Multiscale Analysis And Concurrent Optimization For Ultra-Light Metal Structures And Materials

Light weight design of structures can reduce products' mamufacturing cost and energy consumption, which greatly improve the quality of products. And it has been the focus and forever topics of researchers and engineers with shortage of energy and resources and intense competitions. With the rapid developments in mamufacturing techniques, more and more ultra-light metal porous materials (truss-like materials, linear celluar alloys, metal foams) are utilized in practice engineerings. They have received increasing attentions for their high stiffness-weight and strength-weight ratios together with potential of multifunctional applications.A serial of researches on multiscale analysis and concurrent optimization for ultra-light metal structures and materials have been carried out. And the main works are as follows.1. This paper compares the representative volume element (RVE) method based on Diriehlet and Neumann boundary conditions with the homogenization method for predicting the effective elastic property of truss-like materials with periodic microstructure. The formula of homogenization method are developed and implemented for truss-like materials. Numerical experiments show that, with increase of the number of unit cell, n, the results of RVE method under the Dirichlet and Neumann boundary conditions converge towards those obtained with homogenization method from the above and below sides respectively. For some specific types of the unit cell, RVE method gives the same results as those obtained with homogenization method even if only one unit cell is included. For RVE method, a simple criterion for judging existence of scale effects is whether the equilibrium of the boundary nodal forces is guaranteed under the Dirichlet boundary conditions or whether the deformation compatibility at the unit cell boundaries is satisfied under the Neumann boundary conditions. Finally, shape optimization technique is applied to find the optimal geometric shape of unit cell for truss-Iike materials with the maximum and minimum shear stiffness and the numerical singularity involved is discussed as well. (Chapter Two)2. For LCAs (Linear Celluar Alloys), the precision of classic Cauchy effective continumm and micropolar effective contimumm are compared with the results from exact discrete models in wich each cell wall is modeled as a beam element. Numerical simulations show that micropolar effective continumm is preferred considering either from displacement or stress results. And a fast mapping algorithm for micro-stress distribution in truss-like materials is developmented based on results with micropolar continuum representation obtained by energy method. Baed on the above analysis, optimum stress distribution for hollow plates composed of LCAs is investigated. To reduce the computational cost we model the material as micropolar continua representation. Two classes of design variables, relative density and cell size distribution of truss-like materials are to be determined by optimization under given total material volume constraint. And the concurrent designs of material and structure are obtained for three different optimization formulations. For the first formulation, we aim at minimization of the maximum stress which appears at the initial uniform design; for the second formulation, we minimize the highest stress within the specified point set. Since the yield strength of truss-like material is dependent on the relative material density, we minimize the ratio of stress over the corresponding yield strength along the hole boundary in our third formulation, which maximizes the strength reserve and seems more rational. And the influence of ply angle on the optimum result is discussed. The dependence of optimum design on finite element meshes is also investigated. An approximate discrete model is established to verify the method proposed in this paper and the stress concentration near a hole is reduced significantly. (Chapter Three)3. The optimization model and technique for modular structures and materials are discussed. The effects of acutral dimensions of basic design modules on optimization results are investigated for those structures that are composed by periodic distribution of basic design modules. The concurrent optimizations of macro structures and design modules based on modules assembling are implemented by introducing independent densities in macro and micro scale as design variables. The optimum configuration and distribution of basic design modules are discussed via to topology optimization technique and sub-structure method. (Chapter Four)4. An optimization technique for structures composed of uniform porous materials in macro scale is developed based on manufacturing requirements. The optimization aims at to obtain optimal configurations of macro scale structures and microstructure of materials under certain mechanical and thermal loads with specific base material volume. A concurrent topology optimization method is proposed for structures and materials to minimize compliance of thermoelastic structures. In this method macro and micro densities are introduced as the design variables for structure and material microstructure independently. Penalization approaches are adopted at both scales to ensure clear topologies, i.e. SIMP (Solid Isotropic Material Penalization) in micro-scale and PAMP (Porous Anisotropic Material Penalization) in macro-scale. Optimizations in two scales are integrated into one system with homogenization theory and distribution of base material between two scales can be decided automatically by the optimization model. Microstructure of materials is assumed to be uniform at macro scale to reduce manufacturing cost. The proposed method and computational model are validated by the numerical experiments. The effects of temperature differential, volume of base material, numerical parameters on the optimum results are also discussed. At last, for cases in which only mechanical load apply, the optimum configuration of micro structure is isotropic solid materials; for eases in which both mechanical and thermal loads apply, the configuration of porous material can help to reduce the system compliance. (Chapter Five)5. Cyclic-symmetry structures with both mechanical and centrifugal loads are divided into finite design modules, which have the identical configurations. Concurrent optimization techniques based on homogenization method and penalty technique are applied for cyclic-symmetry structures assembled by basic design modules considering the real dimension of design modules. The effects of solid material volume, different loads combination and nondesign fields on optimum results are discussed. Numerical simulations show that for cases in which both mechanical and centrifugal loads apply, the configuration of porous material can help to reduce the system compliance.