Finite Element Method (FEM) Analysis and Applications

The main content of this course includes: fundamental mathematics and mechanics method, basic properties of the finite element method

开设学校:清华大学;学科:工学、

Finite Element Method (FEM) Analysis and Applications课程:前往报名学习

Finite Element Method (FEM) Analysis and Applications视频慕课课程简介:

The main content of this course includes: fundamental mathematics and mechanics method, basic properties of the finite element method

前往报名学习

Finite Element Method (FEM) Analysis and Applications课程列表:

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0、Course summary

-Finite element, infinite capabilities

--Video

1、Introduction

-1.1 Classification of mechanics:particle、rigid body、deformed body mechanics

--Video 1.1

--1.1 Test

-1.2 Main points for deformed body mechanics

--Video 1.2

--1.2 Test

-1.3 Methods to solve differential equation solving method

--Video 1.3

--1.3 Test

-1.4 Function approximation

--Video 1.4

--1.4 Test

-1.5 Function approximation defined on complex domains

--Video 1.5

--1.5 Test

-1.6 The core of finite element: subdomain function approximation for complex domains

--Video 1.6

--1.6 Test

-1.7 History and software of FEM development

--Video 1.7

--1.7 Test

-Discussion

--Discussion

-Homework

2、Finite element method of bar system based on direct stiffness method

-2.1 Principles of mechanic analysis of springs

--Video 2.1

--2.1 Test

-2.2 Comparison between spring element and bar element

--Video 2.2

--2.2 Test

-2.3 Coordinate transformation of bar element

--Video 2.3

--2.3 Test

-2.4 An example of a four-bar structure

--Video 2.4

--2.4 Test

-2.5 ANSYS case analysis of four-bar structure

--Video 2.5

--ANSYS

-Discussion

--Discussion

3、Mechanical description of deformed bodies with complex geometry 1

-3.1 Mechanical description and basic assumptions for deformed body

--Video 3.1

--3.1 Test

-3.2 Index notation

--Video 3.2

--3.2 Test

-3.3 Thoughts on three major variables and three major equations

--Video 3.3

--3.3 Test

-3.4 Test

-3.4 Construction of equilibrium Equation of Plane Problem

--Video 3.4

-3.5 Test

-3.5 Construction of strain-displacement relations for plane problems

--Video 3.5

-3.6 Test

-3.6 Construction of constitutive relations for plane problems

--Video 3.6

-3.7 Test

-3.7 Two kinds of boundary conditions

--Video 3.7

- Discussion

-- Discussion

4、Mechanical description of deformed bodies with complex geometry 2

-4.1 Test

-4.1 Discussion of several special cases

--Video 4.1

-4.2 Test

-4.2 A complete solution of a simple bar under uniaxial tension based on elastic mechanics

--Video 4.2

-4.3 Test

-4.3 The description and solution of plane beam under pure bending

--Video 4.3

-4.4 Test

-4.4 Complete description of 3D elastic problem

--Video 4.4

-4.5 Test

-4.5 Description and understanding of tensor

--Video 4.5

-Discussion

--Discussion

5、Principle of trial function method for solving mechanical equations of deformed body

-5.1 Test

-5.1Main method classification and trial function method for solving deformed body mechanics equation

--Video 5.1

-5.2 Test

-5.2 Trial function method for solving pure bending beam: residual value method

--Video 5.2

-5.3 Test

-5.3How to reduce the order of the derivative of trial function

--Video 5.3

-5.4 Test

-5.4 The principle of virtual work for solving plane bending beam

--Video 5.4

-5.5 Test

-5.5 The variational basis of the principle of minimum potential energy for solving the plane bending

--Video 5.5

-5.6 Test

-5.6 The general energy principle of elastic problem

--Video 5.6

-Discussion

--Discussion

6、Classic implementation and finite element implementation based on trial function method

-6.1Test

-6.1 Classic method and finite element method based on trial function

--Video 6.1

-6.2 Test

-6.2 Natural discretization and approximated discretization in finite element method

--Video 6.2

-6.3 Test

-6.3 Basic steps in the finite element method

--Video 6.3

-6.4 Test

-6.4 Comparison of classic method and finite element method

--VIDEO 6.4

-Discussion

--Discussion

7、Finite element analysis of bar and beam structures

-7.1 Test

-7.1 Construction and MATLAB programming of bar element in local coordinate system

--Video 7.1

-7.2 Test

-7.2 Construction and MATLAB programming of plane pure bending beam element in local coordinate syste

--Video 7.2

-7.3 Construction of three-dimensional beam element in local coordinate system

--Video 7.3

-7.4 Test

-7.4 Beam element coordinate transformation

--Video 7.4

-7.5 Test

-7.5 Treatment of distributed force

--Video 7.5

-7.6 Case Analysis and MATLAB programming of portal frame structure

--Video 7.6

-7.7 ANSYS case analysis of portal frame structure

--Video 7.7

8、Finite element analysis of continuum structure (1)

-8.1 Test

-8.1 Two-dimensional 3-node triangular element and MATLAB programming

--Video 8.1

-8.2 Test

-8.2 Two-dimensional 4-node rectangular element and MATLAB programming

--Video 8.2

-8.3 Test

-8.3 Axisymmetric element

--Video 8.3

-8.4 Test

-8.4 Treatment of distributed force

--Video 8.4

-8.5 MATLAB programming of 2D plane rectangular thin plate

--Video 8.5

-8.6 Finite element GUI operation and command flow of a plane rectangular thin plate on ANSYS softwar

--Video 8.6

-Discussion

--Discussion

9、Finite element analysis of continuum structure (2)

-9.1 Three-dimensional 4-node tetrahedral element and MATLAB programming

--Video 9.1

-9.2 Three-dimensional 8-node hexahedral element and MATLAB programming

--Video 9.2

-9.3 Principle of the isoparametric element

--Video 9.3

-9.4Test

-9.4Numerical integration

--Video 9.4

-9.5 MATLAB programming for typical 2D problems

--Video 9.5

-9.6 ANSYS analysis case of typical 3Dl problem

--Video 9.6

-Discussion

--Discussion

10、Basic properties in finite element method

-10.1Test

-10.1Node number and storage bandwidth

--Video 10.1

-10.2Test

-10.2 Properties of shape function matrix and stiffness matrix

--Video 10.2

-10.3Test

-10.3 Treatment of boundary conditions and calculation of reaction forces

--Video 10.3

-10.4Test

-10.4 Requirements for construction and convergence of displacement function

--Video 10.4

-10.5Test

-10.5C0 element and C1 element

--Video 10.5

-10.6 Test

-10.6 Patch test of element

--Video 10.6

-10.7 Test

-10.7 Accuracy and property of numerical solutions of finite element analysis

--Video 10.7

-10.8Test

-10.8 Error and average processing of element stress calculation result

--Video 10.8

-10.9 Test

-10.9 Error control and the accuracy improving method of h method and p method

--Video 10.9

-Discussion

--Discussion

11、High-order and complex element

-11.1 Test

-11.1 1D high-order element

--Video 11.1

-11.2 Test

-11.2 2D high-order element

--Video 11.2

-11.3 Test

-11.3 3D high-order element

--Video 11.3

-11.4 Test

-11.4 Bending plate element based on thin plate theory

--Video 11.4

-11.5 Test

-11.5 Sub-structure and super-element

--Video 11.5

12、Introduction to the application of finite element analysis (1)

-12.1Test

-12.1 Finite element analysis for structural vibration: basic principle

--Video 12.1

-12.2 Test

-12.2 Case of finite element analysis for structural vibration

--Video 12.2

-12.3 Test

-12.3 Finite element analysis for elastic-plastic problems: basic principle

--Video 12.3

-12.4 Test

-12.4 Finite element analysis for elastic-plastic problems: solving non-linear equations

--Video 12.4

-Discussion

--Discussion

13、Introduction to the application field of finite element analysis (2)

-13.1 Test

-13.1 Finite element analysis for heat transfer: basic principle

--Video 13.1

-13.2 Test

-13.2 Case of finite element analysis for heat transfer

--Video 13.2

-13.3 Test

-13.3 Finite element analysis for thermal stress problems: basic principle

--Video 13.3

-13.4 Test

-13.4 Finite element analysis for thermal stress problems: solving non-linear equation

--Video 13.4

-Discussion

--Discussion

14、Project

-2D problem: finite element analysis of a 2D perforated plate

--Video I-1

-3D problem: meshing control of a flower-shaped chuck

--Video I-2

-Modal analysis of vibration: Modal analysis of a cable-stayed bridge

--Video I-3

-Elastic-plastic analysis: elastic-plastic analysis of a thick-walled cylinder under internal pressur

--Video I-4

-Heat transfer analysis: transient problem of temperature field during steel cylinder cooling process

--Video I-5

-Thermal stress analysis: temperature and assembly stress analysis of truss structure

--Video I-6

-Probability of structure: Probabilistic design analysis of large hydraulic press frame

--Video I-7

-Modeling and application of methods: Modeling and analysis of p-type elements for plane problem

--Video I-8

Finite Element Method (FEM) Analysis and Applications开设学校:清华大学

Finite Element Method (FEM) Analysis and Applications授课教师:

曾攀-教授-清华大学-

曾攀,清华大学机械工程系教授,博导

雷丽萍-副研究员-清华大学-

雷丽萍,清华大学机械工程系,副研究员。主要从事材料加工中的数值模拟、塑性微成形、大型装备结构设计与分析等方面的研究。

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