吳賴雲Wu, Lai-Yun臺灣大學:土木工程學研究所黃旭輝Huang, Hsu-HuiHsu-HuiHuang2010-07-012018-07-092010-07-012018-07-092009U0001-3012200817464100http://ntur.lib.ntu.edu.tw//handle/246246/187868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。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.Acknowledgement ihinese Abstract iiinglish Abstract iv Preliminaries 1.1 Introduction 1.2 Outline 2 Spline collocation method 3.1 Spline collocation method 3.1.1 Introduction 3.1.2 Theory 5.1.3 Cubic B-spline function 5.1.4 Quintic B-spline function 7.2 Flexural Vibration Analysis of a Geometrically Nonlinear Beam 9.2.1 Introduction 9.2.2 Formulation 9.2.3 Approach by spline collocation method 11.2.4 Numerical Results 16.2.5 Nomenclature 22.3 Elastic Analysis of Rectangular Thin Plates 24.3.1 Introduction 24.3.2 Formulation 24.3.3 Approach by spline collocation method 26.3.4 Numerical Results 28.3.5 Nomenclature 31.4 Shear Buckling Analysis of Rectangular Thin Plates 32.4.1 Introduction 32.4.2 Formulation 33.4.3 Approach by spline collocation method 35.4.4 Numerical Results 42.4.4.1 Definition of Parameters 42.4.4.2 Convergence Study 43.4.4.3 Uni-directional Forces Acting on a Plate 43.4.4.4 Aspect Ratio Effects of Thin Plates 46.4.4.5 Bi-directional Forces Acting on a Plate 51.4.5 Nomenclature 53.5 Buckling Analysis of Rectangular Thin Plates 55.5.1 Introduction 55.5.2 Formulation 56.5.3 Approach by spline collocation method 58.5.4 Numerical Examples and Discussions 61.5.4.1 Linearly Varying Distributed Load 62.5.4.2 Non-uniformly Distributed Load 63.5.5 Nomenclature 64.6 Vibration Analysis of Beams on a Two-Parameter Elastic Foundation 66.6.1 Introduction 66.6.2 Formulation 66.6.3 Approach by spline collocation method 68.6.4 Numerical Examples and Discussions 70.6.5 Nomenclature 74.7 Vibration Analysis of Timoshenko Beam-Columns on Two-Parameter Elastic Foundations 76.7.1 Introduction 76.7.2 Formulation 78.7.3 Approach by spline collocation method 82.7.4 Numerical Examples and Discussions 84.7.4.1 Euler-Bernoulli beam-columns 84.7.4.2 Timoshenko beam-columns 87.7.5 Nomenclature 92.8 Conclusions 94 Radial Spline Collocation Method 95.1 Radial Spline Collocation Method 95.1.1 Introduction 95.1.2 Radial radial Quintic B-spline function 98.1.3 Radial Spline Collocation Method 102.2 Static Analysis of Beams 106.2.1 Approach by Radial Spline Collocation Method 106.2.2 Numerical Results 107.2.3 Nomenclature 120.3 Conclusions 122 Spline Collocation Element Method 123.1 Spline Collocation Element Method 123.2 Static Analysis of Two- dimensional Frame 126.2.1 Discrete Element Equation 126.2.2 Discrete Condition Equation of Joints 129.2.3 Numerical Algorithm 131.2.4 Numerical Examples 132.2.4.1 Orthogonal Frame 132.2.4.2 Two-bay Two-span Orthogonal Frame 135.2.4.3 Non-orthogonal Frame 138.2.4.4 Four-bay Eight-span Orthogonal Frame 141.2.5 Nomenclature 143.3 Conclusions 145eference 147ppendix A Derivation of Cubic B-spline Function 163ppendix B Derivation of Quintic B-spline Function 1652394225 bytesapplication/pdfen-US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)thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/187868/1/ntu-98-D93521004-1.pdf