應用SCM於彈性梁之側向扭轉挫屈之分析

Analysis of Lateral Torsional Buckling of Elastic Beams by Using Spline Collocation Method

周君蔚(Chun-Wei Chou)

指導教授 ： 吳賴雲

共同指導教授 ： 鍾立來

國立臺灣大學/工學院/土木工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.02681

摘要

本文以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SCM(Spline Collocation Method)；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。
　　同時吾人將SCM (Spline Collocation Method)所延伸發展之MSCM(Modified Spline Collocation Method)應用於彈性梁之側向扭轉挫屈(Lateral Torsional Buckling)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、中點撓度與其收斂情況、雙向挫屈形狀以及單向撓曲變形曲線，並導入不同之主要剛度比，再將各項數值解與精確解作比較，觀察其準確性及收斂性。
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

節點佈置 ； 側向扭轉挫屈 ； 特徵現象 ； 主要剛度比

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,I use 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,I use MSCM(Modified Spline Collocation Method) inferred from SCM to solve some eigenvalue problems about lateral torsional buckling of elastic beams,and analysis its every model buckling load and convergence, displacement of middle point and convergence,double direction buckling shapes,and one direction deflection curve.And then,I use different primary stiffiness ratio to solve the numerical analyses solutions,and make a study of the accuracy and astringency by comparing the numerical analyses solutions with exact solutions.
The purpose of this article is used for proving that the advantages of SCM is exellent,and it is a numerical analyses method which has accuracy ,convenience,and applications.Therefore,SCM is worthy to reserch in structral analyses in depth.

並列關鍵字

SCM ； MSCM ； Eigenvalue Problems ； Lateral Torsional Buckling

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