基于整体参数化定义的直升机桨叶结构设计与优化
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摘要
桨叶结构设计是直升机设计中的重要内容，其性能的优劣对直升机有着重要的影响。长期以来，由于复合材料桨叶内部结构复杂，桨叶结构设计一直是在以剖面描述为中心的原准设计体系下开展和实施的。这种设计方式在过去数十年中发挥了重要作用，然而随着直升机技术的发展，这种设计方式逐步暴露出设计效率低、难以精确和直观表达出桨叶的真实三维内部结构以及忽视桨叶设计与制造之间的内在联系等问题。这一系列固有缺陷决定了以剖面描述为中心的桨叶结构原准设计体系已难以适应当前以数字化样机和MBD（Model Based Definition，基于模型定义）为技术特征的直升机数字化研制体系的需要。为此，本论文提出了以全三维描述为中心的复合材料桨叶全组件整体参数化定义方法，并以此为基础系统而深入地开展了复合材料桨叶结构自动三维几何建模、剖面特性与整体特性计算、桨叶结构的优化设计以及整个设计过程的集成，自主研发了BSDS（Blade Structure Digital Design Integration System）复合材料桨叶结构数字化设计集成系统平台，形成了一种新的基于整体参数化定义的桨叶结构设计模式，并提供了该模式下从几何建模、结构特性计算、结构参数优化到设计过程集成的一整套方法。论文主要的研究内容和创新点概括如下：
1.根据直升机复合材料桨叶各组件的几何外形特点及其构成，并综合考虑以数字化样机和MBD为技术特征的产品数字化研制体系的需要，提出了精确反映桨叶组件真实结构外形的整体参数化定义方法。针对桨叶结构中最为复杂的复合材料蒙皮结构，归纳出四大类共十二种子类的蒙皮铺层类型，通过铺层的整体定义和分层定义相结合的方式实现了桨叶蒙皮的参数化定义；对其他组件也依据其结构几何特点制定了相应的整体参数化定义方法。该方法不仅实现了桨叶各类型组件几何外形的整体参数化描述，而且在几何外形参数化定义的基础上引入了诸如铺设顺序、材料类型以及铺放角度等桨叶分析、制造信息，提出了一套较为完整的复合材料桨叶全组件数据结构表达机制，使其不但能够便捷地提供桨叶几何建模及桨叶结构分析所需数据，还能为桨叶制造提供相关数据信息。研发了智能向导的桨叶组件定义模块，引导工程设计人员以简便直观的交互方式实现对各组件的定义。桨叶组件的整体参数化定义方法是本文整个研究工作的基石。
2.提出并实现了一种复合材料桨叶结构的自动化几何建模方法。该方法以本文提出的整体参数化定义方法为基础，通过对桨叶各组件结构特点的总结与归纳，并综合应用B-Rep（Boundary Representation，边界表示法）实体数据结构、NURBS（Non-Uniform Rational B-Spline，非均匀有理B样条）曲面体系、曲面等距、曲面裁剪等几何造型理论及方法，以参数驱动的方式，自动高效地建立复合材料桨叶结构的三维几何外形。针对复合材料蒙皮组件，提出了蒙皮外形分片逐次构造方法和由上一铺层内表面构造当前蒙皮铺层的算法来实现其几何外形的自动构建；针对桨叶其他组件，根据组件参数化定义方法的不同，提出多区段结合式和整体成形式两种不同的几何建模方法。本文提出的桨叶结构自动化几何建模方法是首次系统地对直升机复合材料桨叶结构的三维几何外形建模进行的研究。该自动化建模方法显著提高了桨叶建模的效率，有效地增强了桨叶结构数字化设计的能力，也为基于三维模型定义的数字化制造奠定了基础。
3.提出了一种基于整体参数化组件定义及建模的桨叶结构特性分析方法。该方法适应于桨叶组件的整体参数化定义方法带来的改变，以桨叶剖面特性和整片桨叶结构特性计算为核心内容，分别根据桨叶各剖面和整片桨叶结构特性的定义及物理意义，推导得出相应的计算公式。针对桨叶结构特性分析中的重点及难点——剖面扭转刚度计算，提出了铺层块假设以及长厚比的概念，并基于闭口薄壁梁理论，给出了复合材料桨叶剖面扭转刚度的高效计算方法；对于整片桨叶结构特性，则是在剖面质量线密度和剖面重心分布符合分段线性连续假设的基础上，推导出了相应的计算公式。开发了基于整体参数化组件定义且与桨叶结构自动化三维建模无缝集成的桨叶结构特性分析软件模块，实现了桨叶结构特性参数的自动计算，通过实例验证表明该方法可行、有效。
4.提出了一种基于整体参数化定义的复合材料桨叶结构优化设计方法。该方法是建立在桨叶组件的整体参数化定义方法、桨叶结构的自动化三维几何建模及其结构特性分析方法的基础上，通过对桨叶结构设计问题的分解，将其抽象并转化为剖面优化设计问题和整体优化设计问题。剖面优化设计是通过桨叶结构剖面参数进行优化得出桨叶结构整体优化设计初值的过程。整体优化设计则是通过对桨叶整体结构参数的调整来实现桨叶结构优化的设计过程。该方法不同于以往基于抽象的简化模型所开展的桨叶优化设计研究，其优化设计的参数直接来源于桨叶结构的整体定义参数，优化结果能够直接反映到真实的三维桨叶组件结构上，并且能够对没有参考样机数据的桨叶进行创新结构设计，得出优化的设计方案。方法的有效性和优势通过实际桨叶结构优化设计实验得到了认证。
5.提出了一种桨叶结构的数字化设计集成系统的总体方案，构建了一个基于Web的复合材料桨叶结构数字化设计集成系统平台（BSDS）。不同于已有桨叶结构设计所采用的原准设计、校核、交互设计修改、再校核、再修改的设计流程，本论文提出的设计流程以数字化设计为导向，通过对桨叶结构设计的各环节进行数字化改造，有效整合各流程间的输入、输出关系，提供可拖选、可重构、所见即所得的流程建模方式，不仅能够建立起类似于原有桨叶结构设计的常规顺序式设计流程，也可以根据具体设计任务建立起自动迭代式设计流程。通过对设计过程相关软件的集成，利用工作流引擎的驱动实现设计流程的自动运行。其优点是能够随着桨叶结构设计方法的改进，快速而高效地建立起相应的设计流程，能够通过自动迭代式设计流程的建立提高整个桨叶结构设计的效率。
Blade’s structure design is essential of helicopter design, and its performance greatly influencesthe helicopter. Blade structure design implemented in the prototype design system centered on sectiondescription, which has played an important role in the past few years and made great contribution tothe development of helicopter technology. But with the development of science and technology, someproblems of this design method gradually emerges, such as low efficiency, poor precision, difficulty inexpressing the real structure of blade, neglecting the internal relationship between the design andmanufacture of blade. These inherent defects indicate that the prototype design system focusing onsection description can not meet the need of helicopter digitized development system with technicalcharacteristics of the digitized prototype and MBD (model based definition). Therefore, the moduleparametric definition for composite rotor blade centered in full three-dimensional (3D) description isproposed in this paper. Based on this, several key technologies are further studied systematicly,including3D geometric automatic modeling, sectional and global characteristics calculation,optimization design for blade structure and design process integration. Besides, a new blade structuredesign model based on iinteger-oriented parametric definition has formed, and some approaches basedon this model, such as geometric modeling, structure characteristic computation, structure parameteroptimization and design process integration, are proposed in this paper. The main contents andinnovative points are summarized as follows:
1. According to the geometric characteristics and compositions of helicopter composite blade, theinteger-oriented parametric definition which precisely reflects the real shape of blade structure is firstprovided after a comprehensive considering of the need of product digitized development system withtechnical characteristics of the digitized prototype and MBD. As regards the most complicatedcomposite skin structure in the blade, the paper concludes four main types and twelve subtypes ofblade skin ply, and the parametric definition of blade skin is implemented by combining the globaldefinition with the hierarchical definition of ply; Based on its structure geometric characteristics, theirglobal parametric definitions are made for other components. This method not only realizes the globalparametric description of blade structure, but also introduces blade analysis and manufacturesinformation, such as ply sequence, material types and ply orientation angle based on parametricdefinition. And it puts forward a comparatively complete expression mechanism of data structure forcomposite blade component, which not only provides the required data for blade geometric modeling and structure analysis but also for blade manufacture. The blade component definition module withintelligent guiding is developed to guide engineering designers to realize the component definition inconvenient interactive mode. Therefore, the global parametric definition of blade component is thefoundation of this paper’s research work.
2. A geometric automatic modeling algorithm is put forward for composite blade structure. Basedon the proposed global parametric definition, the algorithm summarizes the structure characteristics ofblade components and comprehensively applies the geometric modeling theory and method includingB-Rep solid data structure, NURBS surface system, surface offset, surface trimming and so on. Andthen the3D shape of composite blade structure is constructed in parametric driving modeautomatically and effectively. According to the composite skin components, the slicing successiveconstruction method of blade skin shape is proposed, and the shape of the current skin ply isautomatically constructed by the last laminated inner surface; as for other blade components, twodifferent geometric modeling algorithms such as segmental combining and integral forming are putforward by the different parametric definition. The proposed blade automatic modeling algorithm isthe first systematic study of helicopter composite blade modeling. The blade modeling is significantlyimproved and the digital design for blade structure is effectively enhanced, which establish the basisfor digital manufacture based on3D model definition.
3. A blade structural characteristics analysis method based on global parametric componentdefinition and modeling is proposed. It can be suitable for the change brought out the globalparametric definition of blade components. The calculations of blade sectional property and bladestructural characteristics are taken as the core, and their calculation formulas are respectively derivedfrom the corresponding definition and physical meaning. According to the emphasis and difficulty inblade structure characteristic analysis such as the sectional torsional stiffness calculation, the conceptsof ply block hypothesis and length to thickness are proposed, and the effective calculation ofcomposite blade sectional torsional stiffness is given by the theory of closed cross section thin-walledbeams; For the whole blade structural characteristic, its calculation formula is derived by assumingthe sectional quality linear density and sectional barycenter distribution are in accordance withpiecewise-linear continuity. The software module of blade structure characteristic analysis with globalparametric definition and seamless integration of blade automatic modeling is developed to realize theautomatic calculation of blade structure characteristic parameters. Experiments demonstrate that theproposed method is available and effective.
4. The optimum design method based on global parametric component definition is put forward for composite blade structure. Based on the global parametric definition of blade components, theautomatic geometric modeling of blade structure and the analysis of blade structural characteristics,the blade structure design problem is decomposed to the sectional and global optimization designproblems. The former is the acquisition process of the initial values of blade structure globaloptimization by optimizing the sectional parameters extracted from global structure parameters. Thelatter is the design process of blade structure optimization by adjusting the blade global structureparameters. Different from the previous research on blade optimization design based on the abstractsimplified model, the optimization design parameters are directly from the global definitionparameters of blade structure, and the corresponding optimization results can be reflected on the realstructure of3D blade component. Therefore, it can effectively improve the efficiency and accuracy ofthe practical blade structure design process. The effectiveness and advantages of the proposed methodare confirmed by means of the practical optimization experiments of blade structure.
5. The overall scheme of digital integrated system of blade structure design is presented, and thecorresponding platform based on Web is established. Different from the existing structure design flowof original-quasi design, check, interactive design and modification, recheck and re-amendment, theproposed design process is first taking digital design as a guide, and then the input and output of theprocesses are effectively integrated by the digital transformation for blade structure design to providethe process modeling method, which can be selected, reconstructed and WYSIWYG (what you see iswhat you get). This method establishes not only the conventional subsequent design process similar tothe origin blade structure design, but also the automatic iterative design process according to theconcrete design task. By integrating the design related software, the driven workflow engine is used torealize the automatic running of the design process. With the improvement of blade structure designmethod, the corresponding design process is rapidly and efficiently established. And it can improvethe design efficiency of global blade structure by establishing the automatic iterative design process.
1.根据直升机复合材料桨叶各组件的几何外形特点及其构成，并综合考虑以数字化样机和MBD为技术特征的产品数字化研制体系的需要，提出了精确反映桨叶组件真实结构外形的整体参数化定义方法。针对桨叶结构中最为复杂的复合材料蒙皮结构，归纳出四大类共十二种子类的蒙皮铺层类型，通过铺层的整体定义和分层定义相结合的方式实现了桨叶蒙皮的参数化定义；对其他组件也依据其结构几何特点制定了相应的整体参数化定义方法。该方法不仅实现了桨叶各类型组件几何外形的整体参数化描述，而且在几何外形参数化定义的基础上引入了诸如铺设顺序、材料类型以及铺放角度等桨叶分析、制造信息，提出了一套较为完整的复合材料桨叶全组件数据结构表达机制，使其不但能够便捷地提供桨叶几何建模及桨叶结构分析所需数据，还能为桨叶制造提供相关数据信息。研发了智能向导的桨叶组件定义模块，引导工程设计人员以简便直观的交互方式实现对各组件的定义。桨叶组件的整体参数化定义方法是本文整个研究工作的基石。
2.提出并实现了一种复合材料桨叶结构的自动化几何建模方法。该方法以本文提出的整体参数化定义方法为基础，通过对桨叶各组件结构特点的总结与归纳，并综合应用B-Rep（Boundary Representation，边界表示法）实体数据结构、NURBS（Non-Uniform Rational B-Spline，非均匀有理B样条）曲面体系、曲面等距、曲面裁剪等几何造型理论及方法，以参数驱动的方式，自动高效地建立复合材料桨叶结构的三维几何外形。针对复合材料蒙皮组件，提出了蒙皮外形分片逐次构造方法和由上一铺层内表面构造当前蒙皮铺层的算法来实现其几何外形的自动构建；针对桨叶其他组件，根据组件参数化定义方法的不同，提出多区段结合式和整体成形式两种不同的几何建模方法。本文提出的桨叶结构自动化几何建模方法是首次系统地对直升机复合材料桨叶结构的三维几何外形建模进行的研究。该自动化建模方法显著提高了桨叶建模的效率，有效地增强了桨叶结构数字化设计的能力，也为基于三维模型定义的数字化制造奠定了基础。
3.提出了一种基于整体参数化组件定义及建模的桨叶结构特性分析方法。该方法适应于桨叶组件的整体参数化定义方法带来的改变，以桨叶剖面特性和整片桨叶结构特性计算为核心内容，分别根据桨叶各剖面和整片桨叶结构特性的定义及物理意义，推导得出相应的计算公式。针对桨叶结构特性分析中的重点及难点——剖面扭转刚度计算，提出了铺层块假设以及长厚比的概念，并基于闭口薄壁梁理论，给出了复合材料桨叶剖面扭转刚度的高效计算方法；对于整片桨叶结构特性，则是在剖面质量线密度和剖面重心分布符合分段线性连续假设的基础上，推导出了相应的计算公式。开发了基于整体参数化组件定义且与桨叶结构自动化三维建模无缝集成的桨叶结构特性分析软件模块，实现了桨叶结构特性参数的自动计算，通过实例验证表明该方法可行、有效。
4.提出了一种基于整体参数化定义的复合材料桨叶结构优化设计方法。该方法是建立在桨叶组件的整体参数化定义方法、桨叶结构的自动化三维几何建模及其结构特性分析方法的基础上，通过对桨叶结构设计问题的分解，将其抽象并转化为剖面优化设计问题和整体优化设计问题。剖面优化设计是通过桨叶结构剖面参数进行优化得出桨叶结构整体优化设计初值的过程。整体优化设计则是通过对桨叶整体结构参数的调整来实现桨叶结构优化的设计过程。该方法不同于以往基于抽象的简化模型所开展的桨叶优化设计研究，其优化设计的参数直接来源于桨叶结构的整体定义参数，优化结果能够直接反映到真实的三维桨叶组件结构上，并且能够对没有参考样机数据的桨叶进行创新结构设计，得出优化的设计方案。方法的有效性和优势通过实际桨叶结构优化设计实验得到了认证。
5.提出了一种桨叶结构的数字化设计集成系统的总体方案，构建了一个基于Web的复合材料桨叶结构数字化设计集成系统平台（BSDS）。不同于已有桨叶结构设计所采用的原准设计、校核、交互设计修改、再校核、再修改的设计流程，本论文提出的设计流程以数字化设计为导向，通过对桨叶结构设计的各环节进行数字化改造，有效整合各流程间的输入、输出关系，提供可拖选、可重构、所见即所得的流程建模方式，不仅能够建立起类似于原有桨叶结构设计的常规顺序式设计流程，也可以根据具体设计任务建立起自动迭代式设计流程。通过对设计过程相关软件的集成，利用工作流引擎的驱动实现设计流程的自动运行。其优点是能够随着桨叶结构设计方法的改进，快速而高效地建立起相应的设计流程，能够通过自动迭代式设计流程的建立提高整个桨叶结构设计的效率。
Blade’s structure design is essential of helicopter design, and its performance greatly influencesthe helicopter. Blade structure design implemented in the prototype design system centered on sectiondescription, which has played an important role in the past few years and made great contribution tothe development of helicopter technology. But with the development of science and technology, someproblems of this design method gradually emerges, such as low efficiency, poor precision, difficulty inexpressing the real structure of blade, neglecting the internal relationship between the design andmanufacture of blade. These inherent defects indicate that the prototype design system focusing onsection description can not meet the need of helicopter digitized development system with technicalcharacteristics of the digitized prototype and MBD (model based definition). Therefore, the moduleparametric definition for composite rotor blade centered in full three-dimensional (3D) description isproposed in this paper. Based on this, several key technologies are further studied systematicly,including3D geometric automatic modeling, sectional and global characteristics calculation,optimization design for blade structure and design process integration. Besides, a new blade structuredesign model based on iinteger-oriented parametric definition has formed, and some approaches basedon this model, such as geometric modeling, structure characteristic computation, structure parameteroptimization and design process integration, are proposed in this paper. The main contents andinnovative points are summarized as follows:
1. According to the geometric characteristics and compositions of helicopter composite blade, theinteger-oriented parametric definition which precisely reflects the real shape of blade structure is firstprovided after a comprehensive considering of the need of product digitized development system withtechnical characteristics of the digitized prototype and MBD. As regards the most complicatedcomposite skin structure in the blade, the paper concludes four main types and twelve subtypes ofblade skin ply, and the parametric definition of blade skin is implemented by combining the globaldefinition with the hierarchical definition of ply; Based on its structure geometric characteristics, theirglobal parametric definitions are made for other components. This method not only realizes the globalparametric description of blade structure, but also introduces blade analysis and manufacturesinformation, such as ply sequence, material types and ply orientation angle based on parametricdefinition. And it puts forward a comparatively complete expression mechanism of data structure forcomposite blade component, which not only provides the required data for blade geometric modeling and structure analysis but also for blade manufacture. The blade component definition module withintelligent guiding is developed to guide engineering designers to realize the component definition inconvenient interactive mode. Therefore, the global parametric definition of blade component is thefoundation of this paper’s research work.
2. A geometric automatic modeling algorithm is put forward for composite blade structure. Basedon the proposed global parametric definition, the algorithm summarizes the structure characteristics ofblade components and comprehensively applies the geometric modeling theory and method includingB-Rep solid data structure, NURBS surface system, surface offset, surface trimming and so on. Andthen the3D shape of composite blade structure is constructed in parametric driving modeautomatically and effectively. According to the composite skin components, the slicing successiveconstruction method of blade skin shape is proposed, and the shape of the current skin ply isautomatically constructed by the last laminated inner surface; as for other blade components, twodifferent geometric modeling algorithms such as segmental combining and integral forming are putforward by the different parametric definition. The proposed blade automatic modeling algorithm isthe first systematic study of helicopter composite blade modeling. The blade modeling is significantlyimproved and the digital design for blade structure is effectively enhanced, which establish the basisfor digital manufacture based on3D model definition.
3. A blade structural characteristics analysis method based on global parametric componentdefinition and modeling is proposed. It can be suitable for the change brought out the globalparametric definition of blade components. The calculations of blade sectional property and bladestructural characteristics are taken as the core, and their calculation formulas are respectively derivedfrom the corresponding definition and physical meaning. According to the emphasis and difficulty inblade structure characteristic analysis such as the sectional torsional stiffness calculation, the conceptsof ply block hypothesis and length to thickness are proposed, and the effective calculation ofcomposite blade sectional torsional stiffness is given by the theory of closed cross section thin-walledbeams; For the whole blade structural characteristic, its calculation formula is derived by assumingthe sectional quality linear density and sectional barycenter distribution are in accordance withpiecewise-linear continuity. The software module of blade structure characteristic analysis with globalparametric definition and seamless integration of blade automatic modeling is developed to realize theautomatic calculation of blade structure characteristic parameters. Experiments demonstrate that theproposed method is available and effective.
4. The optimum design method based on global parametric component definition is put forward for composite blade structure. Based on the global parametric definition of blade components, theautomatic geometric modeling of blade structure and the analysis of blade structural characteristics,the blade structure design problem is decomposed to the sectional and global optimization designproblems. The former is the acquisition process of the initial values of blade structure globaloptimization by optimizing the sectional parameters extracted from global structure parameters. Thelatter is the design process of blade structure optimization by adjusting the blade global structureparameters. Different from the previous research on blade optimization design based on the abstractsimplified model, the optimization design parameters are directly from the global definitionparameters of blade structure, and the corresponding optimization results can be reflected on the realstructure of3D blade component. Therefore, it can effectively improve the efficiency and accuracy ofthe practical blade structure design process. The effectiveness and advantages of the proposed methodare confirmed by means of the practical optimization experiments of blade structure.
5. The overall scheme of digital integrated system of blade structure design is presented, and thecorresponding platform based on Web is established. Different from the existing structure design flowof original-quasi design, check, interactive design and modification, recheck and re-amendment, theproposed design process is first taking digital design as a guide, and then the input and output of theprocesses are effectively integrated by the digital transformation for blade structure design to providethe process modeling method, which can be selected, reconstructed and WYSIWYG (what you see iswhat you get). This method establishes not only the conventional subsequent design process similar tothe origin blade structure design, but also the automatic iterative design process according to theconcrete design task. By integrating the design related software, the driven workflow engine is used torealize the automatic running of the design process. With the improvement of blade structure designmethod, the corresponding design process is rapidly and efficiently established. And it can improvethe design efficiency of global blade structure by establishing the automatic iterative design process.
引文
[1]张广林.我国直升机产业的现状与发展前景[J].中国民用航空,2009,102:30~33.
[2]黄承恭,吴建华.复合材料在直升机上的应用与发展[C].航空复合材料预研二十年回顾展望研讨会,2001:30~33.
[3]卢廷钧.数字化技术在直升机制造企业中的应用与发展[J].航空制造技术,2004,12:26~30
[4]栗琳著.直升机发展历程[M].北京:航空工业出版社,2007:11~16.
[5]徐德康著.蓝天铸春秋——航空科技[M].北京:北京理工大学出版社,2002:239~249.
[6]徐朝梁.谈谈直—8直升机[J].环球飞行,2008,7:240~245.
[7]冯春梅,曹智,李宣良等.甘洒热血写忠诚——人民子弟兵抢险救灾纪实[N].人民日报,2010-09-16(1).
[8]邱光荣,赵伟华.推进直升机产业发展新跨越[J].中国军转民,2009,(9):70~74.
[9]张呈林.直升机旋翼技术的发展[N],中国航空报,2000-10-20.
[10]沈亨业.浅析我国直升机旋翼技术发展问题[J].直升机技术,1998,113(1):45~51.
[11]杨乃宾等.直升机复合材料结构设计[M].北京:国防工业出版社.2008:42~43.
[12]倪先平.直升机百年[J].航空工业经济研究,2008,1:21~28.
[13]倪先平.直升机技术发展现状与展望[J].航空学报,2003,24(1):15~20.
[14]豫章.直升机发展概述[J].直升机技术,2003,136(4):35~41.
[15]布拉图欣，И.П.著；刘谋佶，沈骥译.直升机设计与构造[M].北京：国防工业出版社,1959:138.
[16]孙如林.美国直升机先进旋翼技术发展和现状[J].直升机技术,1995,103(2):43~48.
[17] Yuan K. A. and Friedmann, P. P.. Aeroelasticity and structural optimization of compositehelicopter rotor blades with swept tips[R]. NASA Contractor Report4665,1995.
[18] Bao, J. S.. Development of mach scale rotors with composite tailored couplings forvibration reduction[D]. Maryland: University of Maryland College Park,2004.
[19]冼杏娟.西德MBB公式生产的复合材料产品[J].机械工程材料,1983,3:37~38.
[20]吴跃.再接再厉努力实现直升机旋翼技术的跨越发展[J].直升机技术,2007,3:2~2.
[21]张呈林,林国梁.Y-2直升机玻璃钢旋翼桨叶的研制[J].南京航空航天大学学报,1979,3:154~164.
[22]徐明,徐桂祺.海豚型旋翼桨叶气动弹性稳定分析[J].南京航空航天大学学报,1987,1:26~36.
[23]樊光华.浅析我国直升机技术的新发展[J].航空与航天,2001,4:8~10.
[24] Bielawa, R. L.. Techniques for stability analysis and design optimization with dynamicconstraints of non conservative linear systems[J]. AIAA Paper71-388,1971.
[25] Peters, D. A., Rossow, M. P., Korn, A., et al.. Design of helicopter rotor blades for optimumdynamic characteristics[J]. Journal of Comptuters and Mathematics with Applications,1986,12(1):85~109.
[26] Celi, R. and Friedmann, P. P.. Aeroelastic modeling of swept tip rotor blades using finiteelements[J]. Journal of American Helicopter Society,1988,33(2):
[27]樊光华,侯汝良,程耿东等.复合材料旋翼桨叶的结构优化与控制研究[J].航空学报,1991,12(12):554~559.
[28]顾元宪,刘书田,关振群等.面向设计的复合材料旋翼桨叶动力学优化设计[J].航空学报1998,19(3):338~341.
[29] Hodges, D. H.. A review of composite rotor blade modeling[J]. AIAA Journal,1990,28(3):561~565.
[30]顾元宪,程耿东,孙如林等.直升机旋翼结构优化设计研究综述[J].直升机技术,1995,101(1):16~25.
[31] Celi, R.. Recent applications of design optimization to rotorcraft–a survey[J]. Journal ofAircraft,1999,36(1):176~189.
[32]郭俊贤,向锦武,张晓谷.降低旋翼激振力的动力学优化设计研究综述[J].直升机技术,2000,121(1):7~13.
[33]向锦武,郭俊贤,张晓谷.直升机减振的旋翼桨叶优化设计研究综述[J].北京航空航天大学学报,2001,27(1):32~35.
[34] Ganguli, R.. Survey of recent development in rotorcraft design optimization[J]. Journal ofAircraft,2004,41(3):493~510.
[35] Grandl R.. Vrtual process week in the experimental vehicle build at BMW AG[C].experimental vehicle division, BMW AG, Dept T1-360,80788, Munieh, Germany, Roboticsand Computer Intergrated Manufacturing,2001,17:65~71.
[36]宁振波.数字样机在飞机设计中应用[J].航空制造技术,2002,10:20~22.
[37]冯潼能,王铮阳,孟静晖.MBD技术在数字化协同制造中的应用与展望[J].南京航空航天大学学报,2012,44(S1):132~137.
[38]张景新.数字化设计制造技术在直升机复合材料结构中的应用[J].直升机技术,2005,144(4):23~26.
[39]武美萍,廖文和.虚拟产品开发管理技术在直升机数字样机开发中的应用研究[J].机械科学与技术,2008,27(5):633~639.
[40]余明.数字样机技术在直升机设计中的应用研究[J].直升机技术,2002,129(1):16~21.
[41]吴跃,郑文心.航空制造业数字化总体框架研究[J].CAD/CAM与制造业信息化,2004,(8):11~13.
[42]张景新.直升机结构三维实体数字预装配技术探讨[J].直升机技术,2000,124(4):35~38.
[43]郑朔昉,徐明,倪先平.基于CATIA V5的三维数字化通用零部件/标准件库的创建与使用[J].航空标准化与质量,2001,(6):7~10.
[44]陈阳平,谢强,丁秋林.基于知识的直升机数字化设计研究[J].直升机技术,2005,141(1):5～8.
[45]黄志文.基于CATIA、 VPM的结构三维数字化设计技术[J].直升机技术,2010,165(4):20～25.
[46] Li, L. H.. Structural design of composite rotor blades with consideration ofmanufacturability, durability and manufacturing uncertainties[D]. Atlanta:Georgia Institute ofTechnology,2008.
[47] Volovoi, V. V. and Hodges, D. H.. Assessment of beam modeling methods for rotor bladeapplication[J]. Mathematical and Computer Modelling,2001,33:1099~1112.
[48] Houbolt, J. C. and Brooks, G. W.. Differential equation of motion for combined flapwisebending, chordwise bending, and torsion of twisted nonuinform rotor blades[R]. NACAReport1346,1958.
[49] Hodges, D. H. and Dowell, E. H.. Nonlinear equations of motion for the elastic bending andtorsion of twisted nonuniform rotor blades[R]. NASA TN D-7818,1974.
[50] Rosen, A. and Friedmann, P. P.. Nonlinear equations of equilibrium for elastic helicopter orwind turbine blade undergoing moderate deflection[R]. NASA CR-159478,1978.
[51] Dowell, E. H., Traybar, J. and Hodges, D. H.. An experimental theoretical correlation studyof non-linear bending and torsion deformations of a cantilever beam[J]. Journal of Sound andVibrations,1977,50:533~544.
[52] Rosen, A. and Friedmann, P. P.. Nonlinear behavior of elastic slender straight beamsundergoing small strains and moderate rotations[J]. Jouranl of Applied Mechanics,1979,46:161~168.
[53] Hodges, D. H. and Ormiston, R. A.. Stability of elastic bending and torsion of uniformcantilever rotor blades in hover with variable structural coupling[R]. NASA TN D-8192,1976.
[54] Shamie, J. and Friedmann, P. P.. Effect of moderate deflections on the aeroelastic stabilityof a rotor blade in forward flight[C]. Proc.3rdEuropean Rotorcraft and Powered Lift AircraftForum, Aix-en-Provence,1977:24.1~24.37.
[55] Kaza, K. R. and Kvaternik, R. G.. Nonlinear aeroelastic equations for combined flapwisebending, chordwise bending, torsion and extension of twisted non-uniform rotor blades inforward flight[R]. NASA TM-74059,1977.
[56] Hodges, D. H.. Nonlinear equations for dynamics of pretwisted beams undergoing smallstrains and large rotations[R]. NASA TP-2470,1985.
[57] Hodges, D. H., Hopkins, A. K., Kunz, D. L. and Hinnant, H. E.. Introduction to GRASP–general rotorcraft aeromechanical stability program–a modern approach to rotorcraftmodeling[C]. Proc.42ndAnnual Forum of the American Helicopter Society, Washington D.C.,1986:739~756.
[58] Friedmann, P. P.. Helicopter rotor dynamics and aeroelasticity: some key ideas andinsights[J]. Vertica,1990,14(1):101~121.
[59] Friedmann, P. P. and Hodges, D. H.. Rotary-wing aeroelasticity with application to VTOLVehicles[C]. Chapter6, in Flight-vehicle materials, structures and dynamics[M], Vol.5-Structural dynamics and aeroelasticity, edited by Noor, A.K. and Venneri, S. L., ASME,1993:299~391.
[60] Kunz. D. L.. Survey and comparision of engineering beam theories for helicopter rotorblades[J]. Journal of Aircraft,1994,31(3):473~479.
[61] Masarati, P. and Morandini, M.. On the modeling of rotating beams for rotorcraft bladeanalysis[C].28thEuropean Rotorcraft Forum, UK: Bristol,2002,62.1-11.
[62] Hegemier, G. A. and Nair, S.. A nonlinear dynamical theory for heterogeneous, anisotropic,elastic rods[J]. AIAA Journal,1977,15(1):8~15.
[63] Mansfield, E. H. and Sobey, A. J.. The fiber composite helicopter blade-part1: stiffnessproperties-part2: prospects for aeroelastic tailoring[J]. Aeronautical Quarterly,1979,30:413~449.
[64] Mansfield, E. H.. The stiffness of a two-cell anisotropic tube[J]. Aeronautical Quarterly,1981,32(4):338~353.
[65] Rehfield, L. W.. Design Analysis methodology for composite rotor blades[C]. Proceedingsof the Seventh DoN/NASA conference on Fibrous Composites in Structural Design,AFWAL-TR-85-3094,1985,(V(a)-1)~(V(a)-15).
[66] Smith, E. C. and Chopra, I.. Formulation and evaluation of an analytical model forcomposite box beams[J]. Journal of the American Helicopter Society,1991,36(2):23~35.
[67] Gunguli, R. and Chopra, I.. Aeroelastic optimization of a helicopter rotor with two-cellcomposite blades[J]. AIAA Journal,1996,34(4):835~854.
[68] W rndle, R. and Krahula,1. L.. Calculation of the cross section properties and the shearstresses of composite rotor blades[J]. Vertica,1982,6:111~129.
[69] W rndle, R. and Mang, H.. Zur Schubspannungsverteilung und schubsteifigkeit beiquerkraftbeanspruchten, inhomogenen querschitten beliebiger form, aus orthotropenwerkstoffen[J]. Ingenieur-Archiv,1984,54(1):25~42.
[70] Kosmatka, J. B.. Structural dynamics modeling of advanced composite propellers by thefinite element method[D]. Los Angeles:University of California,1986.
[71] Kosmatka, J. B. and Friedmann, P. P.. Vibration analysis of composite turbo propellersusing a nonlinear beam-type finite element approach[J]. AIAA Journal,1989,27(11):1606~1614.
[72]许钟,邹振民,樊蔚勋.复合材料旋翼桨叶剖面扭转刚度计算[J].南京航空学院学报,1988,20(2):130~134.
[73] Giavotto, V., Borri, M., Mantegazza, P., et al.. Anisotropic beam theory and application[J].Computers and Structures,1983,16(1-4):403~413.
[74] Borri, M. and Merlini, T.. A large displacement formulation for anisotropic beam analysis[J].Meccanica,1986,21:30~37.
[75] Bauchau, O. A.. A beam theory for anisotropic materials[J]. Journal of Applied Mechanics,1985,52(2):416~422.
[76] Bauchau, O. A., Coffenberry, B. S. and Rehfield, L. W.. Composite box beam analysis:theory and experiments[J]. Journal of Reinforced Plastics and Composites,1987,6:25~35.
[77] Hong, C. H. and Chopra, I.. Aeroelastic stability analysis of a composite rotor blades[J].Journal of American Helicopter Society,1985,30(2):57~67.
[78] Hong, C. H. and Chopra, I.. Aeroelastic stability of a composite bearingless rotor blades[J].Journal of American Helicopter Society,1986,31(4):29~35.
[79] Panda, B. and Chopra, I.. Dynamics of composite rotor blades in forward flight[J]. Vertica,1987,11(1/2):187~209.
[80] Smith, E. C. and Chopra, I.. Aeroelastic response and blade loads of a composite rotor inforward flight[C]. Proc.33rdAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamicsand Materials Conf., Dallas, TX,1992:1996~2014.
[81] Bauchau, O. A. and Hong, C. H.. Finite element approach to rotor blade modeling[J].Journal of the American Helicopter Society,1987,32(1):60~67.
[82] Bauchau, O. A. and Hong, C. H.. Large displacement analysis of naturally curved andtwisted composite beams[J]. AIAA Journal,1987,25(11):1469~1475.
[83] Bauchau, O. A. and Hong, C. H.. Nonlinear composite beam theory[J]. Journal of AppliedMechanics,1988,55:156~163.
[84] Hong, C. H.. Finite element approach to the dynamic analysis of composite helicopterblades[D]. New York: Rensselaer Polytechnic Institute,1987.
[85] Minguet, P. and Dugundji, J.. Experiments and analysis for composite blades under largedeflections: part1-static behavior[J]. AIAA Journal,1990,28(9):1573~1579.
[86] Minguet, P. and Dugundji, J.. Experiments and analysis for composite blades under largedeflections: part2-dynamic behavior[J]. AIAA Journal,1990,28(9):1580~1588.
[87] Hodges, D. H.. A mixed variational formulation based on exact intrinsic equations fordynamics of moving beams[J]. International Journal of Solids and Structures,1990,26(11):1253~1273.
[88] Danielson, D. A. and Hodges, D. H.. Nonlinear beam kinematics by decomposition of therotation tensor[J]. Journal of Applied Mechanics,1987,54(2):258~262.
[89] Danielson, D. A. and Hodges, D. H.. A beam theory for large global rotation, moderatelocal rotation and small strains[J]. Journal of Applied Mechanics,1988,55:179~184.
[90] Fulton, M. V. and Hodges, D. H.. Aeroelastic stability of Hingeless, elastically tailored rotorblades in hover[C]. Recent Advances in the Structural Dynamic Modeling of CompositeRotor Blades and Thick Composites, ASME Winter Annel Meeting,1992,30:9~23.
[91] Hodges, D. H., Atilgan, A. R., Cesnik, C. E. S., et al.. On a simplified strain energy functionfor geometrically nonlinear behaviour of anisotropic beams[J]. Composites Engineering,1992,2(5-7):513~526.
[92] Cesnik, C. E. S. and Hodges, D. H.. VABS: a new concept for composite rotor bladecross-sectional modeling[J]. Journal of the American Helicopter Society,1997,42(1):27~38.
[93] Volovoi, V. V., Hodges, D. H., Berdichevsky, V. L., et al.. Dynamic dispersion curves fornon-homogeneous, anisotropic beams with cross sections of arbitrary geometry[J]. Journal ofSound and Vibration,1998,215(5):1101~1120.
[94] Volovoi V. V. and Hodges, D. H.. Theory of anisotropic thin walled beams[J]. Journal ofApplied Mechanics,2000,67(3):453~459.
[95] Yu, W. B., Volovoi, V. V., Hodges, D. H., et al.. Validation of the variational asymptoticbeam sectional (VABS) analysis[J]. AIAA Journal,2002,40(10):2105~2112.
[96] Yu, W. B. and Hodges, D. H.. Generalized Timoskenko theory of the variational asymptoticbeam sectional analysis[J]. Journal of the American Helicopter Society,2005,50(1):46~55.
[97] Berdichevsky, V. L.. Variational-asymptotic method of constructing a theory of shells[J].Journal of Appied Mathematics and Mechanics,1979,43(4):664~687.
[98] Hodges, D. H.. Nolinear composite beam theory[M], Reston, Virginia:AIAA,2006:275~282.
[99] Paik, J., Volovoi, V. V. and Hodges, D. H.. Cross-sectional sizing and optimization ofcomposite blades[C]. Proceedings of the43rdAIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Materials Conference, Denver, Colorado,2002,601~610.
[100] Volovoi, V. V., Yoon, S., Lee, C. Y. et al.. Structural optimization of composite rotorblades[C]. Proceedings of the45thAIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference, Palm Springs, California,2004,19~22.
[101] Volovoi, V. V., Li, L., Ku, J. et al.. Multi-level structural optimization of composite rotorblades[C]. Proceedings of the46thAIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference, Austin, Texas,2005,18~21.
[102] Cesnik, C. E. S., Mok, J., Parikh, A. S. et al.. Optimization design framework for integrallytwisted helicopter blades[C]. Proceedings of the45thAIAA/ASME/ASCE/AHS/ASCStructures, Structural Dynamics and material Conference, Palm Springs, California,2004,2736~2750.
[103] Li, Li., Volovoi, V. V. and Hodges, D. H.. Cross-sectional design of composite rotor bladesconsidering manufacturing constraints[J]. Proceedings of the63th Annual Forum ofAmerican Helicopter Society, Virginia Beach, Virginia,2007.
[104]韩东,高正,王浩文,张虹秋.直升机桨叶刚柔耦合特性及计算方法分析[J].航空动力学报,2006,21(1):36~40.
[105] Johnson, W.. A comprehensive analytical model of rotorcraft aerodynamics and dynamics,part I: analysis development[R]. NASA TM81182,1980.
[106] Wu, X. X. and Sun, C. T.. Simplified theory for composite thin-walled beams[J]. AIAAJournal,1992,30(12):2945~2951.
[107] Johnson, E. R., Vasiliev, V. V. and Vasiliev, D. V.. Anistotropic thin-walled beams withclosed cross-sectional contours[J]. AIAA Journal,2001,39(12):2389~2393.
[108] Yu, W. B., Hodges, D. H., Volovoi, V. V., et al.. On Timoshenko-like modeling of initiallycurved and twisted composite beams[J]. International Journal of Solids and Structures,2002,39(19):5101~5121.
[109] Yu, W. B., Hodges, D. H., Volovoi, V. V., et al.. A generalized Vlasov theory for compositebeams[J]. Thin-Wallde Structures,2005,43:1493~1511.
[110] Miura, H.. Applications of numerical optimization methods to helicopter design problems–a survey[J]. Vertica,1985,9(2):141~154.
[111] Friedmann, P. P.. Helicopter vibration reduction using structural optimization withaeroelsatic/Multidisciplinary constraints–a survey[J]. Journal of Aircraft,1991,28(1):8~21.
[112] Taylor, R. B.. Helicopter vibration reduction by rotor blade modal shaping[C]. Proc.38thAnnual Forum of th AHS, Anaheim, California,1982:223~229.
[113] Shanthakumaran, P. and Friedmann, P. P.. Optimum design of rotor blades for vibrationreduction in forward flight[J]. Journal of the American Helicopter Society,1984,29(4):70~80.
[114]向锦武,张呈林,王适存.低振动旋翼桨叶的动力学优化设计[J].航空动力学报,1996,11(2):125~128.
[115] Chattopadhyay, A. and McCarthy, T. R.. A multidisciplinary optimization approach forvibration reduction in helicopter rotor blades[J]. Computer and Mathematics, withApplications,1993,25(2):59~72.
[116] Weller, W. H. and Davis, M. W.. Wind tunnel tests of helicopter blades designs optimizedfor minimum vibration[J]. Journal of the American Helicopter Society,1989,34(3):40~50.
[117] Weller, W. H. and Davis, M. W.. A modal-based procedure for efficiently predicting lowvibration rotor design[J]. Journal of American helicopter Society,1993,38(1):62~72.
[118] Bennett, R. L.. Optimum structural design[C]. Proc.38thAnnual Forum of th AHS,Anaheim, California,1982:90~101.
[119] Pritchard, J. I., Adelman, H. M., Walsh, J. L., et al.. Optimizing tuning masses for helicopterrotor blade vibration reduction and comparison with test data[J]. Journal of Aircraft,1993,30(6):906~910.
[120]尹春望.复合材料旋翼桨叶结构优化设计技术及应用[C].第二十二届中国直升机年会，2006.
[121] Hardin, J. C. and Lamkin, S. L.. Concepts for reduction of blade/vortex interaction noise[J].Journal of Aircraft,1987,24:120~125.
[122] Wells, V. L., Han, A. Y. and Crossley, W. A.. Acoustic design of rotor blades using a geneticalgorithm[C]. in AGARD Symposium on Aerodynamics and Aeroacoustics of Rotorcraft,1994,35:1~10.
[123] Wells, V. L.. Genetic algorithms in conceptual design of a light-weight, low-noise, tilt-rotoraircraft[R].NASA Report, NASA-CR-201404,1996
[124] Walsh, J. L.. Performance optimization of helicopter rotor blades[R]. NASA TM-104054,1991.
[125] Chattopadhyay, A., Walsh, J. L., Riley, M. F.. Integrated aerodynamic load/dynamicoptimization of helicopter rotor blades [J]. Journal of Aircraft,1991,28(1):58~65.
[126] Walsh, J. L., LaMarsh, W. J. and Adelman, H. M., Fully integrated aerodynamic/dynamicoptimization of helicopter rotor blades [J]. Mathematical and Computer Modelling, SpecialIssue on Rotorcragt Modelling:Part1,1993,18(3/4):53~72.
[127] Walsh, J. L., Young, K. C., Pritchard, J. L.. Multilevel decomposition approach to integratedaerodynamic/dynamic/structural optimization of helicopter rotor blades [R], NASATM-109084,1994.
[128] Walsh, J. L., Young, K. C., et al.. Integrated aerodynamic/dynamic/structural optimizationof helicopter rotor blades using multilevel decomposition [R]. NASA Technical Paper3465,1995.
[129] Callahan, C. B., Straub, F. K.. Design optimization of rotor blades for improvedperformance and vibration[C]. Proceedings of the47thAnnual Forum of the AmericanHelicopter Society,2,1991:869~882.
[130] Barwey, D. and Peters, D. A.. Optimization of composite rotor blades with advancedstructural and aerodynamic modeling[J]. Mathematical and Computer Modeling, SpecialIssue on Rotorcraft Modeling:Part1,1994,19(3-4):37~52.
[131] Peters, D. A., Ko, T., Korn, A., and Rossow, M. P., Design of helicopter rotor blades fordesired placement of natural frequencies[C]. Proceedings of the39thAnnual Forum of theAmerican Helicopter Society, American Helicopter Society, Alexandria, VA,1983,674~689.
[132] Lim, J. W. and Chopra, I.. Aeroelastic optimization of a helicopter rotor[J]. Journal of theAmerican Helicopter Society,1989,34(1):55~62.
[133] Lim, J. W. and Chopra, I.. Response and hub loads sensitivity analysis of a helicopterrotor[J]. AIAA Journal,1990,28(1):75~82.
[134] Lim, J. W. and Chopra, I.. Stability sensitivity of a helicopter rotor[J]. AIAA Journal,1990,28(6):1089~1097.
[135] Lim, J. W. and Chopra, I.. Aeroelastic optimization of a helicopter rotor using an efficientsensitivity analysis[J]. Journal of Aircraft,1991,28(1):29~37.
[136] Spence, A. M. and Celi, R.. Efficent sensitivity analysis for rotary-wing aeromechanicalproblems[J]. AIAA Journal1994,32(12):2337~2344.
[137] Celi, R. and Friedmann, P. P.. Rotor blade aeroelasticity in forward flight with an implicitaerodynamic formulation[J]. AIAA Journal,1988,26(12):1425~1433.
[138] Venkatesan, C., Friedmann, P. P. and Yuan, K. A.. A new sensitivity analysis for structuraloptimization of composite rotor blades[J]. Mathematical and Computer Modeling, SpecialIssue on Rotorcraft Modeling:Part1,1994,19(3-4):1~25.
[139] Vanderplaats, G. N.. Approximation concepts for numerical airfoil optimization[R]. NASATP-1433,1979.
[140] Vanderplaats, G. N.. Numerical optimization techniques for engineering design:withapplication[M]. McGraw-Hill, New York,1984.
[141] Ganguli, R.. Optimal design of a low vibration helicopter rotor using response furfaceapproximation[J]. Journal of Sound and Vibration,2002,258(2):327~344.
[142] Glza, B., Friedmann, P. P. and Liu, L.. Surrogate based optimization of helicopter rotorblades for vibration reduction in forward flight[J]. Structural and MultidisciplinaryOptimization,2008,35:341~363.
[143] Glaz, B., Goel, T., Liu, L., et al.. Multiple-surrogate approach to helicopter rotor bladevibration reduction[J]. AIAA Journal,2009,47(1):271~282.
[144] Crossley, W. A.. Using genetic algorithms as an automated methodology for conceptualdesign of rotorcraft[D]. PhD thesis, Tempe:Arizona State University,1995.
[145] Crossley, W. A., Wells, V. L. and Laananen, D. H.. The potential of genetic algorithms forconceptual design of rotor systems[J]. Engineering Optimization,1995,24:221~238.
[146] Crossley, W. A., Regulski, J., Wells, V. L., et al.. Incorporating genetic algorithms andsizing codes for conceptual design of rotorcraft[C]. in AHS/NASA Vertical Lift AircraftDesign Conference, San Francisco,1995.
[147] Chattopadhyay, A. and Seeley, C. E.. A simulated annealing technique for multiobjectiveoptimization of intelligent structures[J]. Smart Materials and Structures,1994,3(2):98~106.
[148] Chattopadhyay, A. and McCarthy, T. R.. Multiobjective design optimization of helicopterrotor blades with multidisciplinary constraints. In Optimization of Structural Systems andIndustrial Applications[M], Elsevier, London,1991,451~462.
[149] Chattopadhyay, A. and McCarthy, T. R.. Multidisciplinary optimization of helicopter rotorblades including design variable sensitivity[J]. Engineering Composties,1993,3(1):585~599.
[150] Chattopadhyay, A. and Chiu, Y. D.. An enhanced integrated aerodynamic/dynamic approachto optimum rotor blades design[J]. Structural Optimization,1992,4:75~84.
[151] Johnson, W.. A comprehensive analytical model of rotorcraft aerodynamics and dynamics-Johnson aeronautics version, Johnson Aeronautics[M]. Palo Alto, CA,1988.
[152] Booker, A. J., Dennis, J. J., Frank, P. D., et al.. A rigorous framework for optimization ofexpensive functions by surrogates[J]. Structure Optimization,1999,17:1~13.
[153] Shultz, L. A., Panda, B., Tarzanin, F. J., et al.. Interdisciplinary analysis for advanced rotorsapproach, capabilities and status[C]. American Helicopter Society Aeromechanics SpecialistsConf erence,1994:4-1~4~15.
[154] Davis, M. W. and Weller, W. H.. Helicopter rotor dynamics optimization with experimentalverification[J]. Journal of Aircraft,1991,28(1):38~48.
[155] Celi, R. and Friedmann, P. P.. Structural optimization with aeroelastic constraints of rotorblades with straight an swept tips[J]. AIAA Journal,1990,28(5):928~936.
[156]马勇.直升机基础数据库设计与应用系统实现[D].南京:南京航空航天大学硕士学位论文.2009.
[157] Martín, Menayo, Bolinches, Quero.. Computer-aided method of obtaining a ply model ofcomposite component: European, EP1840775A1[P],2007-03-10.
[158] Richard, E. Murrish, Christopher T. Hanson.. Alternate ply representation for compositedesign and manufacturing: US, US7099725B2[P].2006-08-29.
[159]戈德曼著.计算机图形学与几何造型导论.北京:清华大学出版社,2011.09.
[160]詹海生等编著.基于ACIS的几何造型技术与系统开发.北京:清华大学出版社,2002.
[161]莫蓉,常智勇主编.计算机辅助几何造型技术.北京:科学出版社,2009.05.
[162]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:北京航空航天大学出版社,1994:27~30.
[163] Woodward C.D., Cross-sectional design of B-spline surfaces[J]. Computer&graphics,1987,11(2):193~201.
[164] Woodward C. D., Skinning techniques for interactive B-spline surface interpolation[J].CAD,1988,20(8):441~451.
[165]廖文和,周来水,姚一兵,周儒荣.高级曲面设计功能的算法原理及实现[J].航空学报,1993,14(5):291~296.
[166]沈庆云,周来水,张乐年,周儒荣.一种NURBS曲面的裁剪方法[J].南京航空航天大学学报,1997,29(2):138~144.
[167]董洪伟,周来水,周儒荣.一种曲面裁剪的快速新算法[J].工程图学学报,2000(2):46~51.
[168]马翔,罗俊奇,康宝生,周儒荣.一种Trimmed NURBS曲面的裁剪方法[J].工程图学学报,1993(1):41~47.
[169] Pham, B.. Offset curve and surface: A brief survey[J]. Computer Aided Design,1992,24(3):223.
[170] Farouki, R. T.. Exact offset procedures for simple solids[J]. Computer Aided GeometricDesign,1985,2(3):257~279.
[171] Martin, R. R.. Principal patches–a new class of surface patch based on differentialgeometry[C]. in: Hagen P. J, eds., Proc. Eurographics’83, North-Holland, Amsterdam.
[172] Piegl, L. A., Tiler, W.. Computing offsets of NURBS curves and surface[J]. ComputerAided Design,1999,31(2):147~156.
[173] Chen, Y. I., Ravani, B.. Offset surface generation and contouring in computer aideddesign[J]. Journal of Mechanisms, Transmissions and Automation in Design: ASMETransactions,1987,109(3):133~142.
[174] Meakawa, T., Cho, W., Patrikalakis, N. M.. Computation of self-intersections of offsets ofBezier surface pathes[J]. Journal of Mechanical Design: ASME Transactions,1997,119(2):275~283.
[175] Oden J. T.. Mechanics of elastic structures[M]. New York: McGRAW-HILL, Inc.,1967,47~55.
[176]路录祥等.直升机结构与设计[M].北京:航空工业出版社,2009:171~174.
[177]杨卫东.直升机后掠桨尖旋翼气弹稳定性研究[J].南京航空航天大学学报,2003,35(3):248~252.
[178] Tiwari, S.,Koch, P., Fadel, G., et al.. AMGA:an archive-based micro genetic algorithm formulti-objective optimization[C]. In: Proceedings of the genetic and evolutionary computationconference (GECCO2008),12–16July2008, Atlanta, GA. NewYork: ACM,729~736.
[179]黎钧琪,石国桢.遗传算法交叉率与变异率关系的研究[J].武汉理工大学学报(交通科学与工程版),2003,(1):97~99.
[180]周明,孙树栋.遗传算法原理及应用[M].北京:国防工业出版社,1999:11~19.
[181]穆雪峰,姚卫星,余雄庆等.多学科设计优化中常用代理模型的研究[J].计算力学学报,2005,22(5):608~613.
[182]王琦. MDO优化算法研究[D].南京:南京航空航天大学博士学位论文.2008.
[183]崔东亮,冯国奇,王成恩.面向可变流程设计的复杂产品工程数据管理方法[J].计算机集成制造系统,2009,15(10):1908~1913.
[184]于加晴,查建中,陆一平等.面向复杂产品的分布式协同设计系统[J].中南大学学报(自然科学版),2010,41(2):539~545.
[185]吴宝贵,黄洪钟,张旭.复杂机械产品虚拟样机多学科设计优化研究[J].计算机集成制造系统,2006,12(11):1729~1735.
[186]赵勇,许林,陈小前,王振国.基于MDO方法的卫星集成设计系统分析与实现[J].国防科技大学学报,2006,28(4):1~5.
[187] Yang J. L.and Zhang L. Y.. RotorSIM: A coupled multidisciplinary simulation integrationframework for helicopter rotor blade design[C].2009WRI World Congress on SoftwareEngineering, WCSE2009,2:456~460.
[188]张光斌.基于工作流的过程集成及其在旋翼设计中的应用研究[D].南京:南京航空航天大学,2009.
[189]郝玉龙,姜韡.J2EE编程技术[M].北京:清华大学出版社,2005:3~5.
[2]黄承恭,吴建华.复合材料在直升机上的应用与发展[C].航空复合材料预研二十年回顾展望研讨会,2001:30~33.
[3]卢廷钧.数字化技术在直升机制造企业中的应用与发展[J].航空制造技术,2004,12:26~30
[4]栗琳著.直升机发展历程[M].北京:航空工业出版社,2007:11~16.
[5]徐德康著.蓝天铸春秋——航空科技[M].北京:北京理工大学出版社,2002:239~249.
[6]徐朝梁.谈谈直—8直升机[J].环球飞行,2008,7:240~245.
[7]冯春梅,曹智,李宣良等.甘洒热血写忠诚——人民子弟兵抢险救灾纪实[N].人民日报,2010-09-16(1).
[8]邱光荣,赵伟华.推进直升机产业发展新跨越[J].中国军转民,2009,(9):70~74.
[9]张呈林.直升机旋翼技术的发展[N],中国航空报,2000-10-20.
[10]沈亨业.浅析我国直升机旋翼技术发展问题[J].直升机技术,1998,113(1):45~51.
[11]杨乃宾等.直升机复合材料结构设计[M].北京:国防工业出版社.2008:42~43.
[12]倪先平.直升机百年[J].航空工业经济研究,2008,1:21~28.
[13]倪先平.直升机技术发展现状与展望[J].航空学报,2003,24(1):15~20.
[14]豫章.直升机发展概述[J].直升机技术,2003,136(4):35~41.
[15]布拉图欣，И.П.著；刘谋佶，沈骥译.直升机设计与构造[M].北京：国防工业出版社,1959:138.
[16]孙如林.美国直升机先进旋翼技术发展和现状[J].直升机技术,1995,103(2):43~48.
[17] Yuan K. A. and Friedmann, P. P.. Aeroelasticity and structural optimization of compositehelicopter rotor blades with swept tips[R]. NASA Contractor Report4665,1995.
[18] Bao, J. S.. Development of mach scale rotors with composite tailored couplings forvibration reduction[D]. Maryland: University of Maryland College Park,2004.
[19]冼杏娟.西德MBB公式生产的复合材料产品[J].机械工程材料,1983,3:37~38.
[20]吴跃.再接再厉努力实现直升机旋翼技术的跨越发展[J].直升机技术,2007,3:2~2.
[21]张呈林,林国梁.Y-2直升机玻璃钢旋翼桨叶的研制[J].南京航空航天大学学报,1979,3:154~164.
[22]徐明,徐桂祺.海豚型旋翼桨叶气动弹性稳定分析[J].南京航空航天大学学报,1987,1:26~36.
[23]樊光华.浅析我国直升机技术的新发展[J].航空与航天,2001,4:8~10.
[24] Bielawa, R. L.. Techniques for stability analysis and design optimization with dynamicconstraints of non conservative linear systems[J]. AIAA Paper71-388,1971.
[25] Peters, D. A., Rossow, M. P., Korn, A., et al.. Design of helicopter rotor blades for optimumdynamic characteristics[J]. Journal of Comptuters and Mathematics with Applications,1986,12(1):85~109.
[26] Celi, R. and Friedmann, P. P.. Aeroelastic modeling of swept tip rotor blades using finiteelements[J]. Journal of American Helicopter Society,1988,33(2):
[27]樊光华,侯汝良,程耿东等.复合材料旋翼桨叶的结构优化与控制研究[J].航空学报,1991,12(12):554~559.
[28]顾元宪,刘书田,关振群等.面向设计的复合材料旋翼桨叶动力学优化设计[J].航空学报1998,19(3):338~341.
[29] Hodges, D. H.. A review of composite rotor blade modeling[J]. AIAA Journal,1990,28(3):561~565.
[30]顾元宪,程耿东,孙如林等.直升机旋翼结构优化设计研究综述[J].直升机技术,1995,101(1):16~25.
[31] Celi, R.. Recent applications of design optimization to rotorcraft–a survey[J]. Journal ofAircraft,1999,36(1):176~189.
[32]郭俊贤,向锦武,张晓谷.降低旋翼激振力的动力学优化设计研究综述[J].直升机技术,2000,121(1):7~13.
[33]向锦武,郭俊贤,张晓谷.直升机减振的旋翼桨叶优化设计研究综述[J].北京航空航天大学学报,2001,27(1):32~35.
[34] Ganguli, R.. Survey of recent development in rotorcraft design optimization[J]. Journal ofAircraft,2004,41(3):493~510.
[35] Grandl R.. Vrtual process week in the experimental vehicle build at BMW AG[C].experimental vehicle division, BMW AG, Dept T1-360,80788, Munieh, Germany, Roboticsand Computer Intergrated Manufacturing,2001,17:65~71.
[36]宁振波.数字样机在飞机设计中应用[J].航空制造技术,2002,10:20~22.
[37]冯潼能,王铮阳,孟静晖.MBD技术在数字化协同制造中的应用与展望[J].南京航空航天大学学报,2012,44(S1):132~137.
[38]张景新.数字化设计制造技术在直升机复合材料结构中的应用[J].直升机技术,2005,144(4):23~26.
[39]武美萍,廖文和.虚拟产品开发管理技术在直升机数字样机开发中的应用研究[J].机械科学与技术,2008,27(5):633~639.
[40]余明.数字样机技术在直升机设计中的应用研究[J].直升机技术,2002,129(1):16~21.
[41]吴跃,郑文心.航空制造业数字化总体框架研究[J].CAD/CAM与制造业信息化,2004,(8):11~13.
[42]张景新.直升机结构三维实体数字预装配技术探讨[J].直升机技术,2000,124(4):35~38.
[43]郑朔昉,徐明,倪先平.基于CATIA V5的三维数字化通用零部件/标准件库的创建与使用[J].航空标准化与质量,2001,(6):7~10.
[44]陈阳平,谢强,丁秋林.基于知识的直升机数字化设计研究[J].直升机技术,2005,141(1):5～8.
[45]黄志文.基于CATIA、 VPM的结构三维数字化设计技术[J].直升机技术,2010,165(4):20～25.
[46] Li, L. H.. Structural design of composite rotor blades with consideration ofmanufacturability, durability and manufacturing uncertainties[D]. Atlanta:Georgia Institute ofTechnology,2008.
[47] Volovoi, V. V. and Hodges, D. H.. Assessment of beam modeling methods for rotor bladeapplication[J]. Mathematical and Computer Modelling,2001,33:1099~1112.
[48] Houbolt, J. C. and Brooks, G. W.. Differential equation of motion for combined flapwisebending, chordwise bending, and torsion of twisted nonuinform rotor blades[R]. NACAReport1346,1958.
[49] Hodges, D. H. and Dowell, E. H.. Nonlinear equations of motion for the elastic bending andtorsion of twisted nonuniform rotor blades[R]. NASA TN D-7818,1974.
[50] Rosen, A. and Friedmann, P. P.. Nonlinear equations of equilibrium for elastic helicopter orwind turbine blade undergoing moderate deflection[R]. NASA CR-159478,1978.
[51] Dowell, E. H., Traybar, J. and Hodges, D. H.. An experimental theoretical correlation studyof non-linear bending and torsion deformations of a cantilever beam[J]. Journal of Sound andVibrations,1977,50:533~544.
[52] Rosen, A. and Friedmann, P. P.. Nonlinear behavior of elastic slender straight beamsundergoing small strains and moderate rotations[J]. Jouranl of Applied Mechanics,1979,46:161~168.
[53] Hodges, D. H. and Ormiston, R. A.. Stability of elastic bending and torsion of uniformcantilever rotor blades in hover with variable structural coupling[R]. NASA TN D-8192,1976.
[54] Shamie, J. and Friedmann, P. P.. Effect of moderate deflections on the aeroelastic stabilityof a rotor blade in forward flight[C]. Proc.3rdEuropean Rotorcraft and Powered Lift AircraftForum, Aix-en-Provence,1977:24.1~24.37.
[55] Kaza, K. R. and Kvaternik, R. G.. Nonlinear aeroelastic equations for combined flapwisebending, chordwise bending, torsion and extension of twisted non-uniform rotor blades inforward flight[R]. NASA TM-74059,1977.
[56] Hodges, D. H.. Nonlinear equations for dynamics of pretwisted beams undergoing smallstrains and large rotations[R]. NASA TP-2470,1985.
[57] Hodges, D. H., Hopkins, A. K., Kunz, D. L. and Hinnant, H. E.. Introduction to GRASP–general rotorcraft aeromechanical stability program–a modern approach to rotorcraftmodeling[C]. Proc.42ndAnnual Forum of the American Helicopter Society, Washington D.C.,1986:739~756.
[58] Friedmann, P. P.. Helicopter rotor dynamics and aeroelasticity: some key ideas andinsights[J]. Vertica,1990,14(1):101~121.
[59] Friedmann, P. P. and Hodges, D. H.. Rotary-wing aeroelasticity with application to VTOLVehicles[C]. Chapter6, in Flight-vehicle materials, structures and dynamics[M], Vol.5-Structural dynamics and aeroelasticity, edited by Noor, A.K. and Venneri, S. L., ASME,1993:299~391.
[60] Kunz. D. L.. Survey and comparision of engineering beam theories for helicopter rotorblades[J]. Journal of Aircraft,1994,31(3):473~479.
[61] Masarati, P. and Morandini, M.. On the modeling of rotating beams for rotorcraft bladeanalysis[C].28thEuropean Rotorcraft Forum, UK: Bristol,2002,62.1-11.
[62] Hegemier, G. A. and Nair, S.. A nonlinear dynamical theory for heterogeneous, anisotropic,elastic rods[J]. AIAA Journal,1977,15(1):8~15.
[63] Mansfield, E. H. and Sobey, A. J.. The fiber composite helicopter blade-part1: stiffnessproperties-part2: prospects for aeroelastic tailoring[J]. Aeronautical Quarterly,1979,30:413~449.
[64] Mansfield, E. H.. The stiffness of a two-cell anisotropic tube[J]. Aeronautical Quarterly,1981,32(4):338~353.
[65] Rehfield, L. W.. Design Analysis methodology for composite rotor blades[C]. Proceedingsof the Seventh DoN/NASA conference on Fibrous Composites in Structural Design,AFWAL-TR-85-3094,1985,(V(a)-1)~(V(a)-15).
[66] Smith, E. C. and Chopra, I.. Formulation and evaluation of an analytical model forcomposite box beams[J]. Journal of the American Helicopter Society,1991,36(2):23~35.
[67] Gunguli, R. and Chopra, I.. Aeroelastic optimization of a helicopter rotor with two-cellcomposite blades[J]. AIAA Journal,1996,34(4):835~854.
[68] W rndle, R. and Krahula,1. L.. Calculation of the cross section properties and the shearstresses of composite rotor blades[J]. Vertica,1982,6:111~129.
[69] W rndle, R. and Mang, H.. Zur Schubspannungsverteilung und schubsteifigkeit beiquerkraftbeanspruchten, inhomogenen querschitten beliebiger form, aus orthotropenwerkstoffen[J]. Ingenieur-Archiv,1984,54(1):25~42.
[70] Kosmatka, J. B.. Structural dynamics modeling of advanced composite propellers by thefinite element method[D]. Los Angeles:University of California,1986.
[71] Kosmatka, J. B. and Friedmann, P. P.. Vibration analysis of composite turbo propellersusing a nonlinear beam-type finite element approach[J]. AIAA Journal,1989,27(11):1606~1614.
[72]许钟,邹振民,樊蔚勋.复合材料旋翼桨叶剖面扭转刚度计算[J].南京航空学院学报,1988,20(2):130~134.
[73] Giavotto, V., Borri, M., Mantegazza, P., et al.. Anisotropic beam theory and application[J].Computers and Structures,1983,16(1-4):403~413.
[74] Borri, M. and Merlini, T.. A large displacement formulation for anisotropic beam analysis[J].Meccanica,1986,21:30~37.
[75] Bauchau, O. A.. A beam theory for anisotropic materials[J]. Journal of Applied Mechanics,1985,52(2):416~422.
[76] Bauchau, O. A., Coffenberry, B. S. and Rehfield, L. W.. Composite box beam analysis:theory and experiments[J]. Journal of Reinforced Plastics and Composites,1987,6:25~35.
[77] Hong, C. H. and Chopra, I.. Aeroelastic stability analysis of a composite rotor blades[J].Journal of American Helicopter Society,1985,30(2):57~67.
[78] Hong, C. H. and Chopra, I.. Aeroelastic stability of a composite bearingless rotor blades[J].Journal of American Helicopter Society,1986,31(4):29~35.
[79] Panda, B. and Chopra, I.. Dynamics of composite rotor blades in forward flight[J]. Vertica,1987,11(1/2):187~209.
[80] Smith, E. C. and Chopra, I.. Aeroelastic response and blade loads of a composite rotor inforward flight[C]. Proc.33rdAIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamicsand Materials Conf., Dallas, TX,1992:1996~2014.
[81] Bauchau, O. A. and Hong, C. H.. Finite element approach to rotor blade modeling[J].Journal of the American Helicopter Society,1987,32(1):60~67.
[82] Bauchau, O. A. and Hong, C. H.. Large displacement analysis of naturally curved andtwisted composite beams[J]. AIAA Journal,1987,25(11):1469~1475.
[83] Bauchau, O. A. and Hong, C. H.. Nonlinear composite beam theory[J]. Journal of AppliedMechanics,1988,55:156~163.
[84] Hong, C. H.. Finite element approach to the dynamic analysis of composite helicopterblades[D]. New York: Rensselaer Polytechnic Institute,1987.
[85] Minguet, P. and Dugundji, J.. Experiments and analysis for composite blades under largedeflections: part1-static behavior[J]. AIAA Journal,1990,28(9):1573~1579.
[86] Minguet, P. and Dugundji, J.. Experiments and analysis for composite blades under largedeflections: part2-dynamic behavior[J]. AIAA Journal,1990,28(9):1580~1588.
[87] Hodges, D. H.. A mixed variational formulation based on exact intrinsic equations fordynamics of moving beams[J]. International Journal of Solids and Structures,1990,26(11):1253~1273.
[88] Danielson, D. A. and Hodges, D. H.. Nonlinear beam kinematics by decomposition of therotation tensor[J]. Journal of Applied Mechanics,1987,54(2):258~262.
[89] Danielson, D. A. and Hodges, D. H.. A beam theory for large global rotation, moderatelocal rotation and small strains[J]. Journal of Applied Mechanics,1988,55:179~184.
[90] Fulton, M. V. and Hodges, D. H.. Aeroelastic stability of Hingeless, elastically tailored rotorblades in hover[C]. Recent Advances in the Structural Dynamic Modeling of CompositeRotor Blades and Thick Composites, ASME Winter Annel Meeting,1992,30:9~23.
[91] Hodges, D. H., Atilgan, A. R., Cesnik, C. E. S., et al.. On a simplified strain energy functionfor geometrically nonlinear behaviour of anisotropic beams[J]. Composites Engineering,1992,2(5-7):513~526.
[92] Cesnik, C. E. S. and Hodges, D. H.. VABS: a new concept for composite rotor bladecross-sectional modeling[J]. Journal of the American Helicopter Society,1997,42(1):27~38.
[93] Volovoi, V. V., Hodges, D. H., Berdichevsky, V. L., et al.. Dynamic dispersion curves fornon-homogeneous, anisotropic beams with cross sections of arbitrary geometry[J]. Journal ofSound and Vibration,1998,215(5):1101~1120.
[94] Volovoi V. V. and Hodges, D. H.. Theory of anisotropic thin walled beams[J]. Journal ofApplied Mechanics,2000,67(3):453~459.
[95] Yu, W. B., Volovoi, V. V., Hodges, D. H., et al.. Validation of the variational asymptoticbeam sectional (VABS) analysis[J]. AIAA Journal,2002,40(10):2105~2112.
[96] Yu, W. B. and Hodges, D. H.. Generalized Timoskenko theory of the variational asymptoticbeam sectional analysis[J]. Journal of the American Helicopter Society,2005,50(1):46~55.
[97] Berdichevsky, V. L.. Variational-asymptotic method of constructing a theory of shells[J].Journal of Appied Mathematics and Mechanics,1979,43(4):664~687.
[98] Hodges, D. H.. Nolinear composite beam theory[M], Reston, Virginia:AIAA,2006:275~282.
[99] Paik, J., Volovoi, V. V. and Hodges, D. H.. Cross-sectional sizing and optimization ofcomposite blades[C]. Proceedings of the43rdAIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Materials Conference, Denver, Colorado,2002,601~610.
[100] Volovoi, V. V., Yoon, S., Lee, C. Y. et al.. Structural optimization of composite rotorblades[C]. Proceedings of the45thAIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference, Palm Springs, California,2004,19~22.
[101] Volovoi, V. V., Li, L., Ku, J. et al.. Multi-level structural optimization of composite rotorblades[C]. Proceedings of the46thAIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials Conference, Austin, Texas,2005,18~21.
[102] Cesnik, C. E. S., Mok, J., Parikh, A. S. et al.. Optimization design framework for integrallytwisted helicopter blades[C]. Proceedings of the45thAIAA/ASME/ASCE/AHS/ASCStructures, Structural Dynamics and material Conference, Palm Springs, California,2004,2736~2750.
[103] Li, Li., Volovoi, V. V. and Hodges, D. H.. Cross-sectional design of composite rotor bladesconsidering manufacturing constraints[J]. Proceedings of the63th Annual Forum ofAmerican Helicopter Society, Virginia Beach, Virginia,2007.
[104]韩东,高正,王浩文,张虹秋.直升机桨叶刚柔耦合特性及计算方法分析[J].航空动力学报,2006,21(1):36~40.
[105] Johnson, W.. A comprehensive analytical model of rotorcraft aerodynamics and dynamics,part I: analysis development[R]. NASA TM81182,1980.
[106] Wu, X. X. and Sun, C. T.. Simplified theory for composite thin-walled beams[J]. AIAAJournal,1992,30(12):2945~2951.
[107] Johnson, E. R., Vasiliev, V. V. and Vasiliev, D. V.. Anistotropic thin-walled beams withclosed cross-sectional contours[J]. AIAA Journal,2001,39(12):2389~2393.
[108] Yu, W. B., Hodges, D. H., Volovoi, V. V., et al.. On Timoshenko-like modeling of initiallycurved and twisted composite beams[J]. International Journal of Solids and Structures,2002,39(19):5101~5121.
[109] Yu, W. B., Hodges, D. H., Volovoi, V. V., et al.. A generalized Vlasov theory for compositebeams[J]. Thin-Wallde Structures,2005,43:1493~1511.
[110] Miura, H.. Applications of numerical optimization methods to helicopter design problems–a survey[J]. Vertica,1985,9(2):141~154.
[111] Friedmann, P. P.. Helicopter vibration reduction using structural optimization withaeroelsatic/Multidisciplinary constraints–a survey[J]. Journal of Aircraft,1991,28(1):8~21.
[112] Taylor, R. B.. Helicopter vibration reduction by rotor blade modal shaping[C]. Proc.38thAnnual Forum of th AHS, Anaheim, California,1982:223~229.
[113] Shanthakumaran, P. and Friedmann, P. P.. Optimum design of rotor blades for vibrationreduction in forward flight[J]. Journal of the American Helicopter Society,1984,29(4):70~80.
[114]向锦武,张呈林,王适存.低振动旋翼桨叶的动力学优化设计[J].航空动力学报,1996,11(2):125~128.
[115] Chattopadhyay, A. and McCarthy, T. R.. A multidisciplinary optimization approach forvibration reduction in helicopter rotor blades[J]. Computer and Mathematics, withApplications,1993,25(2):59~72.
[116] Weller, W. H. and Davis, M. W.. Wind tunnel tests of helicopter blades designs optimizedfor minimum vibration[J]. Journal of the American Helicopter Society,1989,34(3):40~50.
[117] Weller, W. H. and Davis, M. W.. A modal-based procedure for efficiently predicting lowvibration rotor design[J]. Journal of American helicopter Society,1993,38(1):62~72.
[118] Bennett, R. L.. Optimum structural design[C]. Proc.38thAnnual Forum of th AHS,Anaheim, California,1982:90~101.
[119] Pritchard, J. I., Adelman, H. M., Walsh, J. L., et al.. Optimizing tuning masses for helicopterrotor blade vibration reduction and comparison with test data[J]. Journal of Aircraft,1993,30(6):906~910.
[120]尹春望.复合材料旋翼桨叶结构优化设计技术及应用[C].第二十二届中国直升机年会，2006.
[121] Hardin, J. C. and Lamkin, S. L.. Concepts for reduction of blade/vortex interaction noise[J].Journal of Aircraft,1987,24:120~125.
[122] Wells, V. L., Han, A. Y. and Crossley, W. A.. Acoustic design of rotor blades using a geneticalgorithm[C]. in AGARD Symposium on Aerodynamics and Aeroacoustics of Rotorcraft,1994,35:1~10.
[123] Wells, V. L.. Genetic algorithms in conceptual design of a light-weight, low-noise, tilt-rotoraircraft[R].NASA Report, NASA-CR-201404,1996
[124] Walsh, J. L.. Performance optimization of helicopter rotor blades[R]. NASA TM-104054,1991.
[125] Chattopadhyay, A., Walsh, J. L., Riley, M. F.. Integrated aerodynamic load/dynamicoptimization of helicopter rotor blades [J]. Journal of Aircraft,1991,28(1):58~65.
[126] Walsh, J. L., LaMarsh, W. J. and Adelman, H. M., Fully integrated aerodynamic/dynamicoptimization of helicopter rotor blades [J]. Mathematical and Computer Modelling, SpecialIssue on Rotorcragt Modelling:Part1,1993,18(3/4):53~72.
[127] Walsh, J. L., Young, K. C., Pritchard, J. L.. Multilevel decomposition approach to integratedaerodynamic/dynamic/structural optimization of helicopter rotor blades [R], NASATM-109084,1994.
[128] Walsh, J. L., Young, K. C., et al.. Integrated aerodynamic/dynamic/structural optimizationof helicopter rotor blades using multilevel decomposition [R]. NASA Technical Paper3465,1995.
[129] Callahan, C. B., Straub, F. K.. Design optimization of rotor blades for improvedperformance and vibration[C]. Proceedings of the47thAnnual Forum of the AmericanHelicopter Society,2,1991:869~882.
[130] Barwey, D. and Peters, D. A.. Optimization of composite rotor blades with advancedstructural and aerodynamic modeling[J]. Mathematical and Computer Modeling, SpecialIssue on Rotorcraft Modeling:Part1,1994,19(3-4):37~52.
[131] Peters, D. A., Ko, T., Korn, A., and Rossow, M. P., Design of helicopter rotor blades fordesired placement of natural frequencies[C]. Proceedings of the39thAnnual Forum of theAmerican Helicopter Society, American Helicopter Society, Alexandria, VA,1983,674~689.
[132] Lim, J. W. and Chopra, I.. Aeroelastic optimization of a helicopter rotor[J]. Journal of theAmerican Helicopter Society,1989,34(1):55~62.
[133] Lim, J. W. and Chopra, I.. Response and hub loads sensitivity analysis of a helicopterrotor[J]. AIAA Journal,1990,28(1):75~82.
[134] Lim, J. W. and Chopra, I.. Stability sensitivity of a helicopter rotor[J]. AIAA Journal,1990,28(6):1089~1097.
[135] Lim, J. W. and Chopra, I.. Aeroelastic optimization of a helicopter rotor using an efficientsensitivity analysis[J]. Journal of Aircraft,1991,28(1):29~37.
[136] Spence, A. M. and Celi, R.. Efficent sensitivity analysis for rotary-wing aeromechanicalproblems[J]. AIAA Journal1994,32(12):2337~2344.
[137] Celi, R. and Friedmann, P. P.. Rotor blade aeroelasticity in forward flight with an implicitaerodynamic formulation[J]. AIAA Journal,1988,26(12):1425~1433.
[138] Venkatesan, C., Friedmann, P. P. and Yuan, K. A.. A new sensitivity analysis for structuraloptimization of composite rotor blades[J]. Mathematical and Computer Modeling, SpecialIssue on Rotorcraft Modeling:Part1,1994,19(3-4):1~25.
[139] Vanderplaats, G. N.. Approximation concepts for numerical airfoil optimization[R]. NASATP-1433,1979.
[140] Vanderplaats, G. N.. Numerical optimization techniques for engineering design:withapplication[M]. McGraw-Hill, New York,1984.
[141] Ganguli, R.. Optimal design of a low vibration helicopter rotor using response furfaceapproximation[J]. Journal of Sound and Vibration,2002,258(2):327~344.
[142] Glza, B., Friedmann, P. P. and Liu, L.. Surrogate based optimization of helicopter rotorblades for vibration reduction in forward flight[J]. Structural and MultidisciplinaryOptimization,2008,35:341~363.
[143] Glaz, B., Goel, T., Liu, L., et al.. Multiple-surrogate approach to helicopter rotor bladevibration reduction[J]. AIAA Journal,2009,47(1):271~282.
[144] Crossley, W. A.. Using genetic algorithms as an automated methodology for conceptualdesign of rotorcraft[D]. PhD thesis, Tempe:Arizona State University,1995.
[145] Crossley, W. A., Wells, V. L. and Laananen, D. H.. The potential of genetic algorithms forconceptual design of rotor systems[J]. Engineering Optimization,1995,24:221~238.
[146] Crossley, W. A., Regulski, J., Wells, V. L., et al.. Incorporating genetic algorithms andsizing codes for conceptual design of rotorcraft[C]. in AHS/NASA Vertical Lift AircraftDesign Conference, San Francisco,1995.
[147] Chattopadhyay, A. and Seeley, C. E.. A simulated annealing technique for multiobjectiveoptimization of intelligent structures[J]. Smart Materials and Structures,1994,3(2):98~106.
[148] Chattopadhyay, A. and McCarthy, T. R.. Multiobjective design optimization of helicopterrotor blades with multidisciplinary constraints. In Optimization of Structural Systems andIndustrial Applications[M], Elsevier, London,1991,451~462.
[149] Chattopadhyay, A. and McCarthy, T. R.. Multidisciplinary optimization of helicopter rotorblades including design variable sensitivity[J]. Engineering Composties,1993,3(1):585~599.
[150] Chattopadhyay, A. and Chiu, Y. D.. An enhanced integrated aerodynamic/dynamic approachto optimum rotor blades design[J]. Structural Optimization,1992,4:75~84.
[151] Johnson, W.. A comprehensive analytical model of rotorcraft aerodynamics and dynamics-Johnson aeronautics version, Johnson Aeronautics[M]. Palo Alto, CA,1988.
[152] Booker, A. J., Dennis, J. J., Frank, P. D., et al.. A rigorous framework for optimization ofexpensive functions by surrogates[J]. Structure Optimization,1999,17:1~13.
[153] Shultz, L. A., Panda, B., Tarzanin, F. J., et al.. Interdisciplinary analysis for advanced rotorsapproach, capabilities and status[C]. American Helicopter Society Aeromechanics SpecialistsConf erence,1994:4-1~4~15.
[154] Davis, M. W. and Weller, W. H.. Helicopter rotor dynamics optimization with experimentalverification[J]. Journal of Aircraft,1991,28(1):38~48.
[155] Celi, R. and Friedmann, P. P.. Structural optimization with aeroelastic constraints of rotorblades with straight an swept tips[J]. AIAA Journal,1990,28(5):928~936.
[156]马勇.直升机基础数据库设计与应用系统实现[D].南京:南京航空航天大学硕士学位论文.2009.
[157] Martín, Menayo, Bolinches, Quero.. Computer-aided method of obtaining a ply model ofcomposite component: European, EP1840775A1[P],2007-03-10.
[158] Richard, E. Murrish, Christopher T. Hanson.. Alternate ply representation for compositedesign and manufacturing: US, US7099725B2[P].2006-08-29.
[159]戈德曼著.计算机图形学与几何造型导论.北京:清华大学出版社,2011.09.
[160]詹海生等编著.基于ACIS的几何造型技术与系统开发.北京:清华大学出版社,2002.
[161]莫蓉,常智勇主编.计算机辅助几何造型技术.北京:科学出版社,2009.05.
[162]施法中.计算机辅助几何设计与非均匀有理B样条[M].北京:北京航空航天大学出版社,1994:27~30.
[163] Woodward C.D., Cross-sectional design of B-spline surfaces[J]. Computer&graphics,1987,11(2):193~201.
[164] Woodward C. D., Skinning techniques for interactive B-spline surface interpolation[J].CAD,1988,20(8):441~451.
[165]廖文和,周来水,姚一兵,周儒荣.高级曲面设计功能的算法原理及实现[J].航空学报,1993,14(5):291~296.
[166]沈庆云,周来水,张乐年,周儒荣.一种NURBS曲面的裁剪方法[J].南京航空航天大学学报,1997,29(2):138~144.
[167]董洪伟,周来水,周儒荣.一种曲面裁剪的快速新算法[J].工程图学学报,2000(2):46~51.
[168]马翔,罗俊奇,康宝生,周儒荣.一种Trimmed NURBS曲面的裁剪方法[J].工程图学学报,1993(1):41~47.
[169] Pham, B.. Offset curve and surface: A brief survey[J]. Computer Aided Design,1992,24(3):223.
[170] Farouki, R. T.. Exact offset procedures for simple solids[J]. Computer Aided GeometricDesign,1985,2(3):257~279.
[171] Martin, R. R.. Principal patches–a new class of surface patch based on differentialgeometry[C]. in: Hagen P. J, eds., Proc. Eurographics’83, North-Holland, Amsterdam.
[172] Piegl, L. A., Tiler, W.. Computing offsets of NURBS curves and surface[J]. ComputerAided Design,1999,31(2):147~156.
[173] Chen, Y. I., Ravani, B.. Offset surface generation and contouring in computer aideddesign[J]. Journal of Mechanisms, Transmissions and Automation in Design: ASMETransactions,1987,109(3):133~142.
[174] Meakawa, T., Cho, W., Patrikalakis, N. M.. Computation of self-intersections of offsets ofBezier surface pathes[J]. Journal of Mechanical Design: ASME Transactions,1997,119(2):275~283.
[175] Oden J. T.. Mechanics of elastic structures[M]. New York: McGRAW-HILL, Inc.,1967,47~55.
[176]路录祥等.直升机结构与设计[M].北京:航空工业出版社,2009:171~174.
[177]杨卫东.直升机后掠桨尖旋翼气弹稳定性研究[J].南京航空航天大学学报,2003,35(3):248~252.
[178] Tiwari, S.,Koch, P., Fadel, G., et al.. AMGA:an archive-based micro genetic algorithm formulti-objective optimization[C]. In: Proceedings of the genetic and evolutionary computationconference (GECCO2008),12–16July2008, Atlanta, GA. NewYork: ACM,729~736.
[179]黎钧琪,石国桢.遗传算法交叉率与变异率关系的研究[J].武汉理工大学学报(交通科学与工程版),2003,(1):97~99.
[180]周明,孙树栋.遗传算法原理及应用[M].北京:国防工业出版社,1999:11~19.
[181]穆雪峰,姚卫星,余雄庆等.多学科设计优化中常用代理模型的研究[J].计算力学学报,2005,22(5):608~613.
[182]王琦. MDO优化算法研究[D].南京:南京航空航天大学博士学位论文.2008.
[183]崔东亮,冯国奇,王成恩.面向可变流程设计的复杂产品工程数据管理方法[J].计算机集成制造系统,2009,15(10):1908~1913.
[184]于加晴,查建中,陆一平等.面向复杂产品的分布式协同设计系统[J].中南大学学报(自然科学版),2010,41(2):539~545.
[185]吴宝贵,黄洪钟,张旭.复杂机械产品虚拟样机多学科设计优化研究[J].计算机集成制造系统,2006,12(11):1729~1735.
[186]赵勇,许林,陈小前,王振国.基于MDO方法的卫星集成设计系统分析与实现[J].国防科技大学学报,2006,28(4):1~5.
[187] Yang J. L.and Zhang L. Y.. RotorSIM: A coupled multidisciplinary simulation integrationframework for helicopter rotor blade design[C].2009WRI World Congress on SoftwareEngineering, WCSE2009,2:456~460.
[188]张光斌.基于工作流的过程集成及其在旋翼设计中的应用研究[D].南京:南京航空航天大学,2009.
[189]郝玉龙,姜韡.J2EE编程技术[M].北京:清华大学出版社,2005:3~5.