组合三角Bezier曲面任意截面线GC^1构造及其优化二次表示

截面曲线构造是曲面测量分析，数控加工质量分析等应用中的基本问题之一。针对组合三角Ｂｅｚｉｅｒ曲面／平面求交交点的分布特点，本文系统研究了组合ＧＣ＾１截面曲线构造及其数据精减优化二次表示，并将其转化成ＩＧＥＳ标准格式输出，为实现两类造型系统（拓扑三角曲面和拓扑矩形曲面）之间的数据交换奠定了良好的基础。     

多曲面间的光滑自由过渡和数控加工

本文在分析自由过渡曲面设计方法的基础上，对多曲面间光滑自由过渡曲面的设计方法进行了研究，提出了多边域自由过渡曲面的分割拼接设计方法，由于采用了Bezier曲面模型，图形数据符合IGES标准，可和商品化CAD／CAM系统进行数据交换，因而可解决多曲面间的光滑自由过渡曲面的设计和数据加工问题。     

C-Bezier曲面分割、拼接及其应用

首先在介绍了C-Bezier曲面的几何模型的基础上，给出了C-Bezier曲面在u向和w向两个方向上的任意分割算法，并对曲面所具有的特性进行了分析；同时，研究了两片C-Bezier曲面在不同方向上G^1连续的拼接条件，并通过合理选取控制参数，简化了拼接条件。最后，利用分割和拼接技术，结合C-Bezier曲面能够精确表示二次曲面的特性，将C-Bezier曲面推广到常见的工程曲面上。     

未知曲面的矩形细分自适应测量方法研究

 在介绍已知曲面的自适应测量方法的基础上，重点分析了现有未知曲面测量方法的不足，提出了未知曲面自适应测量的矩形细分法，实现测点的自适应分布，并通过仿真分析和实验研究，验证了该方法的有效性，为提高未知曲面的测量精度和效率提供了一种新方法．     

基于递归分割的曲面造型算法

对常用复杂曲面造型方法的缺点进行了分析，给出了基于递归分割构造任意拓扑结构复杂曲面的有关算法，避免了参数方法在构造复杂曲面时费时而且难于处理的参数曲面求交和曲面拼接等问题，为优质高效建立复杂曲面模型奠定了基础。     

工程曲面的精密变形监测分析

本文探讨了具有二次方程的一类工程曲面的变形监测分析方法，通过确定其原始工程曲面和运营中实际工程曲面方程几何参数之间的差值来确定曲面的变形状态，原理和方法同样用于确定建筑工程曲面的放样质量。     

基于九叉树分割的曲面片上点的快速反解算法

本文针对曲面造型中，”由参数样条曲面上点的笛卡尔坐标，反求其对应参数“的反解问题，提出了一种通过曲面快速分割来逼近最终解的快速，简单，可靠的反解算法；并以Ｂ样条参数曲面为例，介绍了算法的实现过程。     

曲面片的可展切曲面及其映射分析

论文以微分几何可展曲面理论为基础,提出了过曲面曲线构造其可展切曲面的方法,得出了可展切曲面的表达形式,对可展切曲面进行了分类,通过建立两曲面间的映射关系,实现了它们间整体与局部的映射分析,较准确地把握曲面的变形情况,并通过实例对方法进行了验证.曲面片可展切曲面的方法可以应用于曲面设计、曲面近似展开和纹理映射等方面.     

基于九叉树分割的曲面片上点的快速反解算法

本文针对曲面造型中，“由参数样条曲面上点的笛卡尔坐标，反求其对应参数”的反解问题，提出了一种通过曲面快速分割来逼近最终解的快速、简单、可靠的反解算法；并以Ｂ样条参数曲面为例，介绍了算法的实现过程。     

Bezier三角组合曲面的局域设计

 在三角组合曲面的设计中，需要根据曲面间的拼接条件，协调求解曲面的内部控制顶点．在分析Bezier三角组合曲面设计方法的基础上，提出了Bezier三角曲面GC 连续局域设计方法． 内部分割点采用九参数三次曲面设计方法估算，由内部分割点将三角曲面分割为3个子曲面片，通过构造曲面边界的跨界过渡切矢，推导得出了3个分割子曲面的内部控制顶点的代数表达式．应用该方法，可以简化三角组合曲面的设计过程，提高三角组合曲面的设计计算速度．     

固定边界的Coons曲面形状控制应用

基于离散Coons曲面形状控制方法的研究,以第1类Coons曲面为例,对连续Coons曲面的形状控制方法进行了研究。提出了在固定边界条件下通过改变Coons曲面的混合函数来使曲面变形,并达到预期变形目的的方法,并指出混合函数对Coons曲面形状的影响要受到包括边界曲线在内的边界条件的制约,缺乏必要的边界条件就无法仅凭混合函数来达到所需的变形。     

Shape optimization for general two-dimensional structures

Summary The growth-strain method was used for general two-dimensional shape optimization. It was verified in previous papers that the growth-strain method is very effective for shape optimization of structures with only one free surface to be deformed. But it could not provide reasonable optimized shapes for structures with two or more free surfaces such as structures with holes inside. Problems occurred, as the growth-strain method was applied to structures with two or more free surfaces. Then, an improved method was suggested. Finally, an automatic shape optimization system was built by the improved growth-strain method with commercial software using the finite element method. The effectiveness and practicability of the developed shape optimization system was verified by some examples.     

Shape optimization using the boundary element method with substructuring

Applications of the boundary element method for two- and three-dimensional structural shape optimization are presented. The displacements and stresses are computed using the boundary element method. Sub-structuring is used to isolate the portion of the structure undergoing geometric change. The corresponding non-linear programming problem for the optimization is solved by the generalized reduced gradient method. B-spline curves and surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are selected as design variables. The design objective may be either to minimize the weight or a peak stress of the component by determining the optimum shape subject to geometrical and stress constraints. The use of substructuring allows for problem solution without requiring traditional simplifications such as linearization of the constraints. The method has been successfully applied to the structural shape optimization of plane stress, plane strain and three-dimensional elasticity problems.     

OPTIMAL PLASTIC SHAPE DESIGN OF HEADS OF PLANE TENSION MEMBERS WITH SKEW BEARING SURFACES

The paper presents the boundary perturbation method applied to optimal plastic shape design. Perfect plasticity is assumed. The procedure consists of two steps: the class of fully plastic solutions in the limit stale is first determined, and then the optimal shape is chosen from among these solutions. Heads of tension members with skew bearing surfaces are considered. Optimal angle of inclination of such surfaces is also evaluated. The final results are verified by means of the AD1NA program.     

Fabrication of optics by use of plasma chemical vaporization machining with a pipe electrode

We figure optical surfaces by plasma chemical vaporization machining (CVM) with a pipe electrode, in which an rf plasma generated at the electrode tip under approximately atmospheric pressure moves over the surfaces. We propose a shaping method in which the movement of plasma on the surfaces can be determined. Flat and aspheric surfaces are successfully figured with the desired peak-to-valley shape accuracy of 0.1 microm. The root-mean-square roughness of the resultant surfaces is at the subnanometer level. These results confirm that the plasma CVM and the shaping method have the capability to fabricate optics with high accuracy.     

构造两个曲面的拼接曲面

给出了当两个待拼接曲面的拼接线具有参数化形式或者可以参数化时,它们之间 G1光滑拼接曲面的构造方法。所得的拼接曲面是由一个空间曲线集定义的,每一条空间曲线由拼接线上的点对确定。并且拼接曲面都是参数曲面,它们的形状可以通过预设的参数很好地调整和控制。作为实例,讨论了两个截口是平面的或非平面的(由两个二次曲面定义)的二次曲面之间的拼接曲面的构造和一般的参数曲面的拼接曲面的构造。     

Three-dimensional shape measurement beyond the diffraction limit of lens using speckle interferometry

Speckle interferometry is generally known as a method for measuring the deformation of an object with rough surfaces. In this paper, a three-dimensional (3D) shape measurement method is proposed for superfine structures beyond the diffraction limit using the basic property of speckle interferometry. Since the differential coefficient distribution of the shape of such an object can be detected in speckle interferometry by imparting a known lateral shift to the measured object, the shape can be reconstructed by integrating the differential coefficient distribution. Based on experimental results obtained using diffraction gratings as measured objects, it is confirmed that the proposed method can measure 3D shapes that are beyond the diffraction limit of the lens.     

多裁剪曲面的三角划分算法

提出一种新的多裁剪曲面三角划分的方法。把裁剪曲面展开,得到曲面的平面展开图。在平面展开图内进行三角划分,把三角形上点的拓扑关系映射到裁剪曲面,生成三角网格。由于平面展开图上两点的欧氏距离接近这两点在裁剪曲面上的测地距离,所以生成的三角网格保持了平面展开图中三角形的形态,解决了在参数域内进行三角划分所产生的狭长三角形的问题。此外,还提出了一种对带孔的平面散乱点进行三角划分的办法,有效的防止了划分网格出现裂缝和覆盖等现象。     

Springback and forward slip compensation in designing roller cavity surfaces for net-shape rolling compressor blades

Designing roller cavity surfaces for rolling blades is a nontrivial task. This paper presents a new method to design cavity surfaces for rolling compressor blades with considering the springback and forward slip compensation. Firstly, a springback compensation model was proposed to modify the shape of section curves, and a forward slip model was proposed to determine the location of section curves to compensate the springback and forward slip in rolling process. Secondly, an algorithm was proposed to transform the updated section curves to the cavity section curves around the roller axis. The cavities were reconstructed through the transformed section curves. Finally, the designed roller cavities for a variable cross-section compressor blade were validated by the finite element method and experiment. The results revealed that the designed cavities meet the net shape precision at pressure and suction surfaces of the blade. The compensated design of cavities for blade rolling can save both time and costs while keeping excellent design quality.