本文選題：漸進結構優(yōu)化 + 拓撲優(yōu)化　； 參考：《重慶大學》2012年碩士論文

【摘要】：科學技術的不斷發(fā)展對結構的力學性能和經濟性提出了越來越高的要求，，從而促進設計方法的研究和迅速發(fā)展。結構最優(yōu)化設計正是這樣一個迅速發(fā)展的設計領域。結構優(yōu)化方法使得設計人員可進行主動、創(chuàng)造性的設計，而結構拓撲優(yōu)化則是后續(xù)的形狀、尺寸優(yōu)化設計的基礎。 飛輪等回轉體作為一類重要的機械零件結構類型，其拓撲形式不僅影響著這類物體力學性能，同時影響如飛輪轉動慣量等工作性能。本文采用漸進結構優(yōu)化方法（ESO）對含有剛度、轉動慣量、體積要求等信息的回轉體進行拓撲優(yōu)化研究。 本文推導了離心力作用下的單元剛度靈敏度計算公式，并采用“硬殺”策略的雙向漸進結構優(yōu)化方法（BESO）對二維和三維的回轉體進行優(yōu)化分析。依據多目標優(yōu)化的乘除法策略，提出了基于靈敏度乘除法的雙向漸進結構優(yōu)化的多目標處理方法，成功實現了某汽車驅動盤和某飛輪的多目標拓撲優(yōu)化設計。同時對該方法在特殊情形下的失效做了分析。針對剛度靈敏度和轉動慣量靈敏度不同的分布規(guī)律，提出了靈敏度再處理技術，以此平衡兩種不同類型靈敏度對單元刪增的影響，并指出靈敏度再處理技術是一種特殊的過濾技術。 本文就回轉體一定轉動慣量下單元數目不可控的問題，提出了以最大剛度為優(yōu)化目標，以轉動慣量為約束下的漸進結構優(yōu)化方法。結構的漸進變化仍依據體積的進化率，在轉動慣量滿足約束條件時，應盡量增大結構體積以最大程度提高結構剛度。進而實現了以最大剛度為優(yōu)化目標，體積和轉動慣量同時約束的多約束優(yōu)化問題。在結構漸進到體積約束限且轉動慣量不滿足約束條件時，通過構造拉格朗日函數將單元轉動慣量信息包含在單元靈敏度中，從而使轉動慣量逐步向約束范圍內逼近。依據提出的優(yōu)化算法，實現了某飛輪的結構拓撲優(yōu)化，算例表明此方法的正確性和有效性。
[Abstract]:With the development of science and technology, the mechanical properties and economy of structures are required more and more, thus promoting the research and rapid development of design methods. Structural optimization design is such a rapidly developing field of design. The structural optimization method enables designers to design actively and creatively, while structural topology optimization is the basis of subsequent shape and size optimization design. As an important structural type of mechanical parts, the topological form of flywheel iso-rotary body not only affects the mechanical properties of this kind of object, but also affects the working performance such as the moment of inertia of flywheel. In this paper, an evolutionary structural optimization method (ESO) is used to study the topology optimization of a rotary body with information such as stiffness, moment of inertia and volume requirement. In this paper, the formulas for calculating the sensitivity of element stiffness under centrifugal force are derived, and the bi-directional progressive structural optimization method of "hard kill" strategy is used to optimize the two-dimensional and three-dimensional rotary bodies. According to the strategy of multiplication and division of multi-objective optimization, a multi-objective method of bidirectional progressive structural optimization based on sensitivity multiplication and division method is proposed, and the multi-objective topology optimization design of a driving disk and a flywheel is successfully realized. At the same time, the failure of the method in special cases is analyzed. Aiming at the different distribution of stiffness sensitivity and moment of inertia sensitivity, a sensitivity reprocessing technique is proposed to balance the effects of two different types of sensitivity on element deletion. It is pointed out that sensitivity reprocessing is a special filtering technique. In this paper, for the problem that the number of elements is not controllable under a certain moment of inertia of a rotary body, a progressive structural optimization method with the maximum stiffness as the optimization objective and the moment of inertia as the constraint is proposed. The gradual change of the structure is still based on the evolution rate of the volume. When the moment of inertia satisfies the constraint condition, the volume of the structure should be increased as much as possible in order to increase the stiffness of the structure to the maximum extent. Furthermore, the multi-constraint optimization problem with the maximum stiffness as the optimization objective and the volume and moment of inertia simultaneously constrained is realized. When the structure is progressive to the volume constraint limit and the moment of inertia does not satisfy the constraint conditions, the information of the element moment of inertia is included in the element sensitivity by constructing the Lagrangian function, which makes the moment of inertia gradually approximate to the constraint range. According to the proposed optimization algorithm, the structure topology optimization of a flywheel is realized. The example shows that the method is correct and effective.
【學位授予單位】：重慶大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TH133.7

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