Course syllabus of Computational Mechanics (Bilingual Course)    Chinese version

　

1. Basic information

Course No

16A16109

Chinese name

Ji Suan Li Xue

English name

Computational Mechanics

Course property

Core major course

Credit hours

48

Credit core

3

Applicable major

Engineering Mechanics

Early courses

Structural Mechanics, Elastic Mechanics, Methods of Mathematical Physics

Books

  1. Yongliang Wang. Basic Theory of Finite Element Method. Science Press & EDP Press, 2022.

  2. O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. The Finite Element Method: Its Basis & Fundamentals (7th edition). Elsevier Pte Ltd, 2015.

  3. Yongliang Wang. Adaptive Analysis of Damage and Fracture in Rock with Multiphysical Fields Coupling. Science Press & Springer Press, 2021.

  4. O. C. Zienkiewicz, R. L. Taylor著, 曾攀译. 有限元方法: 基本原理(第5卷). 清华大学出版社, 2008.

2. Teaching goals

This course introduces the commonly used methods in computational mechanics, focusing on the finite element method (FEM) which have relatively complete theoretical basis and successful applications in various engineering fields. In the courses, the basic principles, the finite element (FE) equations and the analysis scheme will be introduced step-by-step, furthermore, the elementary program of FEM will be recommended and introduced.. Basic requirements are as following:

 

1. Understand conventional computation methods and computational softwares.

2. Master standard discrete system and computation process of FEM.

3. Master the theoretical basis of weak form and variational principle of FEM.

4. Master various elements and shape function of FEM.

5. Master isoparametric element and numerical integration methods of FEM.

6. Master general principles and formats for elastic problems of FEM.

7. Master numerical methods of linear algebraic equations.

8. Understand some applicable considerations and advanced applications of FEM.

9. Master computer procedures and programing of FEM

 

3. Support of course goals for graduation requirements

No

Indicators of graduation requirements

Goal 1

Goal 2

Goal 3

Goal 4

Goal 5

Goal 6

Goal 7

Goal 8

Goal 9

1

Graduation requirement 3

L1

L2

L2

L2

L2

L2

L2

L2

L5

2

Graduation requirement 4

L1

L3

L3

L3

L3

L3

L3

L3

L5

3

Graduation requirement 5

L1

L1

L1

L1

L1

L1

L1

L1

L5

4. Teaching content

Teaching content modules(Sections)

Content

Corresponding teaching goals

Teaching methods

 　
　

Introduction of Computational Mechanics and FEM

1. Conventional computation methods

2. Computational softwares

3. Development of FEM

Goal 1

Classroom teaching,

Homework

 　

Standard Discrete System of FEM

1. Basic method of FEM

2. Discreteness and assembly of elements

3. Basic concepts of shape function, coordinate transformation, displacement equations, stress and strain solutions.

4. Standard discrete system of Matrix displacement method and FEM

Goal 2

Classroom teaching,

Homework

 　

Basic Theory of FEM

1. Equivalent integral weak form of differential equation

2. Galerkin method

3. Fundamental principles of variational method

4. Variational form of linear self-adjoint operator

Goal 3

Classroom teaching,

Homework

 　

Problems in Linear Elasticity and Fields

1. 1D element

2. 2D element

3. 3D element

4. Hierarchical element

Goal 4

Classroom teaching,

Homework

 　

Elements and Shape Functions

1. Concepts of isoparametric transformation and transformation of element matrix

2. Conditions of isoparametric transformation and convergence of isoparametric elements

3. General format of isoparametric elements for elastic problems

4. Numerical integration method

5. Selection of numerical integration order in isoparametric computation

Goal 5

Classroom teaching,

Homework

 　

Isoparametric Element and Numerical Integration

1. FE format for plane elastic problem

2. General format of FEM in generalized coordinate system

3. Properties and convergence criteria of FE solution

Goal 6

Classroom teaching,

Homework

 　

Solution of Linear Algebraic Equations

1. Gaussian elimination method and its variable form

2. Direct method of striped sparse matrix

3. Direct method utilizing external memory

4. Iteration method

Goal 7

Classroom teaching,

Homework

 　

Advanced Applications

1. Patch test

2. Characteristic and treatment of stress results

3. Super-convergent computation and error estimation

4. Adaptive analysis

Goal 8

Classroom teaching,

Homework

 　

Computer Procedures of FEM

1. Main program of FE analysis

2. Pre-processing procedure

3. Post-processing procedure

Goal 9

Classroom teaching,

Homework

 　

5. Allocation of teaching hours

Teaching content modules(Sections)

Allocation of teaching hours

Theoretical hours

Discussion hours

Experiments hours

Other hours

Self-learning hours

Subtotal

Introduction of Computational Mechanics and FEM

2

 　 　

 

 　

2

Standard Discrete System of FEM

8

 　 　 　 　

8

Basic theory of FEM

6

 　 　 　 　

6

Problems in Linear Elasticity and Fields

8

 　 　 　 　

8

Elements and Shape Functions

4

 　 　 　 　

4

Isoparametric Element and Numerical Integration

8

 　 　 　 　

8

Solution of Linear Algebraic Equations

4

 　 　 　 　

4

Advanced Applications

4

 　 　 　 　

4

Computer Procedures for FEM

4

 　 　 　 　

4

Summation

48

 　 　 　 　

48

6. Course assessment

The final examination adapts closed-book form. The proportion of each term is Daily performance score (60%) and Closed-book examination score (40%), in which Daily performance includes Homework, Classroom test and Program.

No

Course goals

Assessment contents

Proportion in course assessment (%)

Assessment rules

1

Goal 1

Attendance + homework + course examination

5

Assessment of attendance, homework and understanding for main knowledge, 5% of total score.

2

Goal 2

Attendance + homework + course examination

15

Assessment of attendance, homework and understanding for main knowledge, 15% of total score.

3

Goal 3

Attendance + homework + course examination

10

Assessment of attendance, homework and understanding for main knowledge, 10% of total score.

4

Goal 4

Attendance + homework + course examination

10

Assessment of attendance, homework and understanding for main knowledge, 10% of total score.

5

Goal 5

Attendance + homework + course examination

10

Assessment of attendance, homework and understanding for main knowledge, 10% of total score.

6

Goal 6

Attendance + homework + course examination

15

Assessment of attendance, homework and understanding for main knowledge, 15% of total score.

7

Goal 7

Attendance + homework + course examination

10

Assessment of attendance, homework and understanding for main knowledge, 10% of total score.

8

Goal 8

Attendance + homework

5

Assessment of attendance and homework, 5% of total score.

9

Goal 9

Program

20

Assessment of application of FEM, programming codes and computation analysis, 20% of total score.

7. Reference Books

[1] Yongliang Wang. Basic Theory of Finite Element Method. Science Press & EDP Press, 2022.

[2] O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. The Finite Element Method: Its Basis & Fundamentals (7th edition). Elsevier Pte Ltd, 2015.

[3] Yongliang Wang. Adaptive Analysis of Damage and Fracture in Rock with Multiphysical Fields Coupling. Science Press & Springer Press, 2021.

[4] O. C. Zienkiewicz, R. L. Taylor著, 曾攀译. 有限元方法: 基本原理(第5卷). 清华大学出版社, 2008.

　

Computational Rock Mechanics Research Group

State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology (BJ)

Email: wangyl@tsinghua.org.cn, WeChat: WYL659818354