Copyright 2023 - All Right Reserved
Introduction to Finite Element Method

初等有限元素法

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.

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

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

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 exams2*25%
Final exam25%
Homework (about 6 assignments)15%
Attitude & attendance10%

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
課程專區
©2024- NYCU OCW