基于基本形状向量的复杂结构.docx
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基于基本形状向量的复杂结构,摘要形状优化设计作为结构优化设计的一个重要分支，可以通过改变区域的几何形状来达到某种约束条件下的最优，并要求某些物理量在边界上满足某种要求，以改善结构的特性。在以往的形状优化设计过程中，很多是把节点坐标和节点坐标组合作为设计变量，这些描述结构形状的方法设计变量多，不易收敛，且在优化迭代过程中易发生网格畸变的一些问题。如...
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摘 要
形状优化设计作为结构优化设计的一个重要分支，可以通过改变区域的几何形状来达到某种约束条件下的最优，并要求某些物理量在边界上满足某种要求，以改善结构的特性。在以往的形状优化设计过程中，很多是把节点坐标和节点坐标组合作为设计变量，这些描述结构形状的方法设计变量多，不易收敛，且在优化迭代过程中易发生网格畸变的一些问题。如何建立一个能够保证结构分析网格不发生畸变，通过较少的设计变量就可以方便而有效地控制和描述复杂形状变化的方法，是一个受到普遍关注的关键课题。
针对目前形状优化设计的难点问题，本文提出一种基于基本形状向量法的复杂结构形状优化设计方法。建立了一套基本形状向量法的优化设计理论模型，对基本形状向量法的关键问题进行了研究，编制了基本形状向量法的分析和优化程序，最后利用编制的分析和优化程序对基本形状向量法进行了实例验证并取得了良好的优化效果。
本文主要完成了以下几个方面的研究：
（1）深入研究了结构形状优化的基本理论，对结构形状优化的边界描述方法、设计变量和目标函数的选择、约束条件的确定进行了分析。将基本形状向量的概念引入结构形状优化设计中，研究基本形状优化算法，建立了基于基本向量法结构形状优化设计的优化模型。
（2）对基本形状向量法诸如基本形状独立性的检查，基本形状变化时其内部形状的从属变动问题等关键问题进行了研究，并通过算例对其进行验证，得出了基本形状向量法在解决具有工艺约束和结构约束的形状设计的优越性。
（3）对基本形状向量生成方法进行了研究，研究了网格划分软件模块开发难点，提出了关联线（面）法、节点均匀化法、映射变化法等几种基本形状向量的生成方法。
（4）深入研究基本形状向量法的分析程序算法和优化算法，并基于基本形状向量法利用C语言进行了分析程序和优化程序的编制。
（5）利用编制的分析程序和优化程序，结合MATLAB、Hyperworks软件对汽轮机叶根齿形和汽车发动机支架进行了形状优化设计。从设计结果来看，对具有结构约束的结构，利用基本形状向量法在改善结构应力、降低结构重量的形状优化设计中可以达到较好的优化效果。
关键词 形状优化；基本形状向量；有限元分析；优化设计
Abstract
As an important branch of structure optimization design, shape optimization can get the optimum under certain condition by changing geometry shape of some region, and make some physics parameters satisfy certain demand on the border, in order to improve some characteristic of structure. In the past, the combination of node coordinates is often used as design variables during the shape optimization of the structures. These description of the shape methods have many design variables and always difficult to converge. Furthermore, it always have the mesh distortion problems during the shape iterations. How to build a method to ensure the mesh distortion does not occur and through fewer design variables can be easily and effectively control and describe the complex shape of the change in approach is a key issue of universal concern.
Refer to the difficult problem of the shape optimization, this paper presented a shape optimization method based on the basic shape vectors. Established a set of theoretical model based on the basic shape vectors method. Studied on the issue of the basic shape vectors method. Programmed on the analysis and the shape optimization of the shape method. At last, conducted examples certification based on the shape optimization method and achieved good effect of optimization.
In this paper, complete the following aspects:
(1) The fundamental theory of shape optimization was studied deeply. The describe method of border, the selecting of design variables and objective function, and how to determine constraint condition were analyzed. Basic shape vector design was introduced into shape optimization, the basic shape algorithms were studied and the theoretical model was established.
(2) The key issue of the basic shape vector method was studied deeply, such as the independent inspection of the basic vectors, the inner subordinate changes during the shape vectors changes. Draw the basic shape vector method in solving has the craft constraints and the shape of the structure restriction the superiority of the design.
(3) The basic shape vector generation method was studied, and puts forward the related line (surface) method and the mapping method, and attempt to use program to realize basic shape vector generation.
(4) The analysis program algorithm and optimized algorithm based on the basic shape vectors was deeply studied, and formulate the analysis and the optimization procedure using C language .
(5) Based on these studies, using the analysis of programs and optimization program, combined with MATLAB、Hyperworks software to conduct the shape optimization design of steam turbine hub tooth shape and automobile engine stent. From the design result, with the structure of the structural constraint, using the basic shape vector method in improving the structure stress reduce weight of the structure of the shape optimization design can achieve better optimization effect.
Key words : Shape Optimization; Basic Shape Vectors; Finite-Element Analysis;
Optimization design
目 录
摘 要 I
Abstract I..
形状优化设计作为结构优化设计的一个重要分支，可以通过改变区域的几何形状来达到某种约束条件下的最优，并要求某些物理量在边界上满足某种要求，以改善结构的特性。在以往的形状优化设计过程中，很多是把节点坐标和节点坐标组合作为设计变量，这些描述结构形状的方法设计变量多，不易收敛，且在优化迭代过程中易发生网格畸变的一些问题。如何建立一个能够保证结构分析网格不发生畸变，通过较少的设计变量就可以方便而有效地控制和描述复杂形状变化的方法，是一个受到普遍关注的关键课题。
针对目前形状优化设计的难点问题，本文提出一种基于基本形状向量法的复杂结构形状优化设计方法。建立了一套基本形状向量法的优化设计理论模型，对基本形状向量法的关键问题进行了研究，编制了基本形状向量法的分析和优化程序，最后利用编制的分析和优化程序对基本形状向量法进行了实例验证并取得了良好的优化效果。
本文主要完成了以下几个方面的研究：
（1）深入研究了结构形状优化的基本理论，对结构形状优化的边界描述方法、设计变量和目标函数的选择、约束条件的确定进行了分析。将基本形状向量的概念引入结构形状优化设计中，研究基本形状优化算法，建立了基于基本向量法结构形状优化设计的优化模型。
（2）对基本形状向量法诸如基本形状独立性的检查，基本形状变化时其内部形状的从属变动问题等关键问题进行了研究，并通过算例对其进行验证，得出了基本形状向量法在解决具有工艺约束和结构约束的形状设计的优越性。
（3）对基本形状向量生成方法进行了研究，研究了网格划分软件模块开发难点，提出了关联线（面）法、节点均匀化法、映射变化法等几种基本形状向量的生成方法。
（4）深入研究基本形状向量法的分析程序算法和优化算法，并基于基本形状向量法利用C语言进行了分析程序和优化程序的编制。
（5）利用编制的分析程序和优化程序，结合MATLAB、Hyperworks软件对汽轮机叶根齿形和汽车发动机支架进行了形状优化设计。从设计结果来看，对具有结构约束的结构，利用基本形状向量法在改善结构应力、降低结构重量的形状优化设计中可以达到较好的优化效果。
关键词 形状优化；基本形状向量；有限元分析；优化设计
Abstract
As an important branch of structure optimization design, shape optimization can get the optimum under certain condition by changing geometry shape of some region, and make some physics parameters satisfy certain demand on the border, in order to improve some characteristic of structure. In the past, the combination of node coordinates is often used as design variables during the shape optimization of the structures. These description of the shape methods have many design variables and always difficult to converge. Furthermore, it always have the mesh distortion problems during the shape iterations. How to build a method to ensure the mesh distortion does not occur and through fewer design variables can be easily and effectively control and describe the complex shape of the change in approach is a key issue of universal concern.
Refer to the difficult problem of the shape optimization, this paper presented a shape optimization method based on the basic shape vectors. Established a set of theoretical model based on the basic shape vectors method. Studied on the issue of the basic shape vectors method. Programmed on the analysis and the shape optimization of the shape method. At last, conducted examples certification based on the shape optimization method and achieved good effect of optimization.
In this paper, complete the following aspects:
(1) The fundamental theory of shape optimization was studied deeply. The describe method of border, the selecting of design variables and objective function, and how to determine constraint condition were analyzed. Basic shape vector design was introduced into shape optimization, the basic shape algorithms were studied and the theoretical model was established.
(2) The key issue of the basic shape vector method was studied deeply, such as the independent inspection of the basic vectors, the inner subordinate changes during the shape vectors changes. Draw the basic shape vector method in solving has the craft constraints and the shape of the structure restriction the superiority of the design.
(3) The basic shape vector generation method was studied, and puts forward the related line (surface) method and the mapping method, and attempt to use program to realize basic shape vector generation.
(4) The analysis program algorithm and optimized algorithm based on the basic shape vectors was deeply studied, and formulate the analysis and the optimization procedure using C language .
(5) Based on these studies, using the analysis of programs and optimization program, combined with MATLAB、Hyperworks software to conduct the shape optimization design of steam turbine hub tooth shape and automobile engine stent. From the design result, with the structure of the structural constraint, using the basic shape vector method in improving the structure stress reduce weight of the structure of the shape optimization design can achieve better optimization effect.
Key words : Shape Optimization; Basic Shape Vectors; Finite-Element Analysis;
Optimization design
目 录
摘 要 I
Abstract I..
