结构拓扑优化中基于结构骨架的特征尺寸控制方法研究
发布时间：2019-06-19 14:20
【摘要】：虽然经过几十年来的发展,结构拓扑优化已经受到了工业领域的广泛关注,但是随着研究内容的复杂程度不断提高,研究对象的领域不断扩大,结构拓扑优化发展前沿遇到了前所未有的挑战。本文所致力的结构拓扑优化中特征尺寸控制问题研究,正是结构拓扑优化长期发展以来,众多科研工作者力图从不同角度解决却始终未能获得实质性突破的难点问题之一。结构特征尺寸(structural feature size)是指结构中构件长度、截面宽度、倒角半径等能够表现结构几何特征的参数。在工程设计中,有时出于加工设备的能力及精度的考虑,往往要求结构中梁的截面宽度小于某一临界值,或者出于结构稳定性的考虑,需要结构中梁的截面宽度大于某一临界值。在装配系统中,往往要求某些特定构件间的安装位置大于或小于某一特定距离,这样才能确保构件的安全性与稳定性。针对传统特征尺寸控制方法的诸多不足,本文基于结构骨架这一计算图形学领域内的重要概念,进行了大量关于结构特征尺寸控制相关的研究。首先,通过结构骨架概念的引入首次给出了结构尺寸和结构特征尺寸严格的数学定义。提出了一种显式、局部的特征尺寸控制方法,并从理论上证明了该方法的合理性与有效性。其次,基于结构骨架的特征尺寸控制方法是一种纯粹的几何约束,其不依赖于任何物理问题和拓扑优化方法。本文分别针对目前应用最广泛的SIMP (Solid Isotropic Material with Penalization)和水平集(Level Set Method)拓扑优化框架,分别给出了骨架提取策略,特征尺寸约束,优化列式以及灵敏度分析,并通过数值算例证明了本文提出算法的有效性。最后,本文提出的基于结构骨架的特征尺寸控制方法不仅适用于实体结构的特征尺寸控制,同样也适用于孔洞的特征尺寸控制。本文针对构件布局优化中的构件距离控制问题,给出了一套基于特征尺寸控制方法的求解过程,和传统的构件不相交约束相比,构件距离控制问题更加复杂并且更加具有应用前景。本文采用理论推导与数值验证相结合的形式,通过引入结构骨架这一能够充分体现结构几何信息的有力工具,为突破拓扑优化中结构特征尺寸控制这一难题提供了新思路,具有鲜明的创新性。相关研究成果对于拓展结构拓扑优化方法在复杂结构及重大装备创新设计中的应用也有重要的参考价值。
[Abstract]:After several decades of development, structural topology optimization has been widely concerned in the field of industry, but as the complexity of research content is increasing, the field of research object is expanding, and the leading edge of structural topology optimization has encountered an unprecedented challenge. The study of the feature size control in the structure topology optimization, which has been devoted to the optimization of the structure topology, is one of the difficult problems that many researchers have tried to solve at different angles and never get a substantial breakthrough since the long-term development of the structural topology optimization. The structural feature size refers to the parameters that can show structural geometry in the structure, such as the length of the component, the width of the section, the radius of the chamfer, and the like. In engineering design, sometimes for the consideration of the capability and precision of the processing equipment, it is often required that the cross-section width of the beam in the structure is less than a certain critical value, or for structural stability, the cross-section width of the beam in the structure needs to be greater than a certain critical value. In an assembly system, it is often required that the mounting position between certain specific components is greater than or less than a certain distance in order to ensure the safety and stability of the components. In view of the shortcomings of the traditional feature size control method, this paper has carried out a large number of studies on the control of the size of the structural features based on the important concepts in the field of the computational graphics of the structural skeleton. First, a mathematical definition of structural size and structural feature size is given for the first time through the introduction of the concept of the structural framework. An explicit and local method of feature size control is proposed, and the rationality and validity of the method are proved from the theory. Secondly, the feature size control method based on the structure skeleton is a pure geometric constraint, which is independent of any physical problem and topology optimization method. In this paper, the frame extraction strategy, the feature size constraint, the optimization value and the sensitivity analysis are respectively given for the most widely applied SIP (Solid Isotropic Material with Penalization) and the Level Set Method, and the effectiveness of the proposed algorithm is proved by numerical examples. Finally, the feature size control method based on the structure skeleton is not only applicable to the feature size control of the solid structure, but also to the feature size control of the hole. In order to solve the problem of component distance control in component layout optimization, a set of solving process based on feature size control method is given, and the component distance control problem is more complex and has more application prospect than the traditional component non-intersecting constraint. In this paper, the form of the combination of the theoretical derivation and the numerical verification is adopted. By introducing the structure skeleton, it can fully reflect the powerful tools of the structural geometry information, and provides a new idea for breaking the problem of the structural feature size control in the topology optimization. The relevant research results have important reference value to the application of the extended structure topology optimization method in the complex structure and the important equipment innovation design.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O224;TP391.72
本文编号：2502410
[Abstract]:After several decades of development, structural topology optimization has been widely concerned in the field of industry, but as the complexity of research content is increasing, the field of research object is expanding, and the leading edge of structural topology optimization has encountered an unprecedented challenge. The study of the feature size control in the structure topology optimization, which has been devoted to the optimization of the structure topology, is one of the difficult problems that many researchers have tried to solve at different angles and never get a substantial breakthrough since the long-term development of the structural topology optimization. The structural feature size refers to the parameters that can show structural geometry in the structure, such as the length of the component, the width of the section, the radius of the chamfer, and the like. In engineering design, sometimes for the consideration of the capability and precision of the processing equipment, it is often required that the cross-section width of the beam in the structure is less than a certain critical value, or for structural stability, the cross-section width of the beam in the structure needs to be greater than a certain critical value. In an assembly system, it is often required that the mounting position between certain specific components is greater than or less than a certain distance in order to ensure the safety and stability of the components. In view of the shortcomings of the traditional feature size control method, this paper has carried out a large number of studies on the control of the size of the structural features based on the important concepts in the field of the computational graphics of the structural skeleton. First, a mathematical definition of structural size and structural feature size is given for the first time through the introduction of the concept of the structural framework. An explicit and local method of feature size control is proposed, and the rationality and validity of the method are proved from the theory. Secondly, the feature size control method based on the structure skeleton is a pure geometric constraint, which is independent of any physical problem and topology optimization method. In this paper, the frame extraction strategy, the feature size constraint, the optimization value and the sensitivity analysis are respectively given for the most widely applied SIP (Solid Isotropic Material with Penalization) and the Level Set Method, and the effectiveness of the proposed algorithm is proved by numerical examples. Finally, the feature size control method based on the structure skeleton is not only applicable to the feature size control of the solid structure, but also to the feature size control of the hole. In order to solve the problem of component distance control in component layout optimization, a set of solving process based on feature size control method is given, and the component distance control problem is more complex and has more application prospect than the traditional component non-intersecting constraint. In this paper, the form of the combination of the theoretical derivation and the numerical verification is adopted. By introducing the structure skeleton, it can fully reflect the powerful tools of the structural geometry information, and provides a new idea for breaking the problem of the structural feature size control in the topology optimization. The relevant research results have important reference value to the application of the extended structure topology optimization method in the complex structure and the important equipment innovation design.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O224;TP391.72
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