應用SCM於奈米管之挫屈分析

Buckling Analysis of Nanotube by Using Spline Collocation Method

黃奕叡(Yi-Jui Huang)

指導教授 ： 吳賴雲

國立臺灣大學/工學院/土木工程學研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.03287

摘要

本文以前進差分法(Forward Difference Method)所推導出之Spline function為出發點，並配合節點佈置(Collocation)的方式，發展出一種數值分析方法，即為楔型函數結點布置法(Spline Collocation Method ,SCM)；再利用先前所得之各階Spline function，經由反覆迭代之過程，整理製作出完整的B Spline Value Table，以便於使用簡單的查表方式求得相關數值。
　　同時將楔形函數結點布置法(Spline Collocation Method ,SCM)所延伸發展之MSCM(Modified Spline Collocation Method)應用於奈米管之挫屈，此種帶有特徵現象之問題，分析其各模態之臨界負載與其收斂情況，觀察其準確性及收斂性。且考慮奈米管承受軸向及橫向力求解中點撓度、兩端轉角及中點彎矩，並繪其變形曲線、內力曲線並導入不同之邊界條件。
本文的宗旨為證明SCM確有其優勢所在，為一種具有高準確性、便捷性與可應用性的數值方法，值得作進一步之結構分析研究。

關鍵字

楔型函數結點布置法 ； 前進差分法 ； 節點布置 ； 奈米管 ； 挫屈

並列摘要

In this article, I use spline function inferred from Forward Difference Method as a starting point, and it is coordinated with collocation to develop a numerical analyses method, called SCM(Spline Collocation Method).Then, using any order spline function solved early and make a complete B spline value table by calculating repeatedly and it will also be advantageous to our use.
In the same time, using MSCM(Modified Spline Collocation Method) inferred from SCM to solve some eigenvalue problems about buckling of nanotube and analysis its every model buckling load and convergence. make a study of the accuracy and astringency by comparing the numerical analyses solutions with exact solutions. And consider a nanotube under axis load and transvers load to solve displacement of middle point, rotation of end point, shear of middle point and draft a deformation diagram and internal force diagram , substitute different boundary condition to solve the numerical analyses solutions.
The purpose of this article is used for proving that the advantages of SCM is excellent and it is a numerical analyses method which has accuracy ,convenience and applications. Therefore, SCM is worthy to research in structural analyses in depth.

並列關鍵字

Spline Collocation Method (SCM) ； Forward Difference Method ； Collocation ； Nanotube ； buckling

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