Calculation Of The Effective Properties And Topology Optimization Of Composite Materials

Light-weight composite materials are attracting increasing attention for a variety of applications and have been widely used in the aerospace, mechanical, ship-building and defense industries. The advantages of composites lie on energy absorption, high specific strength and high specific stiffness and the designable properties. This thesis is devoted to calculation of the effective properties and topology optimization of light-weight composite materials.The exact predictions of the effective properties of composite materials play an important role in the application of light-weight composite materials. Homogenization method is widely used to predict the properties of periodic materials and to design microstructures. Homogenization method is based on the strict mathematical theory, but the prediction and sensitivity analysis of microstructures are very complicated and time-consuming, which limits the application of homogenization method. It is very necessary to develop an efficient method to predict the effective properties of composite materials.For the orthotropic material, the relationship between the potential energy of microstructure and the homogenous medium under some certain boundary conditions is studied and a new method is proposed to predict the effective elastic properties and thermal expansion coefficients using the potential energy of microstructure. A similar method is developed to calculate the effective thermal conductivity of orthotropic composite material based on the heat dissipation of microstructure. Both of the methods are named as 'energy method'. Based on the finite element discretization of the microstructure, by defining the pseudo-density variable of each element using SIMP method, the sensitivity analysis of the effective properties is derived. Compared with homogenization method, the energy method demonstrates its simplicity in sensitivity analysis and in numerical implementation.Engineers devote themselves to reduce the weight of structures and to improve their performance. The Thrust-Weight Ratio and Weight-Factor of the aircrafts are highly improved because of widely use of light-weight material. A topology model is built to maximize the different combinations of effective properties related to 2D and 3D multiphase materials under the constraints of the total material cost. The dual optimization scheme and the quadratic perimeter constraint are used to solve the problem and control the checkerboard pattern during optimization procedure. Both composite materials with extreme elastic properties and composite materials with thermal conductivity are designed, and furthermore multifunctional materials with extreme elastic properties and thermal conductivity are optimized. Materials with...