基于Mbius变换的五次有理PH曲线C^2 Hermite插值

文章通过Mbius变换引进了参数,在拓展的复平面C∞=C∪{∞}上,构造了五次有理PH曲线C2 Hermite插值,给出了插值算法;基于"弹性弯曲能量"得到满足插值条件的最优曲线,数值实例表明了该算法的有效性。

Research on spring-back behavior of high strength steel sheets

To investigate the spring-back behavior of dual-phase （DP） steel, V-shape spring-back experiments with different bending angles, relative bending radii and blank holding forces were carried out in this paper. It is concluded that with the increase of V-shape angle or blank holding force, the spring-back of DP steel sheets decreases; while raising fiIlet radius of punch, which has the most apparent effects on spring-back, advances spring-back angle. Among DP590, DP780 and DP980, higher strength yields more notable spring-back due to larger elastic deformation. The difference of spring-back among these materials is relevant with the microstructure and mechanical properties. The total elastic deformation approximately equals the ratio of the strength corresponding to the applied load to the modulus of elasticity.

Mbius变换下四次有理抛物-PH曲线的C^2 Hermite插值

目的曲线插值问题在机器人设计、机械工业、航天工业等诸多现代工业领域都有广泛的应用,而已知端点数据的Hermite插值是计算机辅助几何设计中一种常用的曲线构造方法,本文讨论了一种偶数次有理等距曲线,即四次抛物-PH曲线的C2Hermite插值问题。方法基于Mbius变换引入参数,利用复分析的方法构造了四次有理抛物-PH曲线的C^2 Hermite插值,给出了具体插值算法及相应的Bézier曲线表示和控制顶点的表达式。结果通过给出"合理"的端点插值数据,以数值实例表明了该算法的有效性,所得12条插值曲线中,结合最小绝对旋转数和弹性弯曲能量最小化两种准则给出了判定满足插值条件最优曲线的选择方法,并以具体实例说明了与其他插值方法的对比分析结果。结论本文构造了Mbius变换下的四次有理抛物-PH曲线的C^2 Hermite插值,在保证曲线次数较低的情况下,达到了连续性更高的插值条件,计算更为简单,插值效果明显,较之传统奇数次PH曲线具有更加自然的几何形状,对偶数次PH曲线的相关研究具有一定意义。