基于三点分段的三角多项式样条曲线

给出了m(m=1,2,3)次三角多项式样条曲线。与二次B样条曲线类似,曲线的每一段由相继的3 个控制顶点生成;对于等距节点,一次三角多项式样条曲线是C1连续、二次三角多项式样条曲线是G2连续、三次三角多项式样条曲线是C3连续,且讨论了3 种曲线对控制多边形的逼近及与二次B样条曲线的对比。还给出了一次三角多项式样条曲线表示椭圆和整圆的方法。通过加权混合可得到一类三角多项式样条曲线,曲线的形状随着次数m和形状参数λ的变化而改变。     

局部构造C2连续的三次B样条插值曲线和双三次插值曲面

为了避免一般的局部插值算法生成的B样条曲线和曲面在段点处达不到理想的连续性以及出现多重内节点的问题,一种局部构造C2连续的三次B样条插值曲线和双三次插值曲面的方法被介绍。该方法借助节点插入算法逐步地迭代出样条控制顶点,其思想简单、几何直观、算法速度快,在曲线中夹直线段、尖点以及在曲面中夹棱边和平面都能比较容易实现。生成的曲线光滑度高、无重节点。文章最后还利用这种构造方法给出了一种在指定范围内按规定变形曲线的方法。     

基于几何特性的三次均匀B样条曲线构造描述

基于B样条曲线是分段的Bézier曲线段的集合这一数学特性,通过剖析三次均匀B样条曲线的数学表达及其几何意义,由曲线的几何特性给出了各曲线段Bézier点的几何表示。每段B样条曲线段(三次Bézier曲线段)对应的4个Bézier特征顶点,可以导出该曲线段的B样条基函数。依此为基础,描述了三次均匀B样条曲线构造的原理和过程,并给出了不同曲线段数情况下曲线特征构造和插值构造的相关公式。     

基于单位圆弧段逼近的Bézier曲线等距线生成算法

提出一种用四次Bézier曲线逼近单位圆弧段(Unit Circular Arcs)的方法及其详细误差函数分析.使用这种方法,给出一种使用同阶Bézier曲线逼近给定Bézier曲线等距线的算法.在Matlab7.0上实现了该算法,试验表明,新算法比Lee和Ahn所提出的算法有更高的精度和计算效率.由于B样条和NURBS曲线可以认为由多段Bézier曲线组成,因此,新算法为B样条和NURBS曲线等距线的求解提供了一种新的途径.     

带参数的二次三角多项式样条曲线

给出了带有参数λ的二次三角多项式样条曲线。与三次B样条曲线类似,曲线的每一段由相继的4个控制顶点生成。对于等距节点,在一般情形下,曲线达到了C1连续,而当λ=1时,曲线达到了C3连续。λ有明确的几何意义,λ越大,曲线越逼近控制多边形。还给出了用此种曲线表示椭圆和整圆的方法,在相同的控制顶点下,可生成一簇椭圆弧和圆弧。     

基于Kirov定理的带可控参数的多结点造型方法

基于Kirov定理,利用多结点样条函数,研究一类带有可控参数的曲线曲面造型方法。该方法是在普通的多结点样条中加入可控参数,通过调节这些参数可以控制插值曲线(面)在各型值点的切向量(切平面或法向量),从而达到满意的曲线(面)造型效果。该方法保持了多结点样条的基数型和局部性特点,特别是局部性使得可以只对插值曲线(面)作局部调整而不会影响整体,这有助于CAD或CAGD领域的工程人员去设计、调整曲线(面)的形状。     

三次B样条曲线插补算法的VC实现

本文结合三次B样条曲线的数学性质,理论分析了三次B样条曲线的插补过程,推导出了三次B样条曲线的插补运算公式。在对三次B样条曲线进行研究的基础上,介绍三次B样条曲线插补算法实现方法,并在VC环境中对B样条曲线的插补过程进行了实现数控插补的动态运算。     

两种带形状参数的三角曲线

定义了带形状参数的三次三角多项式曲线和三次三角样条曲线。前者具有与二次Bézier曲线类似的端点性质,但逼近性比二次Bézier曲线更好,且在拼接时能达到更高阶的连续性。而后者与二次B样条曲线类似,其每一段由相继的三个控制顶点生成。对于等距节点,在一般情况下曲线C2连续,在特殊条件下可达C3连续。     

与给定多边形相切的C 3连续B3样条曲线

描述了一种与给定多边形相切的B3样条曲线的算法。在算法中，所有的B3样条曲线的控制点可以通过对多边形的顶点简单计算产生，所构造的曲线对多边形具有保形性，曲线可以局部修改，最后给出了两个算例。     

多形状参数的指数均匀B样条曲线曲面

论文构造了一类带多个形状参数的指数均匀B样条曲线曲面,它保持了指数均匀B样条曲线曲面的主要性质(如连续性、凸包性等).此类曲线在不改变控制顶点的情况下,通过改变其形状参数的取值,可以生成多条逼近于控制多边形的曲线,进而实现对曲线的整体或局部调控.此外,它还可以精确表示双曲线、悬链线等超越曲线.此类曲面是通过张量积的方法生成的,所以具有与曲线类似的性质.论文结尾给出了大量数值实例.     

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.     

基于修正样条函数分析滑移边界矩形板的自由振动

提出了一种分析滑移边界各向同性和正交各向异性矩形板振动特性的数值方法一双向样条离散法。该方法适用于各种可能组合边界矩形板的自由振动分析；边界包括自由、简支、固定和滑移边界。在x和y方向，板被离散成N和M个等分区间。为适应任意边界，修改N＋3和M＋3维硝样条函数向量的最前和最后三个函数，得到x方向N＋1个点、y方向M＋1个点和x-y方向两个附加点的修正的邱样条函数向量，并以此作为板的位移试函数。在给定边界下，修正的B3样条函数向量对位移、位移的一阶导数和二阶导数都仅保留一个未知系数。基于矩形板的势能泛函导出其特征方程。与有限元法和样条有限条法相比，本文方法具有自由度少、计算效率高和输入数据少等优点。数值计算结果表明，本方法具有高的计算精度。     

Least-Squares Fitting Algorithms of the NIST Algorithm Testing System

This report describes algorithms for fitting certain curves and surfaces to points in three dimensions. All fits are based on orthogonal distance regression. The algorithms were developed as reference software for the National Institute of Standards and Technology’s Algorithm Testing System, which has been used for 5 years by NIST and by members of the American Society of Mechanical Engineers’ B89.4.10 standards committee. The Algorithm Testing System itself is described only briefly; the main part of this paper covers the general linear algebra, numerical analysis, and optimization methods it employs. Most of the fitting routines rely on the Levenberg-Marquardt optimization routine.     

三维CAD环境下任意曲线的生成方法研究

利用三维CAD软件提供的API工具,对给定的任意曲线方程进行读取和分析,然后采用离散和拟合算法,在指定的草图平面中绘制出光滑的曲线,为进一步在三维CAD环境中精确地完成复杂曲面的三维造型,提供一种草图绘制工具。这有利于实现复杂机械零部件的造型和设计。     

Thermal etching of GaAs (1 1 3) surfaces

We discuss scanning electron micrographs and atomic force microscope images of thermally etched GaAs(1 1 3) surfaces. The GaAs(1 1 3)A and GaAs(1 1 3)B surfaces are compared. The polarity of the surface leads to a different morphology for the two surfaces after thermal etching. It is found that the Ga-enriched droplets, which form under As-deficient conditions at higher temperatures, are sitting on characteristic pedestals, which are different for the two faces. The facets occurring after this thermal etching process are identified. They represent thermally favourable surfaces under the arsenic-deficient conditions of the thermal etching process. © 1998 Chapman & Hall     

Metamodel-assisted distributed genetic algorithms applied to structural shape optimization problems †

This article is concerned with the development of a general optimization tool based on distributed real genetic algorithms (DRGAs) assisted by metamodel evaluation and applied to structural shape optimization problems of general boundary-element models (BEMs). The evaluation fitness function is performed by a surrogate function based on multidimensional Gaussian random field models (MGRFMs) in order to minimize the computational cost of the evolutionary algorithms. The model boundary of a structural system or a mechanical tool is discretized using the BEM, and selected parts of the boundary are modelled using β-spline curves or surfaces in order to facilitate re-meshing and adaptation of the boundary to the external actions. Then a hypercube topology of populations of these models follows a genetic evolution process to determine the optimum shape of the system. The optimum models have minimum weight and satisfy all imposed constraints. A numerical example is presented and discussed in order to show the efficiency and robustness of the developed computational tool. The number of function evaluations is substantially reduced compared with previous versions of the optimization algorithm without the metamodel evaluation technique.     

输电铁塔螺栓节点连接滑移特性及模型参数研究

完成了21组输电铁塔螺栓连接试件的拉伸试验,采用ABAQUS软件对典型试件进行了有限元仿真分析,研究了初始间隙、螺栓扭矩、接触面粗糙程度、螺栓孔直径和连接杆件强度等参数对螺栓节点荷载-变形曲线的影响规律。分别按照指数模型和改进的分段多项式模型,对固定端螺栓数量为1、2和3的荷载-变形试验曲线进行了非线性拟合,确定了两种模型的拟合参数取值,分析了两种模型在输电铁塔结构分析中应用的可行性,推荐采用物理意义明确、适用范围更广的指数模型。对于最大间隙、理想间隙和最小间隙三种情况,指数模型得到的荷载-变形拟合曲线与试验曲线吻合较好,能够准确描述螺栓连接滑移过程;最小间隙工况的拟合曲线与试验曲线在线性增加段误差相对较大,最大相对差值范围约为10%~20%。     

Vibration of shear-deformable beams using a spline-function approach

B-spline functions are used as trial functions in a Rayleigh-Ritz analysis of the free vibration of shear-deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross-sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear-locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B-spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear-locking difficulty is completely eliminated. This has clear significance for the analysis of shear-deformable plates and shells when using B-spline functions.     

Technique for testing aspherical surfaces

Conclusions The above technique was used for measuring and appropriately processing the results obtained for spherical (concave and convex), parabolic, elliptical, and hyperbolic surfaces (in the case of a spherical surface the measured distance d is the radius r).The obtained results were found to be so precise that they can be recommended for application in the technique for precise practical measurements of surface shapes. This method is based on comparison with surfaces of predetermined shape whose meridional cross section can be represented by an equation for a circle, parabola, and hyperbola.After the surface measurements the meridional cross-section curves were identified according to the method under consideration. Discrepancies in the determined parameters were discovered by comparing the parameters of surfaces with a given shape to the identified surfaces. Thus, the discrepancies for the different surfaces are: spherical — 1·10^–3, elliptical and hyperbolic — 2.10^–2, parabolic — 6·10^–3.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 13–15, January, 1981.