以邊界積分方程方法求解尤拉梁的反算外力問題

By Using Boundary Integral Equation Method to Solve the Inverse Problems of Forces of Euler-Bernoulli Beams

許桓誠(Huan-Cheng Hsu)

指導教授 ： 劉進賢

國立臺灣大學/工學院/土木工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201601667

摘要

在梁的分析模型中，通常使用尤拉－伯努力梁方程理論，在正算尤拉梁問題其解決方法則不計其數。然而當問題的待求項變為系統參數之一時，其複雜度則非一般正算問題可比擬。本論文介紹了解決非齊性的尤拉梁方程反問題的一種數值方法，其目的為在梁上找回其外力(源識別問題)。本篇論文將邊界積分方程方法應用至尤拉梁上，以其振態作為伴隨測試函數，再以我們假設的試解帶入積分方程，以數值方法解此代數方程組，即可得到外力源之數值解。在論文中將以數值算例實際求解尤拉梁的反問題，其中包含四種不同邊界條件的梁以及使用傅立葉級數與振型函數兩種試解之基底，並分析其數值結果。

關鍵字

尤拉梁 ； 邊界積分方程方法 ； 反問題 ； 源識別問題 ； 格林第二定理

並列摘要

Euler-Bernoulli beam theory is a typical beam theory when discussing the behavior of beams. There are several methods to obtain the behaviors of the Euler-Bernoulli beam under an external force, but without knowing the external force, the problem becomes an inverse source problem which is the subject of this thesis. Different from the direct problems, the inverse problems are considered more ill-posed. In this thesis, the boundary integral equations method will be adopted to solve the Euler-Bernoulli beam problem, with its mode shape as an adjoint test function. Then, we assume the trail solution of the integral equation. Finally, we can obtain the numerical solution of the external force. Six examples of Euler beam are used to test the performance of the present method.

並列關鍵字

Euler-Bernoulli beam ； Boundary integral equations method ； Inverse problem ； Source identification problem

參考文獻

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