結構拓撲優(yōu)化中基于結構骨架的特征尺寸控制方法研究
發(fā)布時間：2019-06-19 14:20
【摘要】：雖然經過幾十年來的發(fā)展,結構拓撲優(yōu)化已經受到了工業(yè)領域的廣泛關注,但是隨著研究內容的復雜程度不斷提高,研究對象的領域不斷擴大,結構拓撲優(yōu)化發(fā)展前沿遇到了前所未有的挑戰(zhàn)。本文所致力的結構拓撲優(yōu)化中特征尺寸控制問題研究,正是結構拓撲優(yōu)化長期發(fā)展以來,眾多科研工作者力圖從不同角度解決卻始終未能獲得實質性突破的難點問題之一。結構特征尺寸(structural feature size)是指結構中構件長度、截面寬度、倒角半徑等能夠表現(xiàn)結構幾何特征的參數。在工程設計中,有時出于加工設備的能力及精度的考慮,往往要求結構中梁的截面寬度小于某一臨界值,或者出于結構穩(wěn)定性的考慮,需要結構中梁的截面寬度大于某一臨界值。在裝配系統(tǒng)中,往往要求某些特定構件間的安裝位置大于或小于某一特定距離,這樣才能確保構件的安全性與穩(wěn)定性。針對傳統(tǒng)特征尺寸控制方法的諸多不足,本文基于結構骨架這一計算圖形學領域內的重要概念,進行了大量關于結構特征尺寸控制相關的研究。首先,通過結構骨架概念的引入首次給出了結構尺寸和結構特征尺寸嚴格的數學定義。提出了一種顯式、局部的特征尺寸控制方法,并從理論上證明了該方法的合理性與有效性。其次,基于結構骨架的特征尺寸控制方法是一種純粹的幾何約束,其不依賴于任何物理問題和拓撲優(yōu)化方法。本文分別針對目前應用最廣泛的SIMP (Solid Isotropic Material with Penalization)和水平集(Level Set Method)拓撲優(yōu)化框架,分別給出了骨架提取策略,特征尺寸約束,優(yōu)化列式以及靈敏度分析,并通過數值算例證明了本文提出算法的有效性。最后,本文提出的基于結構骨架的特征尺寸控制方法不僅適用于實體結構的特征尺寸控制,同樣也適用于孔洞的特征尺寸控制。本文針對構件布局優(yōu)化中的構件距離控制問題,給出了一套基于特征尺寸控制方法的求解過程,和傳統(tǒng)的構件不相交約束相比,構件距離控制問題更加復雜并且更加具有應用前景。本文采用理論推導與數值驗證相結合的形式,通過引入結構骨架這一能夠充分體現(xiàn)結構幾何信息的有力工具,為突破拓撲優(yōu)化中結構特征尺寸控制這一難題提供了新思路,具有鮮明的創(chuàng)新性。相關研究成果對于拓展結構拓撲優(yōu)化方法在復雜結構及重大裝備創(chuàng)新設計中的應用也有重要的參考價值。
[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.
【學位授予單位】：大連理工大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O224;TP391.72
本文編號：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.
【學位授予單位】：大連理工大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O224;TP391.72
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