基于水平集方法的分布式柔顺机构拓扑优化设计研究

发布时间：2017-12-31 09:28

本文关键词：基于水平集方法的分布式柔顺机构拓扑优化设计研究　出处：《华南理工大学》2014年博士论文　论文类型：学位论文

【摘要】：柔顺机构以其易实现高精度、微型化等独特的优良性能在微纳操作、精密测量等许多尖端领域得到了广泛应用，，已成为近年来国际上的研究热点之一，给机构学带来了革命性的冲击，是现代机构和精密机械装备领域发展的新方向。但是，要真正使得柔顺机构得到广泛应用和长足发展，必须以夯实其理论基础、完善其设计方法为前提。本文正是在这一背景下应用水平集方法对柔顺机构拓扑优化设计的基本理论和方法进行研究。论文首先研究了在应用水平集方法求解拓扑优化问题时的若干难点，具体内容包括：根据符号距离函数的基本性质，构造了一种距离保持泛函，并将其嵌入到柔顺机构拓扑优化设计模型的目标泛函中，这不仅完全避免了耗时的重新初始化，且大大简化了水平集函数的初始化工作；在整合了水平集方法及渐进结构优化算法的基础上，探索了在优化过程中的拓扑调整策略以拓展寻优空间；针对基于水平集法的拓扑优化方法计算复杂性大、效率低等缺点，提出了速度场预测——矫正构造方法，并对所构造的速度方向为目标函数的可行下降方向进行了数学证明；根据水平集算法具体实施过程中速度场在设计域内均为已知量及其分布特点，提出了形状敏度过滤法以增大单个迭代步中零水平集的演化幅度；分别应用上述技术对经典的结构和柔顺机构设计算例进行了优化和分析，验证了上述方法在避免重新初始化、拓展寻优空间以及提高计算效率等方面的可行性和有效性。其次，针对传统柔顺机构拓扑优化中的类铰链(de factohinge)问题，揭示了产生类铰链的内在机理，提出了一种最小化性能差建模方法。在此基础上，应用线性加权组合方式及比例组合方式构造了用于分布式柔顺机构拓扑优化的两类数学模型，并针对加权组合模型中加权因子难以选择的问题，提出了加权因子的自适应调整策略；综合应用不同的设计案例验证了两类数学模型在抑制类铰链产生从而获得分布式柔顺机构方面的可行性和有效性，并应用不同的拓扑优化设计方法对两类模型进行求解验证了其通用性。再次，针对某些特殊工况下柔顺机构拓扑优化设计时的病态问题，在优化模型中引入了输入端和输出端柔度，结合加权因子的自适应调整策略，构造了一种加权和式目标函数，从而在将设计问题由病态转成适定的同时，有效抑制了类铰链的产生，并应用此方法的基本原理针对单输入多输出柔顺机构的设计进行扩展。最后，总结全文并对未来的工作进行了展望。本文的完成对分布式柔顺机构拓扑优化的理论建模以及基于水平集方法的求解算法实现提供了切实可行的思路和方法，对发展柔顺机构拓扑优化领域的理论水平有重要的意义和价值。
[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.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TH112

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