梯度异质材料实体优化设计及成型规划方法研究
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摘要
梯度异质材料实体是一种由多相组分材料光滑过渡形成的功能材料零件，其由于能够同时利用多相组分材料的优良属性而在航空航天、过程装备、光学工程、生物医学工程等领域获得了广泛的应用，以分层制造为特点的快速成型技术的兴起使得低成本、大批量制备梯度异质材料实体成为可能。在这样的背景下，梯度异质材料实体的开发越来越受到专家和学者的关注，这一研究热点涉及到数学、材料学、计算机科学等多个学科，论文系统地研究了梯度异质材料实体的优化设计和制造过程规划的理论和方法，完善了基于有限元方法的梯度异质材料实体的计算机辅助开发流程，具有重要的理论和实践意义。
针对温度场中产生热量最小化以及温度最均匀化的材料设计问题，对温度场中的材料热传递性能进行了有限元分析，深入研究了温度场中的材料分布优化的插值模型、设计目标和约束条件，提出了基于单纯形法和序列线性规划的优化计算模型，设计了基于海维赛函数的体积分数过滤器来保证计算的数值稳定性，并对平面单元和壳单元的热传递行为进行了分析和探讨，通过实例验证了计算模型的可行性和有效性。
传统的材料分布优化所采用的均质单元不能有效地描述连续分布的异质材料，在结构场中提出了基于梯度单元的梯度异质材料实体有限元表达模型，得到在设计空间中连续的材料体积分数函数，为了在优化中体现设计者的意图，提出了基于自适应设计变量下限更新算法对材料的梯度进行局部控制，在有限元网格节点的邻域内实施该算法，结合移动渐近线算法将优化问题转化为一序列的优化子问题进行迭代求解，提出了统一的梯度异质材料实体优化设计方法，通过实例验证了该梯度材料轻量化设计方法的有效性和实用性。
对具有多个冲突的设计目标的材料分布优化问题的特点进行了分析，探讨了异质材料的遗传算法编码方式，针对材料分布优化设计变量的高维特点，提出了基于外部存档式微遗传算法的梯度材料进化方法，通过拉丁超立方抽样和随机排列技术形成初始种群，构造外部存档来保存进化中的精英个体，基于等均值最近邻搜索剪枝方法确定精英个体保留和删除的原则，运用模拟二进制交叉和多项式变异技术对实值编码的个体实施遗传操作，建立了多目标材料分布优化遗传算法的模型，通过实例验证了该模型的可行性和适用性。
为了充分利用计算机软硬件资源提高设计和计算的效率，分析和探讨了梯度异质材料实体优化算法的并行化方案，在单目标优化中对有限元网格进行区域分解，构造预处理共轭梯度方法迭代求解实体平衡方程，将计算任务按照子区域分配至并行的进程分别处理，在多目标优化中采用锥形分割模型对遗传算法的搜索空间进行分解，并将计算任务分配至并行的进程，最终汇总结果，提出了基于消息传递接口的梯度异质材料实体优化设计的并行计算方法，通过实例验证了该方法。
为了对梯度异质材料实体的设计环节和制造环节进行数据集成和并行，提出了基于分层梯度有限元方法的实体制造信息模型，运用标准三角化语言将实体的几何设计模型转换为平面三角形面片格式，采用可扩展标记语言表达实体的几何信息和材料信息，运用均匀切片技术将实体几何模型分层，根据材料的分布特点选择和设计扫描模式，在取样点通过形函数对几何和材料进行插值，提出了面向激光近净成型技术的梯度异质材料实体的制造过程规划方法，并结合仿真实例验证了该方法的有效性。
A graded heterogeneous object is a type of functional material part composed of multi-phasematerials which transition smoothly in the design space. Because they are capable of using desirableproperties of different constituent materials simultaneously, graded heterogeneous objects have beenused in a wide range of applications in aeronautics and astronautics, process equipments, opticalengineering and biomedical engineering etc. The emergence of rapid prototyping technologies whichare characterized by layered manufacturing has made it possible to fabricate graded heterogeneousobjects with low cost and high volume. In this context, the development of graded heterogeneousobjects, which involves mathematics, material science and computer science, has received increasingattention from specialists and scholars. This dissertation investigates the theories and methodologiesof the optimal design and manufacturing process planning of graded heterogeneous objectssystematically. Computer aided development of graded heterogeneous objects based on finiteelement method is perfected, which has both theoretical and practical significance.
Aiming at designing material structure that generate least heat and most uniform temperature inthe temperature field, heat transfer performance of material in temperature field is analyzed withfinite element method. The interpolation model, design objective and constraint conditions for theoptimization of material distribution are studied thoroughly. An optimization model based onsimplex method and sequential linear programming is proposed. Volume fraction filters based onHeaviside function are designed to ensure the numerical stability. The thermal behavior of planeelements and shell elements in heat transfer is analyzed and discussed. The feasibility andeffectiveness of the proposed method are verified with examples.
Traditional homogeneous elements used in material distribution optimization are not capable ofeffectively describing heterogeneous objects with continuously distributing materials. Arepresentation model of graded heterogeneous object based on graded elements is proposed in thestructural field, and continuous volume fraction functions of constituent materials in the design spaceare obtained. An algorithm for locally controlling the material gradient by means of adaptivelyupdating the lower limits of design variables is proposed and applied in the neighborhood of the gridnodes. The intent of the designer for the optimization is embodied in this way. The optimizationformulation is transformed into a sequel of sub-problems by method of moving asymptotes andsolved iteratively. A unified methodology for the optimal design of graded heterogeneous objects isproposed. An example is given to demonstrate the applicability and effectiveness of the proposedmethodology for designing lightweight heterogeneous objects.
The characteristics of material distribution optimization with conflicting objectives areanalyzed. The encoding of heterogeneous object for genetic algorithm is discussed. Because material distribution optimization has a high-dimension design variable vector, a graded material evolutionmethod based on Archive-based Micro Genetic Algorithm (AMGA) is proposed accordingly. Latinhypercube sampling and random shuffle method are used to generate the initial population. Anexternal population is created to store the elite solutions during the evolution. The principle forkeeping and deleting solutions in the external population based on equal average nearest neighborsearch is established. Simulated binary crossover and polynomial mutation are implemented for theoperations of the solutions encoded with real numbers. The model for the multi-objective geneticalgorithm for material distribution optimization is proposed, an example is given to verify thefeasibility and applicability of the proposed model.
In order to make full use of both the software and hardware of the available resources toenhance the efficiency of design and computing, the scheme for the parallelization of materialdistribution optimization is analyzed and discussed. In single objective optimization, the finiteelement mesh is decomposed into sub-domains, preconditioned conjugate gradient method isconstructed on the sub-domains and then the equilibrium equation is solved with it. Computing tasksare distributed to the parallel processes in accordance with the sub-domains. In multi-objectiveoptimization, cone separation method is used to decompose the search space of the genetic algorithm.Computing tasks are distributed to the parallel processes in accordance with the cones and the resultsare collected in the end from the processes. Parallel computing methodology for material distributionoptimization based on message passing interface is proposed and validated with examples.
In order to integrate the design and manufacturing of graded heterogeneous objectsconcurrently, solid manufacturing information model is proposed based on layered graded finiteelements. Standard triangulated language is used to transform the geometric design model intoplanar triangular facets. Extensible markup language is used to represent both the geometric andmaterial information. Uniform slicing method is used to divide the geometric model of the solid intolayers. Scanning pattern is chosen or designed in line with the characteristics of material distribution.Geometric and material data on sampling points are interpolated with shape functions. Amethodology of manufacturing process planning for graded heterogeneous objects conforming tolaser engineered net shaping technology is proposed. Simulation results are given to verify theeffectiveness of the methodology.
针对温度场中产生热量最小化以及温度最均匀化的材料设计问题，对温度场中的材料热传递性能进行了有限元分析，深入研究了温度场中的材料分布优化的插值模型、设计目标和约束条件，提出了基于单纯形法和序列线性规划的优化计算模型，设计了基于海维赛函数的体积分数过滤器来保证计算的数值稳定性，并对平面单元和壳单元的热传递行为进行了分析和探讨，通过实例验证了计算模型的可行性和有效性。
传统的材料分布优化所采用的均质单元不能有效地描述连续分布的异质材料，在结构场中提出了基于梯度单元的梯度异质材料实体有限元表达模型，得到在设计空间中连续的材料体积分数函数，为了在优化中体现设计者的意图，提出了基于自适应设计变量下限更新算法对材料的梯度进行局部控制，在有限元网格节点的邻域内实施该算法，结合移动渐近线算法将优化问题转化为一序列的优化子问题进行迭代求解，提出了统一的梯度异质材料实体优化设计方法，通过实例验证了该梯度材料轻量化设计方法的有效性和实用性。
对具有多个冲突的设计目标的材料分布优化问题的特点进行了分析，探讨了异质材料的遗传算法编码方式，针对材料分布优化设计变量的高维特点，提出了基于外部存档式微遗传算法的梯度材料进化方法，通过拉丁超立方抽样和随机排列技术形成初始种群，构造外部存档来保存进化中的精英个体，基于等均值最近邻搜索剪枝方法确定精英个体保留和删除的原则，运用模拟二进制交叉和多项式变异技术对实值编码的个体实施遗传操作，建立了多目标材料分布优化遗传算法的模型，通过实例验证了该模型的可行性和适用性。
为了充分利用计算机软硬件资源提高设计和计算的效率，分析和探讨了梯度异质材料实体优化算法的并行化方案，在单目标优化中对有限元网格进行区域分解，构造预处理共轭梯度方法迭代求解实体平衡方程，将计算任务按照子区域分配至并行的进程分别处理，在多目标优化中采用锥形分割模型对遗传算法的搜索空间进行分解，并将计算任务分配至并行的进程，最终汇总结果，提出了基于消息传递接口的梯度异质材料实体优化设计的并行计算方法，通过实例验证了该方法。
为了对梯度异质材料实体的设计环节和制造环节进行数据集成和并行，提出了基于分层梯度有限元方法的实体制造信息模型，运用标准三角化语言将实体的几何设计模型转换为平面三角形面片格式，采用可扩展标记语言表达实体的几何信息和材料信息，运用均匀切片技术将实体几何模型分层，根据材料的分布特点选择和设计扫描模式，在取样点通过形函数对几何和材料进行插值，提出了面向激光近净成型技术的梯度异质材料实体的制造过程规划方法，并结合仿真实例验证了该方法的有效性。
A graded heterogeneous object is a type of functional material part composed of multi-phasematerials which transition smoothly in the design space. Because they are capable of using desirableproperties of different constituent materials simultaneously, graded heterogeneous objects have beenused in a wide range of applications in aeronautics and astronautics, process equipments, opticalengineering and biomedical engineering etc. The emergence of rapid prototyping technologies whichare characterized by layered manufacturing has made it possible to fabricate graded heterogeneousobjects with low cost and high volume. In this context, the development of graded heterogeneousobjects, which involves mathematics, material science and computer science, has received increasingattention from specialists and scholars. This dissertation investigates the theories and methodologiesof the optimal design and manufacturing process planning of graded heterogeneous objectssystematically. Computer aided development of graded heterogeneous objects based on finiteelement method is perfected, which has both theoretical and practical significance.
Aiming at designing material structure that generate least heat and most uniform temperature inthe temperature field, heat transfer performance of material in temperature field is analyzed withfinite element method. The interpolation model, design objective and constraint conditions for theoptimization of material distribution are studied thoroughly. An optimization model based onsimplex method and sequential linear programming is proposed. Volume fraction filters based onHeaviside function are designed to ensure the numerical stability. The thermal behavior of planeelements and shell elements in heat transfer is analyzed and discussed. The feasibility andeffectiveness of the proposed method are verified with examples.
Traditional homogeneous elements used in material distribution optimization are not capable ofeffectively describing heterogeneous objects with continuously distributing materials. Arepresentation model of graded heterogeneous object based on graded elements is proposed in thestructural field, and continuous volume fraction functions of constituent materials in the design spaceare obtained. An algorithm for locally controlling the material gradient by means of adaptivelyupdating the lower limits of design variables is proposed and applied in the neighborhood of the gridnodes. The intent of the designer for the optimization is embodied in this way. The optimizationformulation is transformed into a sequel of sub-problems by method of moving asymptotes andsolved iteratively. A unified methodology for the optimal design of graded heterogeneous objects isproposed. An example is given to demonstrate the applicability and effectiveness of the proposedmethodology for designing lightweight heterogeneous objects.
The characteristics of material distribution optimization with conflicting objectives areanalyzed. The encoding of heterogeneous object for genetic algorithm is discussed. Because material distribution optimization has a high-dimension design variable vector, a graded material evolutionmethod based on Archive-based Micro Genetic Algorithm (AMGA) is proposed accordingly. Latinhypercube sampling and random shuffle method are used to generate the initial population. Anexternal population is created to store the elite solutions during the evolution. The principle forkeeping and deleting solutions in the external population based on equal average nearest neighborsearch is established. Simulated binary crossover and polynomial mutation are implemented for theoperations of the solutions encoded with real numbers. The model for the multi-objective geneticalgorithm for material distribution optimization is proposed, an example is given to verify thefeasibility and applicability of the proposed model.
In order to make full use of both the software and hardware of the available resources toenhance the efficiency of design and computing, the scheme for the parallelization of materialdistribution optimization is analyzed and discussed. In single objective optimization, the finiteelement mesh is decomposed into sub-domains, preconditioned conjugate gradient method isconstructed on the sub-domains and then the equilibrium equation is solved with it. Computing tasksare distributed to the parallel processes in accordance with the sub-domains. In multi-objectiveoptimization, cone separation method is used to decompose the search space of the genetic algorithm.Computing tasks are distributed to the parallel processes in accordance with the cones and the resultsare collected in the end from the processes. Parallel computing methodology for material distributionoptimization based on message passing interface is proposed and validated with examples.
In order to integrate the design and manufacturing of graded heterogeneous objectsconcurrently, solid manufacturing information model is proposed based on layered graded finiteelements. Standard triangulated language is used to transform the geometric design model intoplanar triangular facets. Extensible markup language is used to represent both the geometric andmaterial information. Uniform slicing method is used to divide the geometric model of the solid intolayers. Scanning pattern is chosen or designed in line with the characteristics of material distribution.Geometric and material data on sampling points are interpolated with shape functions. Amethodology of manufacturing process planning for graded heterogeneous objects conforming tolaser engineered net shaping technology is proposed. Simulation results are given to verify theeffectiveness of the methodology.
引文
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