【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(nèi)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(yīng)用等優(yōu)點,被廣泛應(yīng)用于航天航空、船舶、汽車制造等領(lǐng)域。但是對于點陣材料構(gòu)成的結(jié)構(gòu)進行力學性能分析時,由于其內(nèi)部含有大量微結(jié)構(gòu),使用傳統(tǒng)的有限元分析技術(shù)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(jié)構(gòu)設(shè)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(yīng)力相關(guān)的點陣結(jié)構(gòu)多尺度并發(fā)優(yōu)化設(shè)計研究。針對點陣結(jié)構(gòu)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(shè)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(shè)計模型Ⅱ。計算中著重討論了尺寸因子對優(yōu)化結(jié)果的影響,計算發(fā)現(xiàn)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(shè)計影響不明顯,結(jié)構(gòu)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(jié)構(gòu)最小重量降低。針對于復(fù)雜的點陣結(jié)構(gòu)分析,最大應(yīng)力可能發(fā)生在任何一個構(gòu)件、單元,使得應(yīng)力約束和穩(wěn)定性約束個數(shù)急劇增加,導(dǎo)致考慮局部應(yīng)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(shù),該函數(shù)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(xiàn)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(shè)計。考慮點陣材料結(jié)構(gòu)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(jié)構(gòu)重量最小為目標,構(gòu)建了宏微觀雙尺度優(yōu)化模型,實現(xiàn)了考慮結(jié)構(gòu)強度和剛度約束下點陣材料結(jié)構(gòu)并發(fā)優(yōu)化設(shè)計。通過數(shù)值模擬研究了負泊松比柵格材料、加筋板結(jié)構(gòu)、夾芯板結(jié)構(gòu)的抗熱屈曲性能,等材料用量的負泊松比柵格結(jié)構(gòu)比正交柵格結(jié)構(gòu)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(jié)構(gòu)設(shè)計時,需要對結(jié)構(gòu)進行合理的選擇和設(shè)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