https://scholars.lib.ntu.edu.tw/handle/123456789/169470
標題: | 具雙軸對稱系統之土壤~結構互制分析 Dynamic Analysis for Biaxial Symmetry Soil-Structure System |
作者: | 陳正興 | 關鍵字: | 對稱邊界元素法;葛勒金法;奇異積分;Symmetric BEM;Galerkin BEM;Singular integrals | 公開日期: | 2005 | 出版社: | 臺北市:國立臺灣大學土木工程學系暨研究所 | 摘要: | 在從事土壤~結構互制之問題時,常用 邊界元素法模擬半無限遠域之阻抗矩陣, 但利用傳統邊界元素法(Collocation BEM) 所建構之系統矩陣為非對稱且不一定為正 定,不但使得要將邊界元素法與有限元素 法連接使用(FEM-BEM coupling)時整個系 統的對稱性會被破壞,且對數值運算亦有 不利影響。對稱葛勒金邊界元素法 (Symmetric Galerkin BEM, SGBEM)以對偶 邊界積分方程為架構,利用對偶式中各基 本解核函數間之對稱關係,配合加權剩餘 法中的Galerkin method,而可獲致對稱且 正定之系統矩陣,且數值穩定性與收斂行 為較傳統Collocation BEM 為佳,在近年來 被廣泛應用在各領域之邊界元素法分析 上。本研究將針對均質等向材料之三維問 題建立SGBEM 分析模式,其中利用座標 轉換與積分域投影技巧處理邊界積分中的 奇異積分問題。經由範例驗證可知本研究 建立之模式能得到相當良好的分析結果。 For soil-structure interaction problems, it is very often to adopt the Boundary Element Method (BEM) to the semi-infinite far-fields. However, the conventional BEM (collocation BEM) has disadvantage because the formulated stiffness-like matrix is asymmetric and is not always positive definite. Therefore, the symmetric virtue of the system matrix is ruined in FEM-BEM coupling and some ill effects are brought to the numerical processes. Symmetric Galerkin BEM, based on dual boundary integral equations, using the symmetry properties of kernel functions in the DBIEs, can produce symmetric and positive-definite stiffness-like matrices and owns better numerical stability and divergence behavior. Hence, SGBEM is widely applied in BEM analysis of many fields in recent years. This paper deals with the regularization of the singular integrals of SGBEM in the case of 3D elastic problems for isotropic homogeneous solids by techniques of coordinate transformation and mapping of the integration domains. In current study, the developed method is used to solve two problems with known analytical solution. The accuracy of the developed method is verified. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/2890 | 其他識別: | 932211E002018 | Rights: | 國立臺灣大學土木工程學系暨研究所 |
顯示於: | 土木工程學系 |
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