基于均匀化极端复合材料微结构拓扑优化设计

发布时间：2018-10-15 12:56

【摘要】：为了发挥材料的最大潜能,减少材料用量,确保最佳使用性能,本文采用均匀化方法和优化准则法开展极端复合材料二维、三维微结构拓扑优化设计以及多功能极端复合材料三维微结构拓扑优化设计。开展了两相极端复合材料微结构拓扑优化设计。首先基于均匀化方法,采用ANSYS结合MATLAB分别对周期性复合材料的等效弹性性能和等效热传导系数进行预测,提出了ANSYS加载求解复合材料等效热传导系数的周期性边界条件的便捷方法,实现了对均匀化方法的数值验证。然后,采用有限元技术,对两相复合材料进行网格划分,分别以等效弹性性能和等效热传导性能的加权组合为目标函数建立极端性能微结构拓扑优化数学模型。其中,以单元的相对密度为设计变量,实体材料体分比为约束条件。采用灵敏度过滤技术实现单元灵敏度的平缓过渡,以消除优化过程中的数值不稳定现象。运用优化准则法对问题进行求解,得到具有极端弹性性能、极端热传导性能的二维、三维微结构,分析了不同体分比最优微结构的材料分布规律,并将最优剪切模量与Hashin-Shtrikman上限值比较,证明了优化结果的合理性和本文方法的可行性。在此基础之上,将均匀化方法结合优化准则法应用到大型风机叶片复合材料三维拓扑优化,同时实现其轻量化和极端性能设计。为了更好满足现代工程应用,以微结构的等效弹性性能和等效热传导系数同时最优为优化目标,对多功能极端复合材料三维微结构拓扑优化设计进行探索,实现了具有极端弹性性能和极端热传导系数的多功能极端复合材料三维微结构拓扑优化设计。本文的研究对复合材料微结构拓扑优化设计具有一定的指导意义。
[Abstract]:In order to maximize the potential of materials, reduce the amount of materials, and ensure the best performance, the homogenization method and optimization criteria are used to carry out two-dimensional extreme composite materials. Three-dimensional microstructural topology optimization design and multi-functional extreme composite three-dimensional microstructural topology optimization design. Topology optimization design of two-phase extreme composite microstructures was carried out. Based on the homogenization method, ANSYS and MATLAB are used to predict the equivalent elastic properties and heat conductivity of periodic composites. A convenient method for solving the periodic boundary conditions of equivalent heat conduction coefficient of composites under ANSYS loading is presented. The numerical verification of the homogenization method is realized. Then, the finite element method is used to mesh the two-phase composite materials, and the mathematical model of topology optimization of microstructures with extreme performance is established using the weighted combination of the equivalent elastic property and the equivalent heat conduction property as the objective function respectively. The relative density of the element is taken as the design variable and the volume fraction of the solid material is taken as the constraint condition. In order to eliminate the numerical instability in the optimization process, the sensitivity filtering technique is used to realize the smooth transition of the unit sensitivity. Two and three dimensional microstructures with extreme elastic properties and extreme heat conduction properties are obtained by solving the problem by using the optimization criterion method. The material distribution laws of the optimal microstructures with different volume fraction are analyzed. By comparing the optimal shear modulus with the upper limit of Hashin-Shtrikman, the rationality of the optimization results and the feasibility of the proposed method are proved. On this basis, the homogenization method combined with the optimization criterion method is applied to the three-dimensional topology optimization of the composite material of the large fan blade, and its lightweight and extreme performance design is realized at the same time. In order to better meet the needs of modern engineering applications, the optimal design of three-dimensional microstructure topology of multifunctional extreme composite materials is explored, in which the equivalent elastic properties and equivalent heat conduction coefficients of microstructures are simultaneously optimized. Three dimensional topology optimization design of multifunctional extreme composite materials with extreme elastic properties and extreme thermal conductivity is realized. The research in this paper has certain guiding significance for the topology optimization design of composite microstructures.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33

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