【摘要】：點陣材料作為一種新型的多功能材料具有高比剛度、比強度,同時由于其內部高孔隙率,使其具有良好的防隔熱、減振降噪、沖擊吸能及多功能應用等優(yōu)點,被廣泛應用于航天航空、船舶、汽車制造等領域。但是對于點陣材料構成的結構進行力學性能分析時,由于其內部含有大量微結構,使用傳統的有限元分析技術不再適用。因此,本文基于擴展多尺度有限元法(Extended Multiscale Finite Element Method, EMsFEM)對該類點陣材料進行力學分析,圍繞點陣材料結構設計時的強度指標、剛度指標及穩(wěn)定性指標等性能要求,開展了大量應力相關的點陣結構多尺度并發(fā)優(yōu)化設計研究。針對點陣結構局部微桿件強度及穩(wěn)定性的不同失效模式,建立了考慮強度約束點陣材料輕量化設計模型Ⅰ和同時考慮強度和穩(wěn)定性約束點陣材料輕量化設計模型Ⅱ。計算中著重討論了尺寸因子對優(yōu)化結果的影響,計算發(fā)現隨著尺寸因子n的增大,優(yōu)化模型Ⅰ強度約束對點陣材料輕量化設計影響不明顯,結構最小重量基本不變；而優(yōu)化模型Ⅱ由于施加穩(wěn)定性約束,隨著尺寸因子n的增大,結構最小重量降低。針對于復雜的點陣結構分析,最大應力可能發(fā)生在任何一個構件、單元,使得應力約束和穩(wěn)定性約束個數急劇增加,導致考慮局部應力約束優(yōu)化模型不再適用。為此,文中提出了一種新的凝聚函數,該函數可有效的將大規(guī)模的局部約束凝聚成一個整體約束,解決了“次峰值”困難,實現了考慮全局強度及穩(wěn)定性約束的點陣材料多尺度優(yōu)化設計�？紤]點陣材料結構微觀尺度和宏觀尺度相互影響,在宏觀尺度上引入宏觀單元的相對密度p和微觀尺度上引入微桿件的截面積A,以微觀桿件的強度和剛度為約束,結構重量最小為目標,構建了宏微觀雙尺度優(yōu)化模型,實現了考慮結構強度和剛度約束下點陣材料結構并發(fā)優(yōu)化設計。通過數值模擬研究了負泊松比柵格材料、加筋板結構、夾芯板結構的抗熱屈曲性能,等材料用量的負泊松比柵格結構比正交柵格結構具有更高的熱屈曲臨界失穩(wěn)載荷；而正交加筋板則比負泊松比加筋板抗熱屈曲性能更好,但是負泊松比夾芯板抵抗熱屈曲性能又優(yōu)于正交夾芯板。因此,在熱承載結構設計時,需要對結構進行合理的選擇和設計,才能滿足工程實際安全可靠的要求。
[Abstract]:As a new type of multifunctional material, lattice material has the advantages of high specific stiffness, specific strength, high internal porosity, good thermal insulation, vibration and noise reduction, shock energy absorption and multifunctional application. It is widely used in aerospace, ship, automobile manufacturing and other fields. However, the traditional finite element analysis technique is no longer suitable for the analysis of mechanical properties of the structure made of lattice materials because of the large number of microstructures in the structure. Therefore, based on the extended multi-scale finite element method (Extended Multiscale Finite Element Method, EMsFEM), the mechanical analysis of this kind of lattice materials is carried out, and the performance requirements such as strength index, stiffness index and stability index in the structural design of lattice materials are discussed. A large number of stress-dependent multiscale concurrent optimization design studies of lattice structures have been carried out. Aiming at the different failure modes of the strength and stability of the local microbars of lattice structures, a lightweight design model for lattice materials with strength constraints and a lightweight design model for lattice materials with both strength and stability constraints is established. In the calculation, the influence of dimension factor on the optimization result is discussed. It is found that with the increase of dimension factor n, the strength constraint of optimization model I has no obvious influence on the lightweight design of lattice materials, and the minimum weight of the structure is basically unchanged. However, the minimum weight of the structure decreases with the increase of the size factor n due to the stability constraints imposed on the optimization model 鈪，

本文編號：2370261