臺灣博碩士論文加值系統

對於海洋波浪作用於大型結構物之波力計算，傳統求解皆以忽略底床擾動、等水深為基礎假設，如Au and Brebbia (1983) 以邊界元素法(Boundary Element Method, BEM)計算波高及波力。然而，若以等水深作為計算基礎，在實際工程應用上是有所限制的。因此，Berkhoff於1972年以線性波理論，導出緩坡方程式(Mild-slope equation, MSE)。此MSE為非齊次之Helmholtz方程式，若以傳統邊界元素法處理會產生繁雜的領域積分。因此Zhu (1993a) 應用雙互換邊界元素法(Dual Reciprocity Boundary Element Method, DRBEM)，如此可以保存BEM只需在邊界離散的優點，並且以徑向基函數(radial basis function, RBF)求解複雜之領域積分。又由於MSE在推導過程中忽略底床之高階項，可能無法反應擾動地形對波浪之影響。因此，Chamberlain and Porter (1995) 提出修正型緩坡方程式(Modified mild-slope equation, MMSE)保存了底床高階項，並且更能準確計算出波場中之相對波高。
緣此，本文將以DRBEM求解MSE與MMSE兩種緩坡方程式，分別計算出波浪場中大型結構物所受之波力值。經由本研究結果顯示，計算結果與前人研究(Liu and Lin (2007), MacCamy and Fuchs (1954), Linton and Evans (1990))之結果比較，其趨勢相當一致；因底床高階項效應的影響，MSE與MMSE於中間性水深中，兩者之平面波場差異較為明顯。並且當波浪入射方向與群樁配置同向時，波力值變動之間距 值也隨之變小；而地形坡度越陡，MSE與MMSE之無因次波力值則差異較大。

The scattering of large-scale ocean structure wave forces by an array of vertical circular cylinders. Au and Brebbia (1983) used the boundary element method (BEM) to calculate wave height and wave force. However, these studies are required as the basis for constant water depth. In practical engineering applications were restricted. Berkhoff (1972) used the linear wave theory to derive for mild-slope equation (MSE), However, MSE was non-homogeneous Helmholtz equation. If calculated by BEM, it will have to complex points of the field. So, Zhu (1993a) application of dual reciprocity boundary element method (DRBEM) calculated for wave diffraction and refraction problem. But MSE derived process ignored bottom curvature term and bottom slope squared term. Bed may not be able to respond to impact of the wave disturbance. Thus, Chamberlain and Porter (1995) derived for modified mild-slope equation (MMSE), which includes the bottom curvature term and bottom slope squared term. The studies showed that the MMSE was more accurate than the MSE calculated on the relative wave field in the wave height.
Therefore, this paper application of DRBEM to calculated large-scale structures surrounding the wave force from MSE and MMSE equation.Study results of this paper, the calculated results were compared with those by Liu and Lin (2007), MacCamy and Fuchs (1954) and Linton and Evans (1990) are conducted, in order to show the applicability of this model. Good agreements were obtained. So the numerical calculations apply to regular waves pass through cylinders making wave force in constant depth、varying depth; Effect with the bottom curvature term and bottom slope squared term, MSE and MMSE wave field have more obvious changes in intermediate water depth. And the dimensionless wave force due to the terrain slope, incident wave direction and position of pile groups. When the incident wave direction and configuration of pile groups in the same direction, Wave force changes range ( value) also became smaller; the bed slope which more steep, MSE and MMSE dimensionless wave force had the greater difference.

中文摘要 I
英文摘要 III
目錄 V
圖目錄 VII
表目錄 XIV
符號表 XV
第一章 緒論 17
1-1研究動機與目的 17
1-2文獻回顧 19
1-3研究方法與內容 21
第二章 理論基礎 23
2-1控制方程式及邊界條件 23
2-2結構物所受之波力公式 26
第三章 數值方法 27
3-1等水深區 28
3-2變水深區 31
3-3雙互換邊界元素法 31
3-3-1領域積分之近似 32
3-3-2領域交界面之邊界條件 36
3-4波力計算 36
第四章 數值驗證與計算例 38
4-1模式驗證 38
4-2計算例配置及入射波浪條件 45
4-3數值計算結果分析 50
第五章 結論與建議 107
5-1結論 107
5-2建議 108
參考文獻 109

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