【摘要】：本課題受國家自然科學基金項目“幾何約束條件下連續(xù)體結構拓撲與形狀統(tǒng)一優(yōu)化設計方法研究(50975107)”的支持。針對當前拓撲優(yōu)化設計方法不能與形狀優(yōu)化、尺寸優(yōu)化相融合的問題，本文提出了一種參數(shù)化水平集拓撲、形狀、尺寸統(tǒng)一優(yōu)化的方法，并將其推廣到連續(xù)體結構的剛度設計，動力學優(yōu)化設計中。 首先，本文介紹了標準水平集法和參數(shù)化水平集法的基本理論，并分別比較了其優(yōu)缺點。在此基礎上，針對規(guī)則孔洞的尺寸或位置設計問題，將規(guī)則孔洞作為幾何約束，，提出了一種參數(shù)化水平集尺寸優(yōu)化設計方法，該方法同時包含了隱式表達和參數(shù)化表達的優(yōu)點，為構建統(tǒng)一優(yōu)化模型提供了前提條件。 第二，將基于水平集法的拓撲形狀優(yōu)化模型與尺寸優(yōu)化模型結合在一起，構建出統(tǒng)一優(yōu)化模型，推導了靈敏度分析公式，并采用基于Kuhn-Tucker條件的優(yōu)化準則法求解。同時，針對統(tǒng)一優(yōu)化設計中出現(xiàn)的數(shù)值問題，如規(guī)則孔洞的多孔干涉問題，孔洞尺寸厚度問題，提出了采用尺寸約束和公差帶的辦法來解決。 第三，提出了一種擴展有限元法來求解統(tǒng)一優(yōu)化模型。拓撲優(yōu)化的鋸齒狀邊界問題一直沒有得到很好的解決，本文采用擴展有限元法有效的解決了這一問題。該方法在邊界單元處計算精度高，不僅提高了優(yōu)化結果的邊界光順度，同時減少了計算時間，使得收斂過程更加穩(wěn)定。 最后，基于本文提出的水平集統(tǒng)一優(yōu)化方法，同時考慮拓撲形狀優(yōu)化和尺寸優(yōu)化，設計了一種新型的LED分揀臂，大幅度提高了分揀臂的一階頻率，該工程案例進一步驗證了統(tǒng)一優(yōu)化方法在動力學設計方面的適用性和精確性。
[Abstract]:This topic is supported by the project of National Natural Science Foundation of China, "study on the Unified Optimization Design method of Topology and shape of Continuum structures under geometric constraints (50975107)". Aiming at the problem that the current topology optimization method can not be combined with shape optimization and dimension optimization, a parameterized horizontal set topology, shape and dimension optimization method is proposed in this paper, which is extended to the stiffness design of continuum structure. Dynamic optimization design. Firstly, the basic theories of standard level set method and parameterized level set method are introduced, and their advantages and disadvantages are compared. On this basis, aiming at the problem of size or position design of regular holes, a parameterized horizontal set size optimization design method is proposed, which includes the advantages of implicit representation and parametric representation. It provides the precondition for constructing the unified optimization model. Secondly, combining the topological shape optimization model based on the level set method with the dimension optimization model, the unified optimization model is constructed, the sensitivity analysis formula is derived, and the optimization criterion method based on Kuhn-Tucker condition is used to solve the problem. At the same time, aiming at the numerical problems in the unified optimization design, such as the porous interference of regular holes and the hole size thickness, the method of dimension constraint and tolerance band is proposed to solve the problem. Thirdly, an extended finite element method is proposed to solve the unified optimization model. The sawtooth boundary problem of topology optimization has not been solved well, and the extended finite element method is used to solve this problem effectively. The method not only improves the boundary smoothness of the optimization results, but also reduces the calculation time and makes the convergence process more stable. Finally, based on the level set optimization method proposed in this paper, considering the topology optimization and size optimization, a new LED sorting arm is designed, which greatly improves the first order frequency of the sorting arm. The engineering case further verifies the applicability and accuracy of the unified optimization method in dynamic design.
【學位授予單位】：華中科技大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TH122

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