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Computational Rock Mechanics Research GroupSchool of Mechanical and Civil EngineeringChina University of Mining and Technology (BJ)

Friday, April 10, 2020

Computational Mechanics(Bilingual Course)

Yongliang Wang

Computational Mechanics(Bilingual Course)

Yongliang Wang

Teachers

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Dr. Yongliang Wang (王永亮)

Tel: +86 13426072664

Email: wangyl@cumtb.edu.cn

Website: www.wangyongliang.net

Address: Minzu Building 105

Teaching Assistant (助教)

Ph.D. student G. L. Zhang (张国龙)

Tel: +86 13021938856

Email: zhangglcumtb@foxmail.com

Address: Minzu Building 306

Online course

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1. 新试书稿，双语教材支撑

2. 录制视频，教学答疑并行

3. 课程主页，电子资源作业一体化

课程保障：签到、抽查、测验

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• 矿业特色的计算力学

双语教学模式

(2017，48学时，3学分)

力学、土木、矿业工程

本研高阶课程:

计算力学课程设计ANSYS、ABAQUS应用COMSOL计算软件应用结构分析与SAP2000应用岩土工程数值分析方法岩石断裂力学计算固体力学计算流体力学岩石破坏理论与数值方法… …

力学、土木、矿业工程

本研基础课程:

材料力学结构力学弹性力学损伤断裂力学张量分析数学物理方法数值分析专业外语编程语言程序设计… …

Bilingual Course

(2020新版培养计划，80学时，5学分)

0.1 Course Content and Requirements

0.2 Introduction of Computational Mechanics

0.3 Origins of Finite Element Method

0.4 Homework

0 Introduction0 Introduction 0.1 Course Content and Requirements

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O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu. The Finite Element Method: Its Basis &

Fundamentals (7th edition). Elsevier Pte Ltd, 2015.—O.C. Zienkiewicz, J.Z. Zhu (Swansea University, UK), R.L.Taylor (University of California, Berkeley, US)

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.

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王勖成. 有限单元法. 清华大学出版社, 2003.

Yongliang Wang, Yang Ju. Computational Mechanics (Lecture notes, 1st edition).

China University of Mining and Technology (Beijing), 2017.

Yongliang Wang. Basic Theory of Finite Element Method (Lecture notes, 2nd edition).

China University of Mining and Technology (Beijing), 2020.

0.1 Course Content and Requirements

Books

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Plato is dear to me,

but dearer still is truth !

尽信《书》，

则不如无《书》！

0.1 Course Content and Requirements

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0. Introduction

1. Standard Discrete System of Finite Element Method

2. Basic Theory of Finite Element Method: Weak Form & Variational Forms

3. Elements and Shape Functions

4. Isoparametric Element and Numerical Integration

5. Problems in Linear Elasticity and Fields

6. Solution of Linear Algebraic Equations

7. Advanced Applications: Error Estimates, Adaptive Finite Element Method

8. Computer Procedures for Finite Element Method

Course Content

Content Homeworks (English): Submit before next Monday(5&6)

Questions time: Friday 15:30-17:00 Online website

Online material: www.wangyongliang.net/computmech.aspxOnline video: www.wangyongliang.net/onlinecomputmech.htm

Programming: Static computation program of FEM Final examination: Week 17

0.1 Course Content and Requirements

Online material Online video

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Total score: Homeworks(20%) and in-class quizzes(20%, 4times,

15mins/time), programming homework(20%, week14) and close-book

exam(40%)

各项成绩比例：课后作业(20%)和随堂测验(20%，共4次，15mins/次) ，

编程大作业(20%，14周开始)，闭卷考试(40%)。

0.1 Course Content and Requirements

Website

Score

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Computation function:

Standard FEM

Stress and strain solutions

Test examples: Different students use different

parameters (Download online )

Code: Fortran/Matlab/C++…

Time: 2 weeks, submit in week 18

0.1 Course Content and Requirements

Static computation program of FEMCompu

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选一位课代表；

请按时交作业（周一课前提交上周作业），晚交不予批改；

作业请独立、认真完成；

随堂测验独立完成；

请按时上课，不迟到、不早退；

请保持课堂的安静(手机静音)；

请遵守网上作业系统的要求（严禁上载课程无关文件）。

0.1 Course Content and Requirements

Requirements

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0.1 Course Content and Requirements

WeChat group for CM course

微信群用于课程讨论、发送即时通知；

请遵守课程要求（严禁发表课程无关讨论）；

实名制：姓名-班级，如：张文明-力学2017-1。

0.1 Course Content and Requirements

0.2 Introduction of Computational Mechanics

0.3 Origins of Finite Element Method

0.4 Homework

0 Introduction0 Introduction

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计算力学: Computational Mechanics(CM)

网格: Mesh 单元: Element

有限元法: Finite Element Method(FEM)

有限元分析: Finite Element Analysis(FEA)

程序: Program 代码: Code

数值方法: Numerical method

数值算法: Numerical algorithm

数值模型: Numerical model

0.2 Introduction of Computational Mechanics

Keywords

0.2 Introduction of Computational Mechanics

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Computational mechanics is the discipline concerned with the use

of computational methods to study phenomena governed by the principles ofmechanics. Before the emergence of computational science (also calledscientific computing) as a “third way” besides theoretical andexperimental sciences, computational mechanics was widely considered tobe a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.

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Numerical methods in computational mechanics

作为力学分支的计算力学，发展了有限元 (finite element

method, FEM)、离散元(discrete element method, DEM) 、有限

差分法 (finite difference method, FDM)、无网格法 (mesh-less

method, MLM)、扩展有限元法(extended finite element method,

XFEM)、边界元(boundary element method, BEM)、半解析方法

(semi-analytic methods）等理论和方法，为虚拟仿真提供了工具。

有限元分析是虚拟设计的基本组成部分，它提供了更快捷和

低成本的方式评估设计的概念和细节，使得人们越来越多地应用

数值试验代替样品原型的物理试验。

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Mining engineering——coal mining

3D numerical model Evolution of Y-stress

0.2 Introduction of Computational Mechanics

Tunnel excavation

Y-stress field Y-displacement field 20

Geotechnical engineering——slope excavation

0.2 Introduction of Computational Mechanics

Y-stress field Y-displacement field

2D numerical model 2D structural mesh Slope excavation

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Rock mechanics——crack initiation and propagation

0.2 Introduction of Computational Mechanics

Displacement field

2D numerical model Crack propagation Rock disc model

Petroleum Engineering——hydraulic fracturing

1 : 1 1 : 1.5

σH σh

0.2 Introduction of Computational Mechanics

Hydraulic fracturing

of tight shale reservoir

Numerical simulation Multiple wells fracturing

Petroleum Engineering——hydraulic fracturing

0.2 Introduction of Computational Mechanics

Hydraulic fracturing

of tight shale reservoir

Numerical simulation Multiple wells fracturing 24

Civil engineering——deformation of buildings

Deformation of high-rise building Deformation of single-story

industrial building

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Civil engineering——vibration of cable-stayed bridge

施工过程仿真和分析

结构动力响应仿真和分析

地震响应时程仿真和分析

荆州长江大桥：全长4397.6m ，接线长4444m ，桥面宽24.5米，其中斜拉桥部分宽度26.5米，双向四车道。大桥由北岸的

引桥、荆江大堤桥、北岸滩桥、北汊通航孔桥、三八洲桥、南汊通航孔桥、南岸滩桥、荆南干堤桥和南岸引桥等九个部分主组成，总投资13.73亿元。北汊桥主桥为双

塔双索面混凝土梁斜拉桥，是目前中国主大跨径的混凝土梁斜拉桥，居同类桥梁世界第二。

0.2 Introduction of Computational Mechanics

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Civil engineering——vibration of cable-stayed bridge

1 0.18459(纵漂)

2 0.28296(一阶对称竖弯)

3 0.36452(一阶对称侧弯)

4 0.47058(一阶反对称竖弯)

5 0.51384(塔反对称侧弯)

6 0.58846(对称扭转)

13 0.66620(竖弯)

32 0.77994(塔对称侧弯)

46 0.82465(竖弯)

50 0.84960(反对称扭转)

0.2 Introduction of Computational Mechanics

Frequencies

1st-oder mode

6th-oder mode

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Structure optimization——Zhaozhou Bridge

0.2 Introduction of Computational Mechanics

Zhaozhou Bridge(赵州桥)

Model and load

Bending moment

该桥是一座空腹式的圆弧形石拱桥，是中国

现存 早、保存 好的巨大石拱桥。赵州桥

是入选世界纪录协会世界 早的敞肩石拱桥

，创造了世界之 。桥长50.82米，跨径37.02米，券高7.23米，两端宽9.6米，桥的设计完

全合乎科学原理，施工技术更是巧妙绝伦。

唐朝的张嘉贞说它“制造奇特，人不知其所

以为”。 28

Mechanical Engineering - vehicle crash simulation

在汽车设计领域中，对初期设计概

念和 终设计细节的评估，碰撞的

仿真正代替整车的试验如布置判定

气囊释放的加速计，内部的缓冲装

置，以及选择材料和满足碰撞准则

的构件截面。

0.2 Introduction of Computational Mechanics

Mesh Numerical model

Flow field simulation

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0.2 Introduction of Computational Mechanics

Aerospace——airplane and aerocraft

Aerocraft simulation

点阵材料翼型结构的拓扑优化 Airplane simulation

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Aerospace——bird strike

0.2 Introduction of Computational Mechanics

鸟撞试验: 1814g bird, 200m/s velocity

1 msec(兆秒) 5 msec(兆秒)

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心脏起搏器，心脏肌肉材料

0.2 Introduction of Computational Mechanics

Biomechanics——organ

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0.2 Introduction of Computational Mechanics

Model and mesh

Biomechanics——bone

Biomechanics——shoes

0.2 Introduction of Computational Mechanics

穿高跟鞋脚骨应力更高、

位移（变形）更大！ 34

Simulation of desk

0.2 Introduction of Computational Mechanics

Physical model

Displacement Von-Mises stress

假设桌子的四只脚同地面完全固定，桌子上存放物品，物品产生的均匀分布压力作用在桌面，模拟分析桌子的变形和应力。

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0.2 Introduction of Computational Mechanics

Numerical model Axial force Bending moment Physical model

Simulation of chair

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Simulation of dressing

0.2 Introduction of Computational Mechanics

3D virtual fitting system Von-Mises stress

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Numerical solutions of elastic mechanics problems

Stress of two dimensional object

0.2 Introduction of Computational Mechanics

Stress of three dimensional object

Concentrated load

Fixed surface

本课程针对有限元方法的

基本理论、算法和程序实施

Finite Element Analysis Program (FEAP)

The EndThe End

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