多相材料及双模量材料布局优化研究

发布时间：2018-03-18 23:13

本文选题：拓扑优化　切入点：双模量材料　出处：《西北农林科技大学》2016年博士论文　论文类型：学位论文

【摘要】：结构优化的目的是结构在满足给定性能条件下尽可能地降低耗费、提高效能。连续体内材料布局(拓扑)优化是最新的结构优化理论,目前已被广泛地应用于诸多工程设计领域。一般地,水工结构中的材料具有如下特点之一:结构中可能包含多种刚度不同的材料(如堆石坝等);结构中的材料呈双模量特性(如混凝土等)。双模量材料是指在同一方向上的拉伸与压缩弹性模量不等的材料。因此,双模量材料的弹性本构张量是应力相关的,使得含双模量材料的结构变形分析需要多次迭代方可获得精确位移场。对于像面板堆石坝这样的复杂结构,其所含刚度不同的材料相数很多时,采用现有的拓扑优化方法无法有效分析其最优材料布局。而采用现有的拓扑优化方法也无法高效分析双模量材料布局优化问题。若不考虑双模量材料特性进行结构优化设计时,容易产生安全隐患。本论文针对以上困难,提出四个典型拓扑优化问题:复杂结构中超多相材料布局优化、单相仅抗拉或仅抗压材料布局优化、单相双模量材料拓扑优化以及病态工况拓扑优化问题,展开研究并独立提出四种优化算法。具体研究成果如下:(1)针对复杂结构含有超多相材料布局优化问题,提出了多相材料布局优化的应变能密度(strain energy density:SED)排序法。本算法的思想是结构中SED高的区域布置高模量材料,低的区域布置低模量材料:首先,将结构中的材料按照模量由高至低依次编号;其次,在结构分析完成后,将满足体积约束(材料指定用量)的材料所在区域设为非设计域,剩余材料所在区域的单元按照SED升序排列;然后,前有限个SED最低的单元中的材料被置换为相邻的低模量材料;最后,多次迭代后所有材料体积约束条件满足时停止分析。通过系列数值算例与变密度法结果的比较验证了算法的有效性,并讨论了材料模量之间的差异,各相材料体积率的差异以及材料种类等因素对布局结果的影响。以此为基础建立了面板堆石坝坝料分区设计的多相材料布局优化模型,通过算例讨论了高面板堆石坝坝体分区规律,为工程设计提供参考。(2)提出了材料替换—参考区间法分析结构中仅抗拉(单拉)或仅抗压(单压)材料布局优化问题。单拉或单压材料属于特殊的双模量材料。首先,为了便于优化过程中的结构重分析,在每次结构分析前将原单拉/压材料替换为一种各向同性材料;其次,利用当前应力状态以及材料的单拉或单压特点计算有效SED;然后,通过比较有效SED与参考区间的上、下界确定局部材料的伪密度的增减,完成设计变量更新;最后,为了满足约束条件(如体积约束、位移约束等),在优化过程中更新参考区间,直至算法收敛。利用梁、桥类水工结构数值算例讨论了本算法在分析结构含单拉或单压材料布局优化时的有效性以及计算效率。讨论了材料的单拉/压特性对优化结果的影响。在该算法基础上还讨论了材料的泊松比对布局结果的影响。(3)提出材料替换—梯度法用于分析普通双模量材料拓扑优化问题。在该算法中,首先,将设计域内的双模量材料替换为两种各向同性材料;其次,根据单元应力状态计算拉伸SED和压缩SED以及单元刚度修正因子;再次,比较拉伸SED与压缩SED的大小确定两种各向同性材料中的一种材料用于下次结构分析;然后,利用单元刚度修正因子修正单元刚度阵,以确保局部刚度在替换前后一致,进而确保结构内的传力路径一致。最后,利用梯度法更新单元的伪密度。利用深梁、台体等数值算例讨论了本方法解决双模量材料拓扑优化问题的有效性以及计算效率。本文算法在计算双模量拓扑优化时的计算效率略低于计算同结构各向同性材料拓扑优化的效率。并采用本文方法分析了线性加权多工况双模量材料布局优化结果对材料拉压模量差异的依赖程度。(4)提出了分数模目标函数法解决病态多工况下结构拓扑的合理设计:首先,讨论了病态工况下主、次传力路径的关系;其次,给出了分数阶范数的定义,并使用分数阶范数定义多工况结构平均柔度的综合目标函数加权方案。然后,讨论了范数的阶(q)在调整各个工况下结构的每个平均柔度对局部材料分布的重要作用,即0q1时,弱荷载的传力路径得到强化,并且q值越小强化程度越高。最后,结合材料替换法分析了病态多工况下双模量材料拓扑优化问题。数值结果表明,当q的值取在[0.1,0.5]时,能够找到极端病态工况(强弱工况差异为1000倍)下的合理设计。综上,使用材料替换法解双模量材料拓扑优化使得结构中的材料具有多种弹性性能。因此,双模量材料拓扑优化问题可看作特殊的多相各向同性材料拓扑优化问题。为后期复杂工况下多相双模量材料布局优化的研究奠定了基础。
[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.

【学位授予单位】：西北农林科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TV641.43;TV41

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