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研究生:方震宇
研究生(外文):Zhen-Yu Fang
論文名稱:無網格數值分析法應用於股骨頭之生物力學
指導教授:鄔蜀威鄔蜀威引用關係
指導教授(外文):Shu-Wei Wu
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:73
中文關鍵詞:股骨頭無網格力場疊加法
外文關鍵詞:fumur headmeshlessfore field superposition
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  • 被引用被引用:2
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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。
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.
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
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