Topology Optimization For Materials And Structures Based On Thermal Conductivity Property

The lightweight composite materials with good performance, such as mechanical shock resistance, thermal resistance, sound insulation and low cost, which are widely used in aerospace, are investigated in this thesis. A new design methodology is proposed for porous materials and structures based on thermal conductivity property, using the technique of homogenization method and topology optimization.Designable porous materials and composite materials can be treated as structures. Prepared for materials design, a homogenization based prediction of effective thermal conductivity of composite materials is investigated in the thesis, firstly. The mathematical theory of homogenization assumes that macrostructures are composed of complex materials with periodic microstructures based on the assumption of continuous media in mechanics and physics. The effective constitutive parameters can be carried out by analyzing the base cell. The effects of volume fraction, cross section shape of fibers and the relative thermal conductivity of fiber and matrix on thermal conductivity of composites are analyzed in this thesis.The recent developments in computer science, theory of finite element method and large-scale optimization algorithms, allow for wide use of topology optimization method in aeronautical and automobile industry. So a new topology optimization criterion algorithm is presented in this thesis using SIMP method. The topology optimization model, which is used to find the structure topology with optimal thermal conduction efficiency, is established for thermal conduction structure.Then, a new method is presented for thermal conductive microstructures of composite materials based on the technique of homogenization method and topology optimization. By defining the pseudo-density variable of each element in the design domain and constraining the total material cost, the topology optimization model with SIMP method is built to maximize either the effective thermal conductivity of the microstructure in specified directions or the thermal conduction efficiency of the macrostructure. The sensitivity of the objective function is then given. The optimal solution can be obtained by means of the dual optimization algorithm and perimeter constraint. Numerical results verify the validity of the proposed topology optimization method in the thermal conduction design of the microstructures.The homogenization method uses the asymptotic expansion of small parameters,and the effective properties of composite materials are extremum, which are different from the real properties of composite materials. The present topology optimization method of microstructures cannot reveal the scale effect upon design configuration in thermal conduction. So an integrated design methodology is proposed for the scale-related topology optimization of porous materials and structures. Compared to the traditional homogenization method, the introduction of the super-element modeling technique for the definition of representative volume element (RVE) and the scale variation of the latter make it possible to reveal the scale effect and meanwhile to deal with the pure material design and pure structural design in a unified way.