Concurrent Analysis And Optimization Of Ultra-Light Material And Structure

As the rapid development of science and technology, conventional solid metals have become inadequate to satisfy the needs of practical applications. People are constantly seeking new materials with some fascinating properties: light, stiff and multifunctional. To achieve this goal, mechanics researchers have developed several innovative structured materials by controlling the configuration of material microstructures, including honeycomb, foam and truss-like material. These materials are very promising for their superior mechanical properties and multifunctional capabilities.The ultra-light materials investigated herein all have periodic microstructures. The existence of microstructure on one hand makes it very convenient to predict material properties, for which, Homogenization theory and Representative Volume Element (RVE) method are two mainstream methods. But if we take into account random imperfections induced during manufacturing process and subsequent practical applications, the prediction of equivalent properties could become very time-consuming. For this reason, there is interest in finding a new methodology which exhibits more efficiency over traditional ones. On the other hand, however, the existence of microstructure also increase the difficulty of elasto-plastic analysis of structures constructed of ultra-light materials, since complex internal configuration requires much more time and computing resources. So it is of great importance to develop a more efficient analytical algorithm, especially in the case that this analysis is for optimization / reliability solution. In the aspect of structure / material concurrent optimization, existing methods always lead to non-uniform microstructures in the macro-scale, which poses insurmountable manufacturing difficulties. Thus it is desirable to have a concurrent optimization scheme considering manufacturing factors. Addressing these problems, the study of this thesis can be divided into three main parts:1. In predicting equivalent properties of materials with imperfections, Monte Carlo simulation is adopted based on the Homogenization theory and the Representative Volume Element method. We have compared different boundary conditions, and discussed the size effect and the influence of different cell selections. To improve the efficiency of computation and refine the results under Dirichlet boundary condition, it is proposed a Representative Volume Element computation based on energy equivalence of inner cells, and therefore better results could be achieved with relatively smaller RVE.2. For the elasto-plastic analysis of structures composed of truss-like materials, we first simplify the unit cell as a truss model, and then present a two-scale analysis based on the numerical homogenization. The original problem is thereby transformed to two interrelated problems in two scales: a nonlinear elastic continuum computation in macro-scale and several elasto-plastic analyses of small-scale truss systems in micro-scale. The proposed method is verified to have the same precision but less used time.3. To address the manufacturing difficulty in existing structure / material optimization, this thesis presents a new concurrent topology optimization scheme to simultaneously achieve the optimum structure and optimum material microstructure. Microstructure is assumed to be uniform in macro-scale to meet manufacturing requirements. Design variables in both scales are independently defined and then integrated into one system with the help of homogenization theory. Penalization approaches are adopted in both scales to ensure clear topologies, i.e. SIMP (Solid Isotropic Material with Penalization) in micro-scale and PAMP (Porous Anisotropic Material with Penalization) in macro-scale. Further, it is proposed another concurrent optimization scheme based on substructure. The size effect and advantages for manufacturing are discussed.