無網格數值分析法應用於股骨頭之生物力學

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姓名

方震宇(Zhen-Yu Fang) 查詢紙本館藏

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機械工程學系

論文名稱

無網格數值分析法應用於股骨頭之生物力學

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摘要(中)

摘要
本文探討一種無網格的數值分析方法－力場疊加法，並應用於股骨近端的二維彈性力學的分析。
力場疊加法的原理是將邊界選取數個與虛擬源點相同數量且具代表性的場點，而虛擬源點為在分析區域外設定的假想源點，這些虛擬源會產生和實體邊界相同的邊界條件，再使用基本解與邊界場點的關係，可求得分析區域內各點的受力情況。此法相較於有網格數值分析法來說是相當的簡單便利，故值得推廣使用。
本文使用兩個實例來測試力場疊加法的正確性，並將其分析股骨近端的結果與有限元素法做比較，來驗證力場疊加法的可行性。

摘要(英)

ABSTRACT
The study investigates a meshless numerical analysis method－Force Field Superposition (FFS) method. The method applys to the two- dimensional proximal femur’s elastostatics analysis.
The basic theorem of Force field superposition method is taking a few representative force points in solution domain boundary which amount are the same with the virtual points. The virtual points are locate outside the solution domain, these points will generate boundary conditions equal to the solution domain. We use the relationship between fundamental solution and force points and virtual points, we can get the fore field situation inside the solution domain. The method is simpler and more convenient than meshing numerical analysis method, so it is worth popularizing.
The study uses two cases to test the accuracy of the force field superposition method, and comparing the proximal femur analysis result with the result of using finite element method. It can prove the practicality of the force field superposition method.

關鍵字(中)

★ 股骨頭
★ 無網格
★ 力場疊加法

關鍵字(英)

★ fumur head
★ meshless
★ fore field superposition

論文目次

目錄
中文摘要
英文摘要
誌謝
目錄
圖目錄
表目錄
第一章序論
1.1 研究動機…………………………………………….. 1
1.2 數值方法簡介……………………………………….. 3
1.3 文獻回顧…………………………………………….. 5
1.4 本文架構…………………………………………….. 7
第二章理論公式
2.1 基礎理論…………………………………………….. 8
2.2 基本解……………………………………………….. 10
2.3 邊界元素法位移與應力積分式…………………….. 14
第三章力場疊加法
3.1 分析區域邊界的處理……………………………….. 19
3.1.1 邊界元素法分析區域邊界的處理……………... 19
3.1.2 力場疊加法分析區域邊界的處理……………... 19
3.1.3 邊界元素法與力場疊加法的比較……………... 21
3.2 虛擬源……………………………………………….. 23
3.3 數值計算…………………………………………….. 25
第四章實例測試與股骨近端分析
4.1 平面應力問題……………………………………….. 33
4.2 平面應變問題……………………………………….. 42
4.3 股骨近端分析……………………………………….. 50
第五章結論…………………………………………………. 58
參考文獻………………………………………………… 60

參考文獻

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指導教授

鄔蜀威(Shu-Wei Wu)

審核日期

2004-7-16

推文