一类加权有理三次样条的区域控制

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题.本文利用分母为二次的有理三次插值样条和仅基于函数值的有理三次插值样条构造了一类加权有理三次插值样条函数,这类新的插值样条中含有权系数,因而增加了处理问题的灵活性,给约束控制带来了方便.给出了将该种插值曲线约束于给定的折线、二次曲线之上、之下或之间的充分条件及将其约束于给定折线之上、之下或之间的充分必要条件.证明了满足约束条件的加权有理样条的存在性.     

插值曲线的形状控制--将值曲线约束于两给定曲线之间的问题

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题。本文利用一种分母为线性的有理三次插值样条,讨论了将该种插值曲线约束于给定的折线、二次曲线之上、之下或之间的条件,并给出了数值例子。     

一类有理三次插值样条曲线的区域控制

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题。构造了一种分母为三次的C^1连续有理三次插值样条。这种有理三次插值样条中含有参数和调节参数,因而给约束控制带来了方便,同时可以通过对参数和调节参数的控制实现孑连续的插值。对该类插值曲线的区域控制进行了研究,给出了将其约束于给定的折线、二次曲线之上、之下或之间的充分条件,最后给出了数值例子。     

插值曲线的形状控制：交曹线约束于两给定曲线之间的问题

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题,本文利用一种分母为线性的有理三次插值样条,讨论了将该种插值曲线约束于约定的折线、二次曲线之上、之下或之间的条件,并给出了数值例子。     

基于函数值的有理二次插值曲线的区域控制

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题.构造了一种基于函数值的分母为二次的C1连续有理二次插值函数,该函数中含有参数,因而可以在插值条件不变的情况下通过对参数的选择进行曲线的局部修改,同时可通过对参数的控制实现C2连续的插值.给出了将该种插值曲线约束于给定的折线、二次曲线之上、之下或之间的充分条件及将其约束于给定折线之上、之下或之间的充分必要条件.     

一类三次有理插值样条的逼近性质

曲线的保形插值是几何外形设计的重要课题。本文构造了一类带控制参数且包含极点的(3,2)k(k=1,2)阶有理插值样条。对于给定的单调和保凸数组,通过对样条中参数的适当选取达到保形的目的。对于(3,2)k(k=1,2)阶插值曲线的形状控制问题进行了研究,推导出了将此插值曲线约束在给定的折线和二次曲线之上、之下或之间的充分条件。最后本文以Peano-Kernel定理为工具,讨论了该插值的逼近性质。给出的数值例子说明这些方法的有效性。     

带有给定切线多边形的保形有理三次B样条曲线

本文给出了带有给定切线多边形的保形有理三次Ｂ样条曲线，其部分权因子可通过选取切点的位置来确定，由此方法还导出了保形有理三次Ｂ样条插值曲线，最后，给出了两个例子。     

一种加权有理三次插值函数的凸性分析

利用带导数的和仅基于函数值的分母为二次的有理三次插值样条构造了一类加权有理三次插值函数.在给定的插值数据条件下,通过调整插值函数中的参数和权系数,给出了插值曲线的保凸方法和该方法得以实现的充分必要条件,推广和改进了一些相关结论.这种条件是对参数和权系数的简单的线性的不等式约束,容易在计算机辅助几何设计中得到实际应用.     

有理三次Hemite插值样条及其逼近性质

提高插值曲线曲面的逼近性是计算辅助几何设计中的一个重要问题.本文构建了一种带单参数的分段有理三次Hermite插值样条.讨论了该样条的逼近性,给出了一种提高插值曲线曲面逼近性的方法,并且给出数值例子.结果表明,对于给定的插值条件,通过选择合适的参数,依本文方法所生成的插值曲线曲面在逼近效果上好于标准三次Hermite插...     

均匀节点的三次参数样条

三次插值样条是函数逼近及数值做积分的最常用的工具之一。可是,当平面曲线不能用单值函数表示或者虽然能用单值函数表示,但其扰度很大时,普通的三次样条就无能为力了。 在实际应用中,有时不仅需要考虑插值样条曲线,同时对样条曲线的凹向也有一定的要求。例如,要求作出的插值样条曲线在每一小区间上保持与被插值曲线或数据点有相同的凹     

一种有理插值曲线的保凸控制问题

在给定的插值数据条件下,利用一种带参数的有理插值方法,通过调整插值函数中的参数,给出了插值曲线的保凸方法和该方法得以实现的充分必要条件。这种条件是对参数的简单的线性的不等式约束,容易在计算机辅助几何设计中得到实际应用;而在理论上,它将一般插值理论上的“插值函数关于插值条件的唯一性”演化为“插值函数关于插值条件和参数的唯一性”。给出的数值例子说明了这种方法的有效性。     

A simple scheme for the finite element solution of a pure advection equation

The present paper deals with the finite element solution of an advection equation. The method of characteristic lines is combined with the finite element method. Three interpolating functions are employed: a cubic, a quadratic and a linear polynomials. The proposed scheme has two key features. One is the simplicity of its algorithm. The other is the combination of the proposed algorithm with the limiting procedure for the purpose of the suppression of numerical oscillations. Three interpolating functions are tested through four numerical examples: the advection of a box-shaped profile, the advection of an elliptic profile, the rotation of a cosine-shaped hill, and the advection of a square-shaped hill. The effectiveness of the proposed scheme is shown by comparing the present numerical results with other popular finite element schemes, i.e., SUPG, Taylor-Galerkin methods and so on. In the present test calculations, the scheme with a quadratic interpolating function has given the best results. The computing time of the proposed scheme is much faster than that of other well-known finite element schemes.     

G~1保凸分段二次多项式插值参数曲线

给定平面上一列凸数据点,导出了用具有一阶几何连续性的分段二次多项式参数曲线插值各型值点且具有保凸性的充分必要条件.并用一些实例进行验证.结果表明,这种方法是正确和有效的.     

三次Pythagorean Bézier速端曲线及其性质

建立了三次PB曲线的显式表示方法，研究了三次PB曲线的特征性质，讨论了它的尖点、重结点及拐点的情况，给出了其控制多边形各边之间的几何关系，得到了以有理五次Bézier曲线精确表示的等距线和多项式形式的弧长表达式．     

An Algorithm for Project Cost-Duration Analysis Problem with Quadratic and Convex Cost Functions

Kuhn-Tucker necessary and sufficient conditions for the nonlinear programming problem are applied to the project cost-duration analysis problem for project networks with convex costs. These conditions give an optimality curve for the problem. A solution is optimal if and only if when the values for activities are plotted on their optimality diagram, the values lie on the optimality curve. An algorithm is given here when the cost is convex and quadratic. The algorithm is also generalized to the case when the cost is convex and piecewise quadratic. The algorithm can be used to solve problems with convex cost functions by approximating them by piecewise quadratic functions.     

Forbidden nodes for curved finite elements

It is shown here that certain interpolating polynomials of degrees four and five may not always be uniquely defined on triangular-shaped elements which have one curved side. Conditions which indicate non-uniqueness are given, together with some geometrical interpretations concerning the location of the node on the curved side. A numerical example is given to demonstrate that there ar curves for which every point is unsuitable to be chosen as a node.     

Lifetime measurements for random loading in the very high cycle fatigue range

The ultrasound technique (20 kHz loading freqeuncy) has been investigated as a time- and energy-saving method for measuring lifetimes under service loading conditions. AISI C1020 steel was tested between 3 × 10⁶ and 3 × 10⁹ cycles with two Gaussian-like random loading programs (Gauss distribution generated with a Markov matrix and straight-line distribution). The resulting lifetime curves can be approximated by straight lines in a log-log plot. If the maximum values are plotted, these lines lie above the S/N curves and have approximately the same slope as the S/N curve for finite lifetimes. The experimentally found lifetimes are compared with predictions according to Miner and the Miner-Haibach rule (with half the slope of the S/N curve in the endurance range). Good agreement is found for measured and calculated results according to the Miner-Haibach rule if the measured amplitude distributiom is introduced into the calculations. This agreement is especially good for Markov random loading. Predictions according to the original Miner's rule give lifetimes that are too long in the very high cycle range. This result is explained by damaging effects of amplitudes below the endurance limit. For linear distribution random loading this effect has not been observed in the cycle range up to 3 × 10⁹.