Multi-scale Concurrent Optimization Design Of Thermoelastic Lattice Structures

With high specific strength, stiffness and other advantages, the ultra-lightweight lattice material as a new advanced material containing many ordered micro-porous structure is widely used in load-bearing structures of the spacecrafts such as high-altitude airships and satellites. Moreover, as its internal connected porous, excellent thermal resistance of thermal protection, efficient heat transfer, and outstanding designability, the periodic lattice materials are considered to be the most promising lightweight material integrating structural and thermal functions. However, the load carrying structures of aerospace vehicles composed of periodic lattice materials are often with large numbers of micro-components, the workload of structural modeling and response analysis is enormous. Especially for the structural optimization, it’s more difficult on the calculation due to structural analysis many times. So the traditional finite element analysis and structural optimization techniques are not applicable. In this thesis, we introduce the new multiscale analysis method of Extended Multiscale Finite Element Method (EFsFEM) to achieve the thermal stress calculation and the concurrent optimization of material and structure of the thermoelastic lattice structures.Firstly, based on EMsFEM, we introduce the thermal load for the periodic lattice structure to deduce the expression of equivalent thermal load and achieve the thermal analysis of thermal elastic lattice material structures. In the problem of thermal analysis, the influence of the size effect on material microstructure to the analysis results is discussed, the applicability of the EMsFEM in the analysis of thermal stress of the lattice structure is verified with many numerical examples by comparing the analysis results with EMsFEM to that with the commercial software Ansys.Secondly, based on EMsFEM, we study the minimum compliance design of thermoelastic structure composed of lattice materials with the sectional areas of micro components as design variables under volume constraints by the method of the sequence quadratic programming (SQP). In the optimization, the lattice structure is forced by mechanical load and thermal load simultaneously and the coupling effects between the macro structure and microstructure of the lattice material is considered. In numerical examples, we discuss the influence of the size effect on lattice material microstructure, the amount of base material and the different ratio of thermal load over the mechanical load on optimization results. The optimal design results show that the compliance decreases with the increase of size factor and the ratio of the thermal load over the mechanical load has a significant effect on the configuration of the microstructure of lattice materials. If the thermal load is dominant, there is an optimal amount of base material, and increasing the material alone can not effectively reduce the structural compliance. So the lightweight is not only the requirement of the structural weight loss, but also a requirement of the structural stiffness performance.Lastly, the concurrent topology optimization of material and structure of thermoelastic lattice structures is studied based on EMsFEM. In the concurrent design model, two kinds of independent design variables are introduced, the sectional areas of micro components in micro-scale and the relative densities of macro elements in macro-scale. The method of Porous Anisotropic Materials with Penalty(PAMP) is used to obtain the clear topology of structure configuration. According to EMsFEM. the micro truss unit cell of lattice materials can be equivalent to a macroscopic homogeneous material element with four nodes. So the material/structural concurrent optimization design can be regard as the optimization of sectional areas of micro components in microscopic scale and the optimal distribution of the optimized lattice material in macroscopic scale so as to achieve the minimum compliance in the two scale of lattice material and macro structure. The superiority of lattice material/structure concurrent optimization relative to the single scale design of microstructures is verified in the thesis. Numerical examples show that the optimal configuration of material unit cell is closely related to the geometry and loading conditions of the macro structure. With the increase of size factor of lattice material unit cell, the design freedom of the structure increases, which is favorable to reduce the structural compliance. The optimal topology of macro structure changes with the size of the thermal load, and the optimum design will change with the loads or ratio of different kinds of loads. So we can not apply a material microstructure with some extreme properties to adapt to all macro structures or apply a macro structure under one certain load condition to achieve optimal material configuration for all environment. It’s necessary to develop the concurrent optimization model taking into account the macro structural form, load/boundary conditions and microstructure topology of the lattice material simultaneously to promote the systematic optimization design to obtain the optimal configuration for specific conditions.