本文關(guān)鍵詞：基于水平集方法的分布式柔順機構(gòu)拓撲優(yōu)化設(shè)計研究　出處：《華南理工大學(xué)》2014年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 柔順機構(gòu) 拓撲優(yōu)化 分布柔順 水平集方法 重新初始化 計算效率

【摘要】：柔順機構(gòu)以其易實現(xiàn)高精度、微型化等獨特的優(yōu)良性能在微納操作、精密測量等許多尖端領(lǐng)域得到了廣泛應(yīng)用，，已成為近年來國際上的研究熱點之一，給機構(gòu)學(xué)帶來了革命性的沖擊，是現(xiàn)代機構(gòu)和精密機械裝備領(lǐng)域發(fā)展的新方向。但是，要真正使得柔順機構(gòu)得到廣泛應(yīng)用和長足發(fā)展，必須以夯實其理論基礎(chǔ)、完善其設(shè)計方法為前提。本文正是在這一背景下應(yīng)用水平集方法對柔順機構(gòu)拓撲優(yōu)化設(shè)計的基本理論和方法進行研究。 論文首先研究了在應(yīng)用水平集方法求解拓撲優(yōu)化問題時的若干難點，具體內(nèi)容包括：根據(jù)符號距離函數(shù)的基本性質(zhì)，構(gòu)造了一種距離保持泛函，并將其嵌入到柔順機構(gòu)拓撲優(yōu)化設(shè)計模型的目標泛函中，這不僅完全避免了耗時的重新初始化，且大大簡化了水平集函數(shù)的初始化工作；在整合了水平集方法及漸進結(jié)構(gòu)優(yōu)化算法的基礎(chǔ)上，探索了在優(yōu)化過程中的拓撲調(diào)整策略以拓展尋優(yōu)空間；針對基于水平集法的拓撲優(yōu)化方法計算復(fù)雜性大、效率低等缺點，提出了速度場預(yù)測——矯正構(gòu)造方法，并對所構(gòu)造的速度方向為目標函數(shù)的可行下降方向進行了數(shù)學(xué)證明；根據(jù)水平集算法具體實施過程中速度場在設(shè)計域內(nèi)均為已知量及其分布特點，提出了形狀敏度過濾法以增大單個迭代步中零水平集的演化幅度；分別應(yīng)用上述技術(shù)對經(jīng)典的結(jié)構(gòu)和柔順機構(gòu)設(shè)計算例進行了優(yōu)化和分析，驗證了上述方法在避免重新初始化、拓展尋優(yōu)空間以及提高計算效率等方面的可行性和有效性。其次，針對傳統(tǒng)柔順機構(gòu)拓撲優(yōu)化中的類鉸鏈(de factohinge)問題，揭示了產(chǎn)生類鉸鏈的內(nèi)在機理，提出了一種最小化性能差建模方法。在此基礎(chǔ)上，應(yīng)用線性加權(quán)組合方式及比例組合方式構(gòu)造了用于分布式柔順機構(gòu)拓撲優(yōu)化的兩類數(shù)學(xué)模型，并針對加權(quán)組合模型中加權(quán)因子難以選擇的問題，提出了加權(quán)因子的自適應(yīng)調(diào)整策略；綜合應(yīng)用不同的設(shè)計案例驗證了兩類數(shù)學(xué)模型在抑制類鉸鏈產(chǎn)生從而獲得分布式柔順機構(gòu)方面的可行性和有效性，并應(yīng)用不同的拓撲優(yōu)化設(shè)計方法對兩類模型進行求解驗證了其通用性。再次，針對某些特殊工況下柔順機構(gòu)拓撲優(yōu)化設(shè)計時的病態(tài)問題，在優(yōu)化模型中引入了輸入端和輸出端柔度，結(jié)合加權(quán)因子的自適應(yīng)調(diào)整策略，構(gòu)造了一種加權(quán)和式目標函數(shù)，從而在將設(shè)計問題由病態(tài)轉(zhuǎn)成適定的同時，有效抑制了類鉸鏈的產(chǎn)生，并應(yīng)用此方法的基本原理針對單輸入多輸出柔順機構(gòu)的設(shè)計進行擴展。最后，總結(jié)全文并對未來的工作進行了展望。 本文的完成對分布式柔順機構(gòu)拓撲優(yōu)化的理論建模以及基于水平集方法的求解算法實現(xiàn)提供了切實可行的思路和方法，對發(fā)展柔順機構(gòu)拓撲優(yōu)化領(lǐng)域的理論水平有重要的意義和價值。
[Abstract]:The compliant mechanism has been widely used in many cutting-edge fields such as micro-nano operation precision measurement and so on because of its easy to achieve high precision and miniaturization. It has become one of the international research hotspots in recent years. It has brought revolutionary impact to mechanism and is a new direction of development in the field of modern mechanism and precision mechanical equipment. However, in order to make the compliant mechanism widely used and develop by leaps and bounds, it is necessary to consolidate its theoretical foundation. It is under this background that the basic theory and method of topology optimization design of compliant mechanism are studied by using level set method. This paper first studies some difficulties in applying the level set method to solve topological optimization problems, including: according to the basic properties of symbolic distance function, a distance preserving functional is constructed. It is embedded into the objective functional of the topology optimization design model of compliant mechanism, which not only avoids the time-consuming reinitialization, but also simplifies the initialization of the level set function. Based on the integration of the level set method and the progressive structure optimization algorithm, the topology adjustment strategy in the optimization process is explored to expand the optimization space. Aiming at the complexity and low efficiency of the topology optimization method based on the level set method, a velocity field prediction-correction method is proposed. It is proved that the velocity direction is the feasible descent direction of the objective function. According to the known velocity field and its distribution in the design domain during the implementation of the level set algorithm, a shape sensitivity filter method is proposed to increase the evolution amplitude of the zero level set in a single iterative step. The design examples of classical structure and compliant mechanism are optimized and analyzed by using the above techniques, and it is verified that the above method can avoid reinitialization. Expand the optimization space and improve the efficiency of the feasibility and effectiveness. Secondly, aiming at the traditional compliant mechanism topology optimization of the hinge-like de factohinge) problem. In this paper, the inherent mechanism of producing hinge-like chain is revealed, and a modeling method for minimizing the poor performance is proposed. Two kinds of mathematical models for topology optimization of distributed compliant mechanism are constructed by linear weighted combination and proportional combination. The adaptive adjustment strategy of weighting factor is proposed. Comprehensive application of different design cases to verify the feasibility and effectiveness of the two kinds of mathematical models in restraining the generation of hinge-like mechanism to obtain the distributed compliance mechanism. Using different topology optimization design methods to solve the two kinds of models to verify its versatility. Thirdly, aiming at the ill-condition of topology optimization design of compliant mechanism under some special conditions. In the optimization model, the input and output flexibility are introduced, and a weighted sum objective function is constructed by combining the adaptive adjustment strategy of the weighting factor, so that the design problem can be transformed from ill-conditioned to suitable at the same time. The basic principle of this method is applied to expand the design of single-input multi-output compliant mechanism. Finally, the paper summarizes the full text and prospects for future work. The completion of this paper provides practical ideas and methods for the theoretical modeling of topology optimization of distributed compliant mechanism and the realization of the algorithm based on the level set method. It is of great significance and value to develop the theoretical level of topological optimization of compliant mechanism.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TH112

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