PRACTICAL G~2 CONTINUITY ALGORITHMS BETWEEN ADJACENT NURBS PATCHES

Geometriccontinuityiswidelyrecognizedastheappropriatewaytofittogethertwoadja-centsurfacepatchesinCAD/CAM.ItavoidsdePendenceofparametrizatinnandprovidesaddi-tionalparametersformodelingtheshapes.Apatchworktechniqueconstructsanycompositesurfacestraightforwardly,patchbypatch.ThetangentplanecontinuityG1andcurvaturecon-tinuityG2ofparametricsurfacepatcheshavebeenstudied[1~6J-AlltheseresearchersworkwithsurfacepatchesinBezierformandrationalBezierform.IncontrasttoNURBSsurface,BezierandrationalBe…     

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell(RUC)is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element(DFE)method,and merely applying Periodic Displacement Boundary Conditions(PDBCs)to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions(PTBCs,also known as traction continuity conditions)are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element(FE)analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional(UD)fiber-reinforced composites.     

关于有理Bézier曲面片的几何连续拼接问题

本文深入研究了有理Bézier曲面片的几何连续拼接问题,给出了GC~1拼接条件的显式表示和判断两曲面片GC~1拼接状况的判定条件。用此条件可编写一简单程序,通过输入两曲面片的控制顶点及权因子,便可以“YES”或“NO”的输出回答两曲面片的拼接是否为GC~1连续。在非GC~1拼接时,可对称地修改两曲面片使其GC~1拼接。最后,本文给出了几种CAD/CAM工程中实用的充分条件。     

A new error-controllable method for smoothing the G01 commands

In real machining, the tool paths are composed of a series of short line segments, which constitute groups of sharp corners correspondingly leading to geometry discontinuity in tangent. As a result, high acceleration with high fluctuation usually occurs. If these kinds of tool paths are directly used for machining, the feedrate and quality will be greatly reduced. Thus, generating continuous tool paths is strongly desired. This paper presents a new error-controllable method for generating continuous tool path. Different from the traditional method focusing on fitting the cutter locations, the proposed method realizes globally smoothing the tool path in an error-controllable way. Concretely, it does the smoothing by approaching the newly produced curve to the linear tool path by taking the tolerance requirement as a constraint. That is, the error between the desired tool path and the G01 commands are taken as a boundary condition to ensure the finally smoothed curve being within the given tolerance. Besides, to improve the smoothing ability in case of small corner angle, an improved local smoothing method is also proposed by symmetrically assigning the control points to the two adjacent linear segments with the constrains of tolerance and G3 continuity. Experiments on an open five-axis machine are developed to verify the advantages of the proposed methods.     

洛尔定理的推广和柯西中值定理的证明

本文对洛尔定理进行了推广，并给出了柯西中值定量的三种证法。     

四边Bézier曲面与三角B-B曲面的光滑拼接

 <正> 三角B-B曲面具有许多类似于四边B（?）zier曲面的性质,如果将二者结合使用,则可以处理比较复杂的问题,有重要的实用意义。最近,刘鼎元教授给出了四边B（?）zier曲面片G¹拼接的充分必要条件,并给出了G^拼接的两个充分条件:简单连接条件和升阶连接条件。本文将升阶连接条件用于四边B（?）zier曲面和三角B-B曲面的G¹拼接。结合使用简单连接条件,解决了在一般G¹连续的四边B（?）zier曲面中嵌入G¹连续的三角B-B曲面片的问题。     

函数光滑性的特征表示及其性质

函数在某点的光滑程度可用其在这点的连续性和各阶导数描述,但更细致的描述是用函数在这点的Ｌｉｐｓｃｈｉｔｚ指数来刻划的;而函数在一个区间上的光滑性则可以用函数的一致连续和导函数来考察,更精确的是用一致Ｌｉｐｓｃｈｉｔｚ指数与考虑。首先,给出了函数在某点的伪导数定义,它能描述函数的光滑性,然后,讨论了它与函数的导数、Ｌｉｐｓｃｈｉｔｚ指数之间的关系,以及一个区间上的伪导函数与函数的一致Ｌｉｐｓｃｈｉｔ     

模糊σ-代数上的模糊数值测度及应用(Ⅰ)

设(Χ,A,μ)是一个全有限测度空间,H为由A生成的模糊σ-代数。通过计算H中模糊子集的截集的测度,运用一维模糊数的嵌入定理,构造了一种定义在H上取值于一维模糊数空间的测度,这种测度限制在A上就是测度μ,并且具有可列可加性、下连续性、上连续性、自连续性等性质。这种测度取值一维模糊数,保留了模糊子集较多的信息,所以它可以更为细致地刻划模糊子集。作为在模糊聚类理论方面的应用,把(Χ,A,μ)上用于度量普通集合间不相似性的度量推广到了H上的模糊子集间,得到了一种基本的H上不相似度量。     

广义Fuzzy数值测度的绝对连续性和奇异性探讨

给出了广义Fuzzy数值测度的绝对连续性和奇异性的定义,利用Hahn分解结论探讨了广义Fuzzy数值测度与其上变差、下变差和全变差的绝对连续性和奇异性的关系。     

曲率连续的非轴对称短舱气动型面参数化设计方法研究

为了进一步提高短舱内外流的气动性能,基于类别形状函数方法建立了曲率连续的非轴对称短舱气动型面参数化设计方法。主要思路是先设计关键截面型线,再设计纵向型线,最后通过纵向型线周向有序组合建立气动型面。为评价所建立的短舱气动型面设计方法的适用性,从曲率半径分布、主要工况下的流动特性和气动性能三个方面对所发展的方法和基于圆锥曲线的方法设计的超大涵道比(UHBPR)短舱进行了对比研究。结果表明：与基于圆锥曲线的方法设计的短舱相比,所建立的方法设计的短舱气动型面不存在轴向曲率半径波动。由于消除了曲率波动引起的短舱壁面附近局部过度加速形成的高速低压区,在马赫数为0.8的巡航条件下外罩壁面局部阻力降低了4.5%；在马赫数为0.82的飞行工况下,外罩壁面局部阻力降低了5.5%。进气道气动型面设计方法的改进,使得大攻角爬升条件下进气道总压恢复系数提高了0.41%,稳态周向总压畸变指数减小了8.82%。