應用SCM於無阻尼薄板或梁結構之動力反應分析

Dynamic response analysis for undamped thin plate and beam structure using SCM

潘慶澤(Ching-Je Pan)

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(2010年)

https://doi.org/10.6342/NTU.2010.02680

摘要

現今大量的梁與薄板元素已運用於實務之中，故我們有致力於其力學行為探討之必要，以求其更精確穩定之分析，而使工程結構物無論在使用上與安全皆達無虞之要求。故梁與薄板各類邊界支承形式求解之簡易性、普遍性、與精確性也逐漸受到人們所重視。
目前已有很多學者對梁與薄板之動力反應問題進行切實有效的研究，但其所用方法過程繁瑣且其分析時間過於冗長。本文更提出SCM 數值求解方法，對於梁與薄板之橫向動力荷載加以模擬推算。本文以 Spline function 為出發點，並配合結點佈置(Collocation)的方式，發展出SCM(Spline Collocation Method)應用於梁與薄板的動力學分析。並以測試其動力反應的應用範圍，此法大大增加其運算速度且可增加其實用性；並使其解都能達到工程上所要求的誤差範圍之內，而終能確認SCM 為一種具有高準確性、便捷性與可應用性的數值方法，是為本文的宗旨。

關鍵字

薄板 ； SCM動力分析 ； 數值方法

並列摘要

Today a large amount of beam and plate element has been applied into practice. Therefore, its ability to in-depth study of behavior, and let there improve the accuracy and stability analysis to improve the safety performance of structures. Therefore, various types of beam and thin plate bearing the form of boundary condition of solving including simple, universality, accuracy is gradually being recognized. At present, many researchers of the dynamic response of beam and thin plate problems to conduct effective research practicable. But all of method are cumbersome and the process of analysis time too long. In this paper, numerical method of SCM extension to be able to handle of the dynamic problem. And simulate the beam and thin plate by the lateral dynamic load. In this paper, spline function is the starting point with the knot Collocation method. Develop a SCM (Spline Collocation Method) used in beam and thin plate on dynamic analysis. And test the application of its dynamic response analysis. This method increases the computing speed and increase the availability.

並列關鍵字

SCM ； Spline collocation method ； Dynamic analysis

參考文獻

[11] 陳昇元，“新結點佈置法之SCM於薄板分析＂，碩士論文，吳賴雲、鍾立來教授指導，國立台灣大學土木工程學研究所，2008。

[2] Bert, C. W. & Youngkwang Sheu, “Static Analyses of Beams and Plates by Spline Collocation Method”, Journal of Engrg. Mevhanics, 1996, pp.375-378.

[3] Prenter, P. M., “Spline and Variational Methods”, John Wiley & Sons, Inc., New York, N.Y.,1975.

[4] K.R. Raslan, “Collocation method using quartic B-spline for the equal width (EW) equation”, Applied Mathematics and Computation, (2005) 795–805

[5] Ali Sahin, “A B-spline algorithm for the numerical solution of Fisher’s equation”, Kybernetes.. Vol. 37 No. 2, 2008. 326-342