應用SCM於Winkler彈性基礎薄板受載重分析

Dynamic Analysis of Thin Plates on Winkler Elastic Foundation by Using SCM

楊士弘(Shih-Hong Yang)

指導教授 ： 吳賴雲

共同指導教授 ： 鍾立來(Li-Lai Chung)

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.2011.02734

摘要

Winkler彈性基礎應用在薄板上已經非常普遍，由於其廣泛地運用在各類結構物中，所以對於其受荷載後的力學行為有探討研究之必要，以往有許多學者對於Winkler彈性基礎薄板受載重問題進行了研究，本文提出另一種分析問題的數值方法SCM(Spline Collocation Method)，對於各種型式的問題諸如靜力問題、自由振動、動力反應進行了模擬分析。
SCM是以Spline function為基礎，配合結點佈置(Collocation)的方式，只需取得欲分析構件之控制方程式，變可將系統離散化得到解答的數值方法，利用建立之B spline table，配合邊界條件的運用，即能求得令人滿意之近似解。
本文將利用所推導之Winkler彈性基礎薄板之控制方程式，並將其應用於各Winkler彈性基礎薄板力學問題上，結合SCM求解的過程，利用編寫出的程式進行分析，最後也利用其他工程數值軟體來與SCM數值方法進行比較，以確認SCM為一種具有高準確性、便利性與可發展性的數值方法。

關鍵字

楔型函數結點佈置法 ； Winkler彈性基礎 ； 靜力分析 ； 自由振動 ； 動力反應

並列摘要

The application of winkler elastic foundation plate is very general, because of its widely used in various types of structures, the research of its mechanical behavior under loading is essential, in the past, many Scholars just studied this problem, in this paper, we just presented an alternative numerical method to analyze issues which called SCM (Spline Collocation Method), applied it into various types of problems such as static problems, free vibration and dynamic response.
SCM is based on spline function, combined with knots collocation. After we getting system’s govern equation, withing B spline table and system’s boundary condition, this method can discrete system to receive approximation solutions.
This article will use winkler elastic foundation plate’s G.E. and apply it into all kinds of mechanics problems. Combined with the process of solving the SCM, using program to analysis questions.
Finally, this paper just used another engineering software analysis results compared with SCM. We can obtain and confirm SCM is a high-accuracy, convenience and can be developed numerical method.

並列關鍵字

Spline Collocation Method ； Winkler elastic foundation ； static problems ； free vibration ； dynamic response

參考文獻

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