有限元素法與邊界積分式於流固互制問題的應用

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李細貞(Xi-Zhin Li ) 查詢紙本館藏

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機械工程研究所

論文名稱

有限元素法與邊界積分式於流固互制問題的應用

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摘要(中)

本文應用耦合有限元素法與邊界積分式探討結構體與流體互制作用在三維聲場的分析，單獨使用有限元素法對無限域聲場作離散，需要輸入龐大的資料，而且大型矩陣的計算相當費時。故一般分析外部聲場的結構體與流體互制作用所採用的方法以邊界元素法居多，但是邊界積分方程場點的選擇與源點重合，會產生奇異性積分問題增加計算的困難度。本文耦合有限元素法與邊界積分式避免了上述的問題，結構體與部份流體以有限元素分割，結構體與流體接觸的界面及流體外部的邊界以邊界元素分割，最後將耦合有限元素法與邊界積分式應用在三維聲場的放射和散射問題中，與解析解相比十分一致，證明此數值方法的可靠性。

摘要(英)

This study presents the application of the coupled Finite Element Method (FEM) and Boundary Integral Equation (BIE) to determine the three dimensional fluid-structure interaction problems.
It is very complex to discrete the infinite space and needs a large of data and time to compute exterior acoustic field by Finite Element Method.
In general,
analysis of the fluid-structure interaction in the exterior acoustic potential field uses the Boundary Element Method (BEM).
It creates difficulty of compute that the singularity exists when the source point and the field point are the same point by using Boundary Integral Equation.
This paper adopts the coupled Finite Element Method and Boundary Integral Equation to avoid above difficulties.
Twenty-noded isoparametric quadrilateral element is used to discrete the finite region,
and the boundary using eight-noded isoparametric element.
Finally,
applying the coupled Finite Element Method and Boundary Integral Equation in three dimension be acoustic radiation and scattering problems,
the results we got are shown to be very accurate compared with the analytical solutions.
It proves the reliability of the numerical method.

關鍵字(中)

★ 放射
★ 散射
★ 數值方法
★ 有限元素法
★ 流體
★ 結構體
★ 聲壓
★ 邊界積分式

關鍵字(英)

★ Boundary integral equation
★ Finite element method

論文目次

中文摘要.........................................I
英文摘要.........................................II
目錄.............................................III
圖表目錄.........................................V
符號說明.........................................VI
第一章緒論....................................1
1.1研究動機......................................1
1.2文獻回顧......................................3
1.3本文架構......................................5
第二章三維聲場之公式推導......................6
2.1有限元素公式推導..............................6
2.2邊界積分方程公式推導..........................10
第三章三維聲場數值分析........................15
3.1二十節點的六面體元素..........................15
3.2八個節點的四邊形元素..........................21
第四章三維結構體之有限元素分析................25
第五章結構體與流體互制作用方程式之耦合........32
第六章實例測試與討論..........................38
6.1球形體放射.....................................38
6.2剛體圓球散射..................................41
6.3彈性厚球殼散射................................44
第七章結論....................................47
參考文獻.........................................48
參考文獻

參考文獻

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指導教授

鄔蜀威(Shu-Wei Wu)

審核日期

2001-6-21

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