computer technology. Another important characteristic of composite materials is that their properties are designable. Engineers can obtain composite materials with specific properties by using proper design methods.In this investigation, by integrating the parametric finite element software and the finite element program with homogenization method, the design optimization method for composite materials are developed. The thesis is arranged as:In chapter 1, The mathematical theory of the homogenization method and their applications to equivalent elastic coefficients, thermal conduction coefficients and thermoelastic coefficients of the composite materials are introduced.In chapter 2, The basic theories of finite element method of homogenization is discussed. Examples are presented to show that the homogenization method is an accurate and efficient technique to simulate the multi-scale physical problems.In chapter 3, The software platform of parametric finite element analysis and shape design optimization system which can be used for designing the micro structure of composite material properties is developed.In chapter 4, The study of design optimization for composite material properties using the above integrated software systems is presented. The parametric design optimization of microstructure for composite material with special properties is validated by using several examples.In chapter 5, The finite element analysis system with Multi-Level Sub-structure is introduced to validate the results of the shape design optimization. Numerical examples show that the Multi-Level Sub-structure finite element analysis is very effective for the numerical analysis of periodic composite material structures.The research of the dissertation is supported by National Natural Science Foundation of China (NO. 10402005), National Basic Research Program of China(No. 2005CB321704), Innovative Research Team in University((10421202)).