三次样条曲线等外力端概念及其处理方法

常用的三次样条曲线几种端值条件如简支端、抛物端已不能完全满足曲线光顺的要求。本文从样条曲线精密光顺准则出发,提出一个新的端值条件——等外力端的概念、分类和处理方法。同时从能量最小原理出发,用变分的方法推导出几种端值条件,说明它们的力学背景。在本文中,还提出了连续梁的初始剪力定理。 作者把等外力端应用于样条曲线精密光顺试验,效果十分满意。

THE CONCEPT AND PROCESS OF EQUAL EXTERIOR FORCE END FOR CUBIC SPLINE

Several commonly adopted end value conditions for cubic spline do not meet the requirements of curve fairing comple-tely. A novel end value condition, i.e. equal exterior force end, and its concept, classification and processing method are presented on the basis of strict fairing criterion for spline curves. Some end value condition derived by varia-tional method in accordance with the least energy loss prin-ciple and their mechanical background are also dealt with.The author suggests the principle of initial shearing force for continuous beam and also gives proofs for it.The results of trial applications of equal exterior force end in strict fairing of spline curves are quite satisfactory.