# 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

## 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

## {{'上次学习:'+learn_list['thuP08551000430intl']['last_leaf_name']}}

#### 0、Course summary

-Finite element, infinite capabilities

--Video

#### 1、Introduction

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

--1.1 Test

-1.2 Main points for deformed body mechanics

--1.2 Test

-1.3 Methods to solve differential equation solving method

--1.3 Test

-1.4 Function approximation

--1.4 Test

-1.5 Function approximation defined on complex domains

--1.5 Test

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

--1.6 Test

-1.7 History and software of FEM development

--1.7 Test

-Discussion

-Homework

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

-2.1 Principles of mechanic analysis of springs

--2.1 Test

-2.2 Comparison between spring element and bar element

--2.2 Test

-2.3 Coordinate transformation of bar element

--2.3 Test

-2.4 An example of a four-bar structure

--2.4 Test

-2.5 ANSYS case analysis of four-bar structure

--ANSYS

-Discussion

#### 3、Mechanical description of deformed bodies with complex geometry 1

-3.1 Mechanical description and basic assumptions for deformed body

--3.1 Test

-3.2 Index notation

--3.2 Test

-3.3 Thoughts on three major variables and three major equations

--3.3 Test

-3.4 Test

-3.4 Construction of equilibrium Equation of Plane Problem

-3.5 Test

-3.5 Construction of strain-displacement relations for plane problems

-3.6 Test

-3.6 Construction of constitutive relations for plane problems

-3.7 Test

-3.7 Two kinds of boundary conditions

- Discussion

#### 4、Mechanical description of deformed bodies with complex geometry 2

-4.1 Test

-4.1 Discussion of several special cases

-4.2 Test

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

-4.3 Test

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

-4.4 Test

-4.4 Complete description of 3D elastic problem

-4.5 Test

-4.5 Description and understanding of tensor

-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

-5.2 Test

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

-5.3 Test

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

-5.4 Test

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

-5.5 Test

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

-5.6 Test

-5.6 The general energy principle of elastic problem

-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

-6.2 Test

-6.2 Natural discretization and approximated discretization in finite element method

-6.3 Test

-6.3 Basic steps in the finite element method

-6.4 Test

-6.4 Comparison of classic method and finite element method

-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

-7.2 Test

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

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

-7.4 Test

-7.4 Beam element coordinate transformation

-7.5 Test

-7.5 Treatment of distributed force

-7.6 Case Analysis and MATLAB programming of portal frame structure

-7.7 ANSYS case analysis of portal frame structure

#### 8、Finite element analysis of continuum structure (1)

-8.1 Test

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

-8.2 Test

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

-8.3 Test

-8.3 Axisymmetric element

-8.4 Test

-8.4 Treatment of distributed force

-8.5 MATLAB programming of 2D plane rectangular thin plate

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

-Discussion

#### 9、Finite element analysis of continuum structure (2)

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

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

-9.3 Principle of the isoparametric element

-9.4Test

-9.4Numerical integration

-9.5 MATLAB programming for typical 2D problems

-9.6 ANSYS analysis case of typical 3Dl problem

-Discussion

#### 10、Basic properties in finite element method

-10.1Test

-10.1Node number and storage bandwidth

-10.2Test

-10.2 Properties of shape function matrix and stiffness matrix

-10.3Test

-10.3 Treatment of boundary conditions and calculation of reaction forces

-10.4Test

-10.4 Requirements for construction and convergence of displacement function

-10.5Test

-10.5C0 element and C1 element

-10.6 Test

-10.6 Patch test of element

-10.7 Test

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

-10.8Test

-10.8 Error and average processing of element stress calculation result

-10.9 Test

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

-Discussion

#### 11、High-order and complex element

-11.1 Test

-11.1 1D high-order element

-11.2 Test

-11.2 2D high-order element

-11.3 Test

-11.3 3D high-order element

-11.4 Test

-11.4 Bending plate element based on thin plate theory

-11.5 Test

-11.5 Sub-structure and super-element

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

-12.1Test

-12.1 Finite element analysis for structural vibration: basic principle

-12.2 Test

-12.2 Case of finite element analysis for structural vibration

-12.3 Test

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

-12.4 Test

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

-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

-13.2 Test

-13.2 Case of finite element analysis for heat transfer

-13.3 Test

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

-13.4 Test

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

-Discussion

#### 14、Project

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

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

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

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

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

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

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

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