Study On Multi-scale Concurrent Optimization Design Of Lightweight Lattice Structures

Due to the advantages such as excellent strength and stiffness/weight ratio, damping, sound absorption, heat dissipation and the potential of multi-functional applications, lattice material as a new ultra-lightweight material are widely used in automotive, shipbuilding, aerospace fields. Because structures composed of lattice materials include a large number of micro components usually, the workload of structural modeling and response analysis is enormous. Moreover, the results of structural analysis and optimization design are affected by the geometries of the material microstructures significantly. Therefore, conventional finite element techniques are not applicable for the above problems. In this thesis, a new multiscale analysis method called Extended Multiscale Finite Element Method (EMsFEM) is introduced. A series of studies about multiscale analysis and concurrent optimization design of structures composed of lattice materials, about the structural deformation, stress, stability and equivalent mechanical properties, are carried out.1. The size effects of the macrostructural response caused by the micro structural geometries of lattice materials are studied with EMsFEM. With the same volume of base material and configuration, the structural displacement and maximum stress of micro components of lattice materials increase and approach to the solution of the homogenization method gradually with the growth of the number of basic sub-unit cell. Numerical experiments show that EMsFEM is suggested to be adopted to improve computational efficiency with high accuracy when the actual size of the micro-components is small and the number of micro truss unit cell is relatively large.2. Multiscale concurrent optimization designs of lattice material microstructures and macro topologies for minimum compliance are studied based on EMsFEM. in order to meet the requirements of the manufacturing process and cost. lattice material microstructures are assumed uniformly everywhere in macro-scale. The cross-sectional area of the micro components as design variables are introduced to achieve optimal distribution of base material in the truss unit cell with EMsFEM in material scale. The relative densities of macro element as design variables are applied with Porous Anisotropic Materials with Penalty (PAMP) to obtain the optimal topologies in structrue scale. The superiority of material/structure concurrent optimization relative to the single scale design of microstructures and the correctness of the optimization model are verified. Numerical examples show that the optimal configuration of the macrostructures are closely related to the Macro geometries and loading conditions. And Compared with commercial software, optimization model based on EMsFEM analysis can improve computational efficiency significantly.3. Considering the strength failure and buckling instability of micro components within structures composed of lattice materials, optimization design of micro materials and multiscale concurrent optimization design of lattice material microstructures and macro topologies, respectively, are implemented with critical failure stress of micro components regarded as constraint functions for the target of lightweight. Smooth envelope functions are introduced to solve the singularity of stress constraints effectively in the optimization model. P-normmethod is applied to condense the huge amount of yield stress constraints. And an exponential smooth interpolation function is proposed to solve the problem resulted from the cohesion of buckling stress constraints with P-norm method tentatively and improve the stability of the convergence of the optimization process effectively.4. A new computational scheme is proposed to achieve the prediction of the elastic properties of porous material based on mathematical homogenization method. The step of achieving homogenization conveniently is put forward. And the mechanical concept and interpretation of formulas of mathematical homogenization method are revealed. The equivalent elastic properties of lattice materials, grille materials and cellular materials are obtained with the new calculation format.