Introduction to Finite Element Method
本課程是由 國立陽明交通大學土木工程學系提供。
To help the students understand the fundamental theory of the finite element method and its application to analyzing problems.
Textbook：Wahyu Kuntjoro, An Introduction to the Finite Element Method, McGraw-Hill Education (Asia), 2005. (高立圖書顏俊 杰，TEL:(02)2290-0318#222，e-mail: gauli@ms37.hinet.net).
For perfect learning results, please buy textbooks!
| Instructor(s) | Department of Civil Engineering Prof. Judy P. Yang |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 105 Academic Year |
| Level | Junior |
| Prior Knowledge | Applied Mechanics and Mechanics of Materials |
| Related Resources | Course Video Course Syllabus Course Calendar Course Handout |
課程目標
To help the students understand the fundamental theory of the finite element method and its application to analyzing problems.
課程章節
| 單元主題 |
| 1. Introduction |
| 2. Matrix Algebra |
| 3. Direct Approach |
| 4. Strong Form and Weak Form |
| 5. Approximating Functions |
| 6. Weighted Residual Methods |
| 7. Finite Element Formulation |
| 8. Finite Element Mesh |
課程書目
Wahyu Kuntjoro, An Introduction to the Finite Element Method, McGraw-Hill Education (Asia), 2005. (高立圖書顏俊 杰，TEL:(02)2290-0318#222，e-mail: gauli@ms37.hinet.net)
參考書目
E-book available in NCTU online library: Liu, G.R. and Quek, S.S., The Finite Element Method: A Practical Course, 2nd ed., Oxford: Butterworth-Heinemann, 2014.
評分標準
| 項目 | 百分比 |
| Midterm exams | 2*25% |
| Final exam | 25% |
| Homework (about 6 assignments) | 15% |
| Attitude & attendance | 10% |
本課程行事曆提供課程進度與考試資訊參考。
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課程講義 Course Handout
| 章節 | 下載連結 |
Chapter 1 Introduction (Week 1) 1.1 Basic Description – Features of FEM – Advantages of FEM 1.2 Historical Background 1.3 Specific Application | |
Chapter 2 Matrix Algebra (Week 2) 2.1 Definitions 2.2 Addition and Subtraction 2.3 Multiplication 2.4 Determinant 2.5 Inverse Matrix 2.6/2.7 Linear Equations 2.8 Quadratic Forms and Positive Definiteness 2.9 Partitioning 2.10 Differentiation and Integration | |
Chapter 3 Direct Approach: Axial Springs (Week 3) 3.1 Axial Springs 3.2 The Element Equation 3.3 Assembly of Element Equations to Obtain the Structural Equation 3.4 Boundary Conditions 3.5 Examples | |
Chapter 4 Direct Approach: Bar Structures (Week 4) 4.1 Bar Structures 4.2 Element Equation 4.3 Assembly 4.4 Element Force 4.5 Examples | |
Chapter 5 Direct Approach: Truss Analysis (Week 5) 5.1 Truss Structures 5.2 Vector Transformation in Two Dimensions 5.3 The Element Stiffness Matrix in Global Coordinates 5.4 Assembly 5.5 Element Stress 5.6 Examples | |
Chapter 6 Approximating Functions: One-Dimensional Element (Week 6) 6.1 Linear One-Dimensional Element 6.2 Selecting Approximation Functions for Displacements 6.3 Quadratic One-Dimensional Element 6.4 Cubic and Quartic One-Dimensional Elements | |
Chapter 7 Convergence Criteria (Week 7) 7.1 Convergence Criteria 7.2 Rate of Convergence 7.3 Pascal’s Triangle 7.4 Elementwise Approximation Procedure | |
Chapter 8 Beam and Frame Analysis (Week 8) Beam Analysis –8.1 Beam Element –8.2 Element Equation –8.3 Examples –8.4 Beam Element Equation in Global Coordinates | |
Chapter 8 Beam and Frame Analysis (Week 9) Beam Analysis –8.5 The Frame Element Equation in Global Coordinates –8.6 Examples –8.7 Completeness and Compatibility Requirements for (Bernoulli) Beam Elements | |
Chapter 9 Principle of Minimum Total Potential Energy (Week 10) 9.1 Concept of Potential Energy 9.2 Potential Energy of a Bar Member 9.3 Element Stiffness Matrix of a Bar 9.4 Element Stiffness Matrix of a Beam | |
Chapter 10 Isoparametric Formulation and Numerical Integration (Week 11) 10.1 Isoparametric Formulation –Element stiffness matrix 10.2 Gauss Quadrature | |
Chapter 11 Strong and Weak Formulations 11.1 Strong Form of One-Dimensional Heat Equation (Week 12) 11.2 Strong Form of Axially Loaded Elastic Bar 11.3 Strong Form of Flexible String | |
Chapter 11 Strong and Weak Formulations (Week 13) 11.4 Weak Form of One-Dimensional Heat Flow 11.5 Advantages of the Weak Formulation Compared with the Strong Form 11.6 Weak Form to Strong Form | |
Chapter 12 Weighted Residual Methods (Week 14) 12.1 Weighted Residual Method 12.2 Point Collocation Method 12.3 Subdomain Collocation Method 12.4 Least-Squares Method 12.5 The Galerkin Method | |
Chapter 13 Finite Element Formulation (Week 15) 13.1 FE Formulation of One Element 13.2 Axially Loaded Elastic Bar | |
Chapter 14 Variational Method for One-Dimensional FE Formulation (Week 16) 14.1 Variational Formulation for 1D Finite Element | |
Chapter 15 Guidelines for Finite Element Mesh and Global Nodal Numbering (Week 17) 15.1 FE Mesh 15.2 Method of Solution |
