【摘要】：為了發(fā)揮材料的最大潛能,減少材料用量,確保最佳使用性能,本文采用均勻化方法和優(yōu)化準則法開展極端復合材料二維、三維微結構拓撲優(yōu)化設計以及多功能極端復合材料三維微結構拓撲優(yōu)化設計。開展了兩相極端復合材料微結構拓撲優(yōu)化設計。首先基于均勻化方法,采用ANSYS結合MATLAB分別對周期性復合材料的等效彈性性能和等效熱傳導系數(shù)進行預測,提出了ANSYS加載求解復合材料等效熱傳導系數(shù)的周期性邊界條件的便捷方法,實現(xiàn)了對均勻化方法的數(shù)值驗證。然后,采用有限元技術,對兩相復合材料進行網格劃分,分別以等效彈性性能和等效熱傳導性能的加權組合為目標函數(shù)建立極端性能微結構拓撲優(yōu)化數(shù)學模型。其中,以單元的相對密度為設計變量,實體材料體分比為約束條件。采用靈敏度過濾技術實現(xiàn)單元靈敏度的平緩過渡,以消除優(yōu)化過程中的數(shù)值不穩(wěn)定現(xiàn)象。運用優(yōu)化準則法對問題進行求解,得到具有極端彈性性能、極端熱傳導性能的二維、三維微結構,分析了不同體分比最優(yōu)微結構的材料分布規(guī)律,并將最優(yōu)剪切模量與Hashin-Shtrikman上限值比較,證明了優(yōu)化結果的合理性和本文方法的可行性。在此基礎之上,將均勻化方法結合優(yōu)化準則法應用到大型風機葉片復合材料三維拓撲優(yōu)化,同時實現(xiàn)其輕量化和極端性能設計。為了更好滿足現(xiàn)代工程應用,以微結構的等效彈性性能和等效熱傳導系數(shù)同時最優(yōu)為優(yōu)化目標,對多功能極端復合材料三維微結構拓撲優(yōu)化設計進行探索,實現(xiàn)了具有極端彈性性能和極端熱傳導系數(shù)的多功能極端復合材料三維微結構拓撲優(yōu)化設計。本文的研究對復合材料微結構拓撲優(yōu)化設計具有一定的指導意義。
[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.
【學位授予單位】：湘潭大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TB33

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