本文選題：拓撲優(yōu)化　切入點：雙模量材料　出處：《西北農(nóng)林科技大學》2016年博士論文　論文類型：學位論文

【摘要】：結(jié)構(gòu)優(yōu)化的目的是結(jié)構(gòu)在滿足給定性能條件下盡可能地降低耗費、提高效能。連續(xù)體內(nèi)材料布局(拓撲)優(yōu)化是最新的結(jié)構(gòu)優(yōu)化理論,目前已被廣泛地應用于諸多工程設計領域。一般地,水工結(jié)構(gòu)中的材料具有如下特點之一:結(jié)構(gòu)中可能包含多種剛度不同的材料(如堆石壩等);結(jié)構(gòu)中的材料呈雙模量特性(如混凝土等)。雙模量材料是指在同一方向上的拉伸與壓縮彈性模量不等的材料。因此,雙模量材料的彈性本構(gòu)張量是應力相關(guān)的,使得含雙模量材料的結(jié)構(gòu)變形分析需要多次迭代方可獲得精確位移場。對于像面板堆石壩這樣的復雜結(jié)構(gòu),其所含剛度不同的材料相數(shù)很多時,采用現(xiàn)有的拓撲優(yōu)化方法無法有效分析其最優(yōu)材料布局。而采用現(xiàn)有的拓撲優(yōu)化方法也無法高效分析雙模量材料布局優(yōu)化問題。若不考慮雙模量材料特性進行結(jié)構(gòu)優(yōu)化設計時,容易產(chǎn)生安全隱患。本論文針對以上困難,提出四個典型拓撲優(yōu)化問題:復雜結(jié)構(gòu)中超多相材料布局優(yōu)化、單相僅抗拉或僅抗壓材料布局優(yōu)化、單相雙模量材料拓撲優(yōu)化以及病態(tài)工況拓撲優(yōu)化問題,展開研究并獨立提出四種優(yōu)化算法。具體研究成果如下:(1)針對復雜結(jié)構(gòu)含有超多相材料布局優(yōu)化問題,提出了多相材料布局優(yōu)化的應變能密度(strain energy density:SED)排序法。本算法的思想是結(jié)構(gòu)中SED高的區(qū)域布置高模量材料,低的區(qū)域布置低模量材料:首先,將結(jié)構(gòu)中的材料按照模量由高至低依次編號;其次,在結(jié)構(gòu)分析完成后,將滿足體積約束(材料指定用量)的材料所在區(qū)域設為非設計域,剩余材料所在區(qū)域的單元按照SED升序排列;然后,前有限個SED最低的單元中的材料被置換為相鄰的低模量材料;最后,多次迭代后所有材料體積約束條件滿足時停止分析。通過系列數(shù)值算例與變密度法結(jié)果的比較驗證了算法的有效性,并討論了材料模量之間的差異,各相材料體積率的差異以及材料種類等因素對布局結(jié)果的影響。以此為基礎建立了面板堆石壩壩料分區(qū)設計的多相材料布局優(yōu)化模型,通過算例討論了高面板堆石壩壩體分區(qū)規(guī)律,為工程設計提供參考。(2)提出了材料替換—參考區(qū)間法分析結(jié)構(gòu)中僅抗拉(單拉)或僅抗壓(單壓)材料布局優(yōu)化問題。單拉或單壓材料屬于特殊的雙模量材料。首先,為了便于優(yōu)化過程中的結(jié)構(gòu)重分析,在每次結(jié)構(gòu)分析前將原單拉/壓材料替換為一種各向同性材料;其次,利用當前應力狀態(tài)以及材料的單拉或單壓特點計算有效SED;然后,通過比較有效SED與參考區(qū)間的上、下界確定局部材料的偽密度的增減,完成設計變量更新;最后,為了滿足約束條件(如體積約束、位移約束等),在優(yōu)化過程中更新參考區(qū)間,直至算法收斂。利用梁、橋類水工結(jié)構(gòu)數(shù)值算例討論了本算法在分析結(jié)構(gòu)含單拉或單壓材料布局優(yōu)化時的有效性以及計算效率。討論了材料的單拉/壓特性對優(yōu)化結(jié)果的影響。在該算法基礎上還討論了材料的泊松比對布局結(jié)果的影響。(3)提出材料替換—梯度法用于分析普通雙模量材料拓撲優(yōu)化問題。在該算法中,首先,將設計域內(nèi)的雙模量材料替換為兩種各向同性材料;其次,根據(jù)單元應力狀態(tài)計算拉伸SED和壓縮SED以及單元剛度修正因子;再次,比較拉伸SED與壓縮SED的大小確定兩種各向同性材料中的一種材料用于下次結(jié)構(gòu)分析;然后,利用單元剛度修正因子修正單元剛度陣,以確保局部剛度在替換前后一致,進而確保結(jié)構(gòu)內(nèi)的傳力路徑一致。最后,利用梯度法更新單元的偽密度。利用深梁、臺體等數(shù)值算例討論了本方法解決雙模量材料拓撲優(yōu)化問題的有效性以及計算效率。本文算法在計算雙模量拓撲優(yōu)化時的計算效率略低于計算同結(jié)構(gòu)各向同性材料拓撲優(yōu)化的效率。并采用本文方法分析了線性加權(quán)多工況雙模量材料布局優(yōu)化結(jié)果對材料拉壓模量差異的依賴程度。(4)提出了分數(shù)模目標函數(shù)法解決病態(tài)多工況下結(jié)構(gòu)拓撲的合理設計:首先,討論了病態(tài)工況下主、次傳力路徑的關(guān)系;其次,給出了分數(shù)階范數(shù)的定義,并使用分數(shù)階范數(shù)定義多工況結(jié)構(gòu)平均柔度的綜合目標函數(shù)加權(quán)方案。然后,討論了范數(shù)的階(q)在調(diào)整各個工況下結(jié)構(gòu)的每個平均柔度對局部材料分布的重要作用,即0q1時,弱荷載的傳力路徑得到強化,并且q值越小強化程度越高。最后,結(jié)合材料替換法分析了病態(tài)多工況下雙模量材料拓撲優(yōu)化問題。數(shù)值結(jié)果表明,當q的值取在[0.1,0.5]時,能夠找到極端病態(tài)工況(強弱工況差異為1000倍)下的合理設計。綜上,使用材料替換法解雙模量材料拓撲優(yōu)化使得結(jié)構(gòu)中的材料具有多種彈性性能。因此,雙模量材料拓撲優(yōu)化問題可看作特殊的多相各向同性材料拓撲優(yōu)化問題。為后期復雜工況下多相雙模量材料布局優(yōu)化的研究奠定了基礎。
[Abstract]:The structure of the optimization objective is to meet the given performance under the condition of the structure as far as possible to reduce the cost and improve efficiency. The continuum material layout (topological) optimization is a new structural optimization theory, has been widely used in many engineering design field. In general, the hydraulic structure has the following characteristics: one of the possible materials contains a variety of different stiffness of the structure of the material (such as dam etc.); structure of the material is in the form of double modulus characteristics (such as concrete). Double refers to the tensile modulus of materials in the same direction and compression elastic modulus varying materials. Therefore, the double modulus elastic constitutive tensor is related to stress that makes the structure with double modulus of deformation analysis requires many iterations can obtain accurate displacement field. For complex structures such as rockfill dam, the material stiffness of different phase number, using the existing extension Flutter optimization method can not effectively analyze the optimal material layout. And also cannot be efficiently analysis layout optimization of double modulus using topology optimization method. Without considering the existing dual modulus material properties for structure optimization design, prone to security risks. This thesis focuses on the above difficulties, puts forward four typical topology optimization problem of complex structures in multiphase material layout optimization, only the tensile or compressive material only single-phase layout optimization, topology optimization of single-phase double modulus materials and morbid condition topology optimization problem, independent research and put forward four kinds of optimization method. The main research results are as follows: (1) aiming at the complex structure with super multi layout optimization phase material, put forward multi phase the strain energy density distribution optimization (strain energy density:SED) method. This algorithm is the regional layout of high SED structure of high modulus material, low The regional layout of low modulus material: first, the structure of the materials in accordance with the modulus from high to low in number; secondly, the structure analysis is completed, will meet the volume constraint (material specified amount) material area for non design domain, the remaining material area of the unit in accordance with the SED in ascending order; then, before Co. a minimum of SED unit in the material is the replacement for the low modulus material adjacent; finally, stop the analysis after several iterations of all material volume constraints. Through a series of numerical examples with variable density comparison results demonstrate the effectiveness of the algorithm, and discuss the difference between the modulus of materials, effects of various materials different volume ratio and material types and other factors on the layout result. Based on the multiphase material layout optimization model of concrete faced rockfill dam material subarea design, through the examples discussed high rockfill Stone dam zoning rules, provide a reference for engineering design. (2) proposed replacing material analysis structure only tensile reference interval method (single pull) or compressive (single pressure) material layout optimization problem. A single pull or single pressure double modulus materials belong to special materials. First of all, in order to facilitate the optimization analysis the structure in the process of structural analysis in each before the single tension / compression material replacement for a kind of isotropic material; secondly, using the current stress state and the material of the single pull or single pressure characteristics to calculate the effective SED; then, by comparing the SED and reference area between the upper and lower bounds on the pseudo density of local material the changes in the design variables the update is complete; finally, in order to satisfy the constraints (such as volume constraint, displacement constraint etc.), updating the reference interval in the optimization process, until convergence. By using the beam bridge, hydraulic structure numerical examples are discussed in the analysis of this algorithm Structure with single pull or single pressure material layout optimization effectiveness and computational efficiency are discussed. The characteristics of single material tension / compression effect on optimization results. On the basis of the algorithm also discussed the influence of Poisson's ratio on the layout of the material. (3) proposed material replacement method is used for the analysis of gradient topology optimization the ordinary bimodulous material. In this algorithm, firstly, the design of the double modulus domain is replaced with two kinds of isotropic materials; secondly, according to the state of SED and SED and the calculation of tension compression unit stiffness correction factor stress element; thirdly, comparison of tensile and compression SED SED to determine the size of a material two isotropic material in the structure for the next analysis; then, using the unit stiffness correction factor correction element stiffness matrix, to ensure that the local stiffness in the replacement of consistent, and to ensure that the force transmission path consistency within the structure. Finally, the use of The pseudo density gradient method. Using the update unit deep beams, etc. platform are discussed. The method to solve the problem of topology optimization of bimodulous material effectiveness and computational efficiency of this algorithm. The efficiency in the calculation of bimodulous optimization calculation efficiency is slightly lower than the same structure of isotropic material topology optimization and analysis of linear. Weighted multi condition double modulus layout optimization results of tensile and compressive modulus difference depends on this method. (4) proposed a fractional model objective function method to solve the reasonable design of structural topology of morbid under multiple conditions: first, discuss the pathological conditions, the relationship of the path of force transfer; secondly, gives the definition of the fractional order norm, comprehensive weighting scheme and fractional norm defined multi condition structure average compliance. Then, discuss the norm of the order (q) structure adjustment in different conditions The average of each flexibility plays an important role in the distribution of local materials, namely 0q1, the force transmission path of weak load have been strengthened, and the lower the Q value the higher the degree of enhancement. Finally, combined with the material replacement method to analyze the pathological conditions of double multi modulus topology optimization problems. The numerical results show that when the value of Q in [0.1,0.5], to find the extreme pathological conditions (the strength condition difference of 1000 times) under reasonable design. To sum up, the use of material replacement method for solving topology optimization of double modulus material makes the structure of the material has many elastic properties. Therefore, optimization problem can be viewed as a special extension on the double modulus of multiphase anisotropic topology optimization problem of isotropic material. Laid the foundation for the later complex conditions of multiphase optimization layout double modulus materials research.

【學位授予單位】：西北農(nóng)林科技大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：TV641.43;TV41

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