Course syllabus of Computational Mechanics (Bilingual Course) Chinese version
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 

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 stepbystep, 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
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 
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 selfadjoint 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. Superconvergent computation and error estimation 4. Adaptive analysis 
Goal 8 
Classroom teaching, Homework 

Computer Procedures of FEM 
1. Main program of FE analysis 2. Preprocessing procedure 3. Postprocessing procedure 
Goal 9 
Classroom teaching, Homework 
Teaching content modules(Sections) 
Allocation of teaching hours 

Theoretical hours 
Discussion hours 
Experiments hours 
Other hours 
Selflearning 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 
The final examination adapts closedbook form. The proportion of each term is Daily performance score (60%) and Closedbook 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. 
[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