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標題: | 楔形函數配點法及其在工程問題應用之研究 Study of Spline Collocation Method and its Application on Engineering Problems |
作者: | Hsu-Hui Huang 黃旭輝 |
指導教授: | 吳賴雲(Lai-Yun Wu) |
關鍵字: | 楔形函數配點法,徑向楔形函數配點法,楔形函數配點元素法, spline collocation method (SCM),radial spline collocation method (RSCM),spline collocation element method (SCEM), |
出版年 : | 2009 |
學位: | 博士 |
摘要: | 楔形函數配點法是以楔形函數作為基底函數所構成之近似函數,搭配配點法以獲取最佳之近似函數,具有基本理論與計算步驟簡單,計算速度與收斂速度快…等優點,早期被應用於曲線擬合,後期乃因工程問題所對應之控制方程式與邊界條件趨於複雜,很難甚至無法推導其解析解,因而採用楔形函數配點法分析工程問題以求其近似解,但目前僅有少數文獻採用楔形函數配點法進行工程問題分析之研究。
本文研究採用楔形函數配點法與延伸發展之徑向楔形函數配點法與楔形函數配點元素法,針對連續梁、幾何非線性梁與矩形薄板等問題進行彈性分析、頻率分析與挫屈荷載分析,並與解析解與其他數值方法(例如:有限元素法)進行比較。分析結果顯示,楔形函數配點法應用於工程問題之數值分析時,不輸於其他數值方法,值得繼續發展楔形函數配點法分析更複雜的工程問題。 In this thesis, we study the spline collocation method (SCM), radial spline collocation method (RSCM) and spline collocation element method (SCEM) for solving engineering problems: beam, beam-column, frame, and plate problem. The popularity of the collocation method is in part due to their conceptual simplicity, wide applicability, and ease of implementation. In comparison to finite element difference methods, the CM provides approximations to the solution and its spatial derivatives at mesh point of the domain of problems. The obvious advantage of collocation method over Galerkin methods is that the calculation of the coefficients in the system of algebraic equations determining the approximate solution is very fast since no integrals need to be evaluated or approximated. Moreover, numerical experiments illustrate that the collocation method provide high order accuracy and super-convergence feature for a wide range of physical and engineering problems. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/9470 |
全文授權: | 同意授權(全球公開) |
顯示於系所單位: | 土木工程學系 |
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