初等有限元素法 Introduction to Finite Element Method | 土木工程學系楊子儀老師

Introduction to Finite Element Method

初等有限元素法

課程首頁
課程影音
課程綱要
課程行事曆
課程講義

To help the students understand the fundamental theory of the finite element method and its application to analyzing problems.

課程用書：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).

為求學習成效完美，請購買課本！

授課教師	土木工程學系楊子儀老師
課程學分	3學分
授課年度	105學年度
授課對象	大學3年級
預備知識	Applied Mechanics and Mechanics of Materials
課程提供	課程影音課程綱要課程行事曆課程講義

每頁顯示個資料列

搜尋:

週次	課程內容	課程影音	課程下載
第1週	課程介紹	線上觀看	MP4下載
	Chapter 1 Introduction 1.1 Basic Description 1.2 Historical Background 1.3 Specific Application	線上觀看	MP4下載
第2週	Chapter 2 Matrix Algebra 2.1 Definitions 2.2 Addition and Subtraction 2.3 Multiplication 2.4 Determinant 2.5 Inverse Matrix	線上觀看	MP4下載
	Chapter 2 Matrix Algebra 2.6/2.7 Linear Equations 2.8 Quadratic Forms and Positive Definiteness 2.9 Partitioning 2.10 Differentiation and Integration	線上觀看	MP4下載
第3週	Chapter 3 Direct Approach: Axial Springs 3.1 Axial Springs 3.2 The Element Equation 3.3 Assembly of Element Equations to Obtain the Structural Equation	線上觀看	MP4下載
	Chapter 3 Direct Approach: Axial Springs 3.4 Boundary Conditions 3.5 Examples	線上觀看	MP4下載
第4週	Chapter 4 Direct Approach: Bar Structures 4.1 Bar Structures 4.2 Element Equation 4.3 Assembly 4.4 Element Force	線上觀看	MP4下載
	Chapter 4 Direct Approach: Bar Structures 4.5 Examples	線上觀看	MP4下載
第5週	Chapter 5 Direct Approach: Truss Analysis 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	線上觀看	MP4下載
	Chapter 5 Direct Approach: Truss Analysis 5.6 Examples	線上觀看	MP4下載
第6週	Chapter 6 Approximating Functions: One-Dimensional Element 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	線上觀看	MP4下載
第7週	Chapter 7 Convergence Criteria 7.1 Convergence Criteria 7.2 Rate of Convergence 7.3 Pascal’s Triangle 7.4 Elementwise Approximation Procedure	線上觀看	MP4下載
第8週	Chapter 8 Beam and Frame Analysis 8.1 Beam Element 8.2 Element Equation 8.3 Examples 8.4 Beam Element Equation in Global Coordinates	線上觀看	MP4下載
第9週	Chapter 8 Beam and Frame Analysis 8.5 The Frame Element Equation in Global Coordinates	線上觀看	MP4下載
	Chapter 8 Beam and Frame Analysis 8.6 Examples	線上觀看	MP4下載
第10週	Chapter 9 Principle of Minimum Total Potential Energy 9.1 Concept of Potential Energy 9.2 Potential Energy of a Bar Member 9.3 Element Stiffness Matrix of a Bar	線上觀看	MP4下載
	Chapter 9 Principle of Minimum Total Potential Energy 9.4 Element Stiffness Matrix of a Beam	線上觀看	MP4下載
第11週	Chapter 10 Isoparametric Formulation and Numerical Integration 10.1 Isoparametric Formulation – Element stiffness matrix	線上觀看	MP4下載
	Chapter 10 Isoparametric Formulation and Numerical Integration 10.2 Gauss Quadrature	線上觀看	MP4下載
第12週	Chapter 11 Strong and Weak Formulations 11.1 Strong Form of One-Dimensional Heat Equation	線上觀看	MP4下載
	Chapter 11 Strong and Weak Formulations 11.2 Strong Form of Axially Loaded Elastic Bar	線上觀看	MP4下載
	Chapter 11 Strong and Weak Formulations 11.3 Strong Form of Flexible String	線上觀看	MP4下載
第13週	Chapter 11 Strong and Weak Formulations 11.4 Weak Form of One-Dimensional Heat Flow	線上觀看	MP4下載
	Chapter 11 Strong and Weak Formulations 11.5 Advantages of the Weak Formulation Compared with the Strong Form	線上觀看	MP4下載
第14週	Chapter 12 Weighted Residual Methods 12.1 Weighted Residual Method	線上觀看	MP4下載
	12.2 Point Collocation Method	線上觀看	MP4下載
	Chapter 12 Weighted Residual Methods 12.3 Subdomain Collocation Method 12.4 Least-Squares Method 12.5 The Galerkin Method	線上觀看	MP4下載
第15週	Chapter 13 Finite Element Formulation 13.1 FE Formulation of One Element	線上觀看	MP4下載
	13.2 Axially Loaded Elastic Bar	線上觀看	MP4下載
第16週	Chapter 14 Variational Method for One-Dimensional FE Formulation 14.1 Variational Formulation for 1D Finite Element	線上觀看	MP4下載
	14.1 Variational Formulation for 1D Finite Element	線上觀看	MP4下載
第17週	Chapter 15 Guidelines for Finite Element Mesh and Global Nodal Numbering 15.1 FE Mesh 15.2 Method of Solution	線上觀看	MP4下載

目前顯示第 1 至第 32 個資料列，總計 32 個資料列

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。

學期週次	參考課程進度
第一週	Introduction to finite element method
第二週	Matrix algebra and operation
第三週	Direct approach: axial springs
第四週	Direct approach: bar structures
第五週	Direct approach: truss analysis
第六週	Approximating functions: one-dimensional element
第七週	Midterm I Convergence criteria
第八週	Beam analysis
第九週	Frame analysis
第十週	Principle of minimum total potential energy
第十一週	Isoparametric formulation and numerical integration
第十二週	Midterm II Strong formulation
第十三週	Weak formulation
第十四週	Weighted residual methods
第十五週	Finite element formulation
第十六週	Variational method for one-dimensional FE formulation
第十七週	Guidelines for finite element mesh and global nodal numbering
第十八週	Final

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	PDF
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	PDF
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	PDF
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	PDF
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	PDF
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	PDF
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	PDF
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	PDF
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	PDF
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	PDF
Chapter 10 Isoparametric Formulation and Numerical Integration (Week 11) 10.1 Isoparametric Formulation –Element stiffness matrix 10.2 Gauss Quadrature	PDF
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	PDF
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	PDF
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	PDF
Chapter 13 Finite Element Formulation (Week 15) 13.1 FE Formulation of One Element 13.2 Axially Loaded Elastic Bar	PDF
Chapter 14 Variational Method for One-Dimensional FE Formulation (Week 16) 14.1 Variational Formulation for 1D Finite Element	PDF
Chapter 15 Guidelines for Finite Element Mesh and Global Nodal Numbering (Week 17) 15.1 FE Mesh 15.2 Method of Solution	PDF