复杂三维曲梁结构的无闭锁等几何分析算法研究

梁结构在工程中应用广泛,梁结构的仿真分析是计算力学的一个重要研究内容。该文研究了复杂三维曲梁结构的等几何分析方法,首次应用拟协调有限元中的多套函数技术,使用降阶基函数逼近梁内应变项,解决复杂三维曲梁结构仿真中的闭锁问题。利用全局坐标系列式方法,避免了单元刚度阵组装时的复杂坐标变换过程,提高计算效率。使用多片NURBS （非均匀有理B样条）数据表示复杂三维梁结构,可精确描述曲梁结构的几何形状,与有限元方法等仿真技术相比避免了网格生成过程,减少了几何误差。数值结果表明该文算法可有效解决闭锁问题,适于复杂三维曲梁结构的仿真分析。     

基于断层超声、磁共振和三维磁共振重建的女性肛提肌影像学研究

目的:应用断层超声成像(Tomographic Ultrasound Imaging,TUI)、磁共振成像(Magnetic Resonance Imaging,MRI)及磁共振三维重建对未育女性肛提肌解剖结构进行影像学研究。方法:以10例未育女性为研究对象。采用经会阴三维超声取得肛提肌TUI图像,MRI对其进行盆底扫描,获得肛提肌薄层图像,采用医学图像重建软件Mimics重建出肛提肌的三维立体几何模型。结果:TUI可以显示盆底耻骨直肠肌、耻骨肛管肌、耻骨会阴肌,MRI可以显示盆底耻骨直肠肌、耻骨肛管肌、耻骨会阴肌、髂尾肌,TUI和MRI都难以显示耻骨阴道肌,MRI三维重建可以空间多角度观察耻骨直肠肌、耻骨肛管肌、耻骨会阴肌、髂尾肌的形态及其组成部分。结论:TUI和MRI均可识别肛提肌的结构与组成,MRI对于髂尾肌的识别较TUI更佳,MRI三维重建可以更直观地显示肛提肌立体形态。     

Mechanics of three-dimensional braided structures for composite materials – part I: fabric structure and fibre volume fraction

This paper is the first part of a series on the mechanics of three-dimensional braided structures for composite materials which include fabric structure and fibre volume fraction models, prediction of mechanical properties, finite element analysis and simulation of deformations. In the present paper, the normalized pitch length is introduced as a key parameter of three-dimensional braided structures. It is demonstrated that the braiding angles and fibre volume fractions can be represented as functions of this key parameter. The structures of three-dimensional braids were simulated and the braided fabrics and preforms were designed and produced. Fibre volume fraction models were established. The predictions from the fibre volume fraction models are supported by experimental results.     

空间钢框架结构的改进双重非线性分析

为了探讨三维结构的高等分析方法,给出基于UL法的严格三维单元虚功增量方程,详细推导了考虑剪切变形影响的三维梁柱单元的几何非线性切线刚度矩阵和基于三维单元简化塑性区模型的双重非线性刚度方程,并编制空间钢框架结构的双重非线性分析程序。使用包括几何与材料双重非线性的数值算例来验证方法和计算机程序的可行性、精确度与有效性。利用该程序,只需一个单元/构件即可准确预测空间钢框架结构的极限承载力与失稳模态,提高了结构的非线性分析效率。     

具有中等组分不同网状结构功能梯度构件的三维动力特性分析

功能梯度材料具有复杂的细部结构,其内部构造远比匀质材料复杂,因此其构件动力分析很难求得其解析解。该文建议一种新颖的功能梯度构件动力分析的细观元法。细观力学研究的目的在于建立材料的宏观性能同其组分材料性能及细观结构之间的定量关系,它可揭示不同的材料组合具有不同的宏观性能的内在机制。此法可实现材料细观结构到构件宏观响应的直接过渡分析,而计算单元与自由度又等同一般常规有限元,却使得组成功能梯度材料构件的各种材料细观构造得到反映。通过细观元技术,对具有中等组分不同网状结构功能梯度构件进行三维动力特性分析,并给出其三维固有频率及振型的三维分布,特别是给出了不同网格结构功能梯度板件应力振型的平面等值线图差异。结果表明:不同细观网格结构对功能梯度材料结构三维动力响应有较明显影响。     

基于连续切片的三维重构技术在材料凝固组织研究中的应用

讨论了在材料科学与工程研究中进行三维重构的意义和必要性,介绍了基于连续切片的三维重构技术的理论、方法及在材料科学与工程中的研究和应用进展.指出基于切片的三维重构技术对材料凝固过程中微观结构定量分析、微观组织-性能的研究提供了有力支持,结合数值模拟技术可为材料凝固过程中复杂组织的形成机理及凝固理论的发展提供理论和精确的实验依据,从而对新材料的设计与开发产生重要作用.最后简要介绍了三维重构技术在定向凝固过程中多相组织分析的应用,并展望了三维重构技术的发展方向.     

The average rate of growth of individual cells in a cellular structure: Effect of the number of topological elements

Equations are derived for the average rate of growth or shrinkage of individual cells in two-and three-dimensional cellular structures, when the driving forces for displacement are the excess free energies associated with faces and edges. Curvature effects are neglected. It is shown that in three-dimensional structures, such as polycrystals, cells (grains) with fourteen or more faces tend to grow while those with thirteen or less faces tend to shrink, the rate of growth/shrinkage increasing as the number of faces increases/decreases. In two-dimensional structures, the threshold between growth and shrinkage is for cells with six sides. The specific behaviour of particular cells can be predicted from a simple geometrical construction and can be quite different from the behaviour of the average cell with the same number of edges.     

Three-dimensional fabrication on GaAs surfaces using electron-beam-induced carbon deposition followed by wet chemical etching

We propose a method for fabricating three-dimensional structures on GaAs surfaces using electron beam (EB) irradiation followed by wet chemical etching. An etch-resistant hydrocarbon layer forms on the GaAs surface with the EB irradiation. Structures can be fabricated after etching using the hydrocarbon layer to block the etching. The height dependence on the irradiation and etching conditions was investigated as a means of controlling the height of the structures. A higher structure was fabricated at higher doses. The etching selectivity changed with the concentration of the etchant. A three-dimensional structure was fabricated based on these results, demonstrating the possible use of this method as a novel three-dimensional fabrication method for GaAs surfaces.     

三维实体结构NURBS等几何分析

等几何分析是近年来在有限元法基础上发展起来的一种新的数值方法,它消除了有限元的几何误差,具有高阶连续性。该文研究了三维结构等几何分析中NURBS几何体的表示方式及载荷、约束的施加方法,分别从计算精度和仿真效率两个方面对比了等几何分析的计算结果与有限元法一阶单元和二阶单元的计算结果,展示了等几何分析相对于标准有限元法的优势,并以厚壁圆筒模型算例验证了等几何分析的实用性。将NURBS单元应用于几何形状精度要求高的齿轮和变截面圆筒,数值结果表明三维NURBS等几何分析方法在复杂三维结构的仿真计算中具有较好的灵活性和适用性,可得到连续的应力场,有望在工程中得到广泛应用。     

复杂形状功能梯度板件的三维动力特性分析

从细观力学角度出发根据材料细观组分分布对具有不同复杂形状功能梯度材料构件进行三维动力特性分析,并相应给出其三维固有频率及其基频对应的位移振型和应力振型沿厚度方向的三维分布。结果发现对同样材料细观组分分布的不同功能梯度结构,其固有频率和相应的振型分布均有很大差异。此结果为建立专门的功能梯度板壳理论提供定量的资料依据。     

细编穿刺织物的数学建模理论与实例

针对细编穿刺织物,采用具有参数连续性的样条线作为纤维丝束的轨迹特性函数,建立了三维立体织物结构的数学抽象与三维建模方法。基于MicroCT方法实际测量的细编穿刺织物结构特征参数,采用四种丝束轨迹特性函数和两种丝束截面建立了八种穿刺织物结构的三维数字模型,通过丝束结构与孔隙率的对比,三维数字模型与织物真实结构符合较好。该织物结构数学抽象与三维建模方法,可用于小尺度的亚单胞模型与大尺度的宏观模型分析,具有较高的适应性。     

Reconfigurable, braced, three-dimensional DNA nanostructures

DNA nanotechnology makes use of the exquisite self-recognition of DNA in order to build on a molecular scale. Although static structures may find applications in structural biology and computer science, many applications in nanomedicine and nanorobotics require the additional capacity for controlled three-dimensional movement. DNA architectures can span three dimensions and DNA devices are capable of movement, but active control of well-defined three-dimensional structures has not been achieved. We demonstrate the operation of reconfigurable DNA tetrahedra whose shapes change precisely and reversibly in response to specific molecular signals. Shape changes are confirmed by gel electrophoresis and by bulk and single-molecule F?rster resonance energy transfer measurements. DNA tetrahedra are natural building blocks for three-dimensional construction; they may be synthesized rapidly with high yield of a single stereoisomer, and their triangulated architecture conveys structural stability. The introduction of shape-changing structural modules opens new avenues for the manipulation of matter on the nanometre scale.     

空隙、杂质及组分突变对功能梯度构件动力特性的影响

功能梯度材料具有复杂的细部结构, 其内部构造远比匀质材料复杂, 因此其构件动力分析很难求得其解析解。本文中提出了一种新颖的功能梯度构件动力分析的细观元法, 其目的在于建立材料的宏观性能与其组分材料性能及细观构造之间的定量关系, 以便揭示不同的材料组合及其变异所具有不同的宏观性能的内在机制。利用细观元法对含有空隙、 杂质及组分突变等情况下的功能梯度构件进行动力分析, 求得其三维固有频率及振型的三维分布。从而可知空隙、 杂质及组分突变均对功能梯度材料构件的宏观动力特性有很大的影响。      

考虑位移要求的大型三维连续体结构拓扑优化数值技术研究

大型复杂三维结构拓扑优化设计既具有理论意义,又具有重要的应用价值。基于等效转换的非奇异的结构优化模型,研究结构位移要求的最小结构重量设计问题。首先,介绍了位移约束的三维结构优化准则和公式。而后,为了提高拥有数万个单元以上的三维结构的计算效率,结合结构位移计算的迭代方法,在分析用于结构特性参数计算模型的基础上,建立了一套三维结构拓扑优化的求解策略和算法。最后,给出了几个典型和复杂的三维结构的拓扑优化设计算例。算例表明求解策略和算法是正确和有效的,且具有广泛的工程应用前景。     

三维波流耦合水槽模拟模型

水中结构物通常会受到波浪和水流的联合作用,为了得到作用在结构上的波流荷载,该文基于Flow-3D软件建立了三维波流水槽的模拟模型。为了准确模拟波浪和水流的相互作用,避免将造波边界和水流边界同时叠加在入口边界处,采用质量源造波法来实现内造波。利用Flow-3D的二次开发功能在水槽两端设置海绵层消波区,并结合Sommerfeld辐射边界条件来实现水槽的通流消波。对波浪的传播、波流相互作用试验的流场以及波流和柱体结构相互作用试验的流场进行数值模拟,结果表明:所建立的三维波流水槽模型可以准确地模拟波浪和水流的相互作用以及波流对结构的联合作用,并有效地进行消波,避免了二次反射,可用于波浪和水流联合作用下水中结构物波流荷载的研究。     

Diamond-structured photonic crystals

Certain periodic dielectric structures can prohibit the propagation of light for all directions within a frequency range. These 'photonic crystals' allow researchers to modify the interaction between electromagnetic fields and dielectric media from radio to optical wavelengths. Their technological potential, such as the inhibition of spontaneous emission, enhancement of semiconductor lasers, and integration and miniaturization of optical components, makes the search for an easy-to-craft photonic crystal with a large bandgap a major field of study. This progress article surveys a collection of robust complete three-dimensional dielectric photonic-bandgap structures for the visible and near-infrared regimes based on the diamond morphology together with their specific fabrication techniques. The basic origin of the complete photonic bandgap for the 'champion' diamond morphology is described in terms of dielectric modulations along principal directions. Progress in three-dimensional interference lithography for fabrication of near-champion diamond-based structures is also discussed.     

Transfer printing of 3D hierarchical gold structures using a sequentially imprinted polymer stamp

Complex three-dimensional (3D) hierarchical structures on polymeric materials are fabricated through a process referred to as sequential imprinting. In this work, the sequentially imprinted polystyrene film is used as a soft stamp to replicate hierarchical structures onto gold (Au) films, and the Au structures are then transferred to a substrate by transfer printing at an elevated temperature and pressure. Continuous and isolated 3D structures can be selectively fabricated with the assistance of thermo-mechanical deformation of the polymer stamp. Hierarchical Au structures are achieved without the need for a corresponding three-dimensionally patterned mold.     

线路构造物三维景观仿真方法研究

线路是由诸多构造物组成,构造物的三维景观仿真是线路整体三维景观仿真的重要组成部分。针对OpenGL建模能力不强的特点,提出了基于外部3DS模型的线路构造物建模方法。基于Visual C＋＋和Oracle数据库建立了构造物模型库,实现了对模型的有效管理。解决了构造物模型与线路三维场景精确匹配与控制问题,实现了构造物模型在线路三维景观仿真中的应用,建立了具有较高真实度的线路三维景观。     

Protein structure determination in solution by two-dimensional and three-dimensional nuclear magnetic resonance spectroscopy

Over the last decade, nuclear magnetic resonance (NMR) spectroscopy has evolved into a powerful method for determining structures of biological macromolecules. This has opened a unique opportunity for obtaining high-resolution three-dimensional structures in solution, in contrast to the well-established methods of X-ray diffraction, which are applicable only to solids and in particular single crystals. This rapid development has been spurred by several key advances in the field, especially the introduction of two- and three-dimensional NMR experiments, high field spectrometers (500 and 600 MHz), and computational algorithms for converting NMR derived restraints into three-dimensional structures. This review outlines the methodology employed for solving protein structures in solution, describing the basic NMR experiments necessary as well as introducing the concepts upon which the computational algorithms are founded. A variety of examples is discussed, illustrating the present state of the art, and future possibilities are indicated.     

Structural features of cubic “polyhedra” up to 24 vertices with four-, five- and six-sided faces

We present a complete list of three-dimensional structures corresponding to all cubic polyhedral graphs with the number of vertices up to 24, which have only square, pentagonal and hexagonal cycles. It can be considered as an Atlas of possible small- and middle-sized cages of three-dimensional 4-coordinated frameworks. Adhering to graph-theoretical terminology, we use the term “polyhedron”. But, strictly speaking, most of the constructed three-dimensional figures are not polyhedra because their “faces” are not planar. In addition, many polyhedra are significantly different in shape from conventional fullerenes. The spiral codes are used as the main topological identifier of the polyhedra. Three-dimensional coordinates of polyhedra are calculated by minimizing the sum of the squared deviations of the edge lengths and distances between the second neighbors from the idealized values. It is concluded that the minimum value of this sum can be considered as a new supplementary identifier of polyhedra and as a measure of deviation of the polyhedral structure from the set of true face-regular polyhedra. An algorithm for constructing polyhedral structures with edges of the same length is proposed. Also, we discuss the geometric properties of the constructed polyhedra and their relation to the stability of molecular systems.