Finite Element Method (FEM) Analysis and Applications

Overview

The finite element method has already become part of the fundamental knowledge for people work in the field of machinery, aerospace, civil engineering, mechanics and other professional fields. The finite element method is based on elastic mechanics. Usually the Galerkin method and functional maximum principles are used to solve these equations. The most common finite element analysis software packages such as ANSYS are based on the combination of mathematics, mechanical methods, numerical discretization and advanced computer technology.

Syllabus

0、Course summary

Finite element, infinite capabilities

1、Introduction

1.1 Classification of mechanics：particle、rigid body、deformed body mechanics
1.2 Main points for deformed body mechanics
1.3 Methods to solve differential equation solving method
1.4 Function approximation
1.5 Function approximation defined on complex domains
1.6 The core of finite element: subdomain function approximation for complex domains
1.7 History and software of FEM development
Discussion

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

2.1 Principles of mechanic analysis of springs
2.2 Comparison between spring element and bar element
2.3 Coordinate transformation of bar element
2.4 An example of a four-bar structure
2.5 ANSYS case analysis of four-bar structure
Discussion

3、Mechanical description of deformed bodies with complex geometry 1

3.1 Mechanical description and basic assumptions for deformed body
3.2 Index notation
3.3 Thoughts on three major variables and three major equations
3.4 Construction of equilibrium Equation of Plane Problem
3.5 Construction of strain-displacement relations for plane problems
3.6 Construction of constitutive relations for plane problems
3.7 Two kinds of boundary conditions
Discussion

4、Mechanical description of deformed bodies with complex geometry 2

4.1 Discussion of several special cases
4.2 A complete solution of a simple bar under uniaxial tension based on elastic mechanics
4.3 The description and solution of plane beam under pure bending
4.4 Complete description of 3D elastic problem
4.5 Description and understanding of tensor
Discussion

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

5.1Main method classification and trial function method for solving deformed body mechanics equation
5.2 Trial function method for solving pure bending beam: residual value method
5.3How to reduce the order of the derivative of trial function
5.4 The principle of virtual work for solving plane bending beam
5.5 The variational basis of the principle of minimum potential energy for solving the plane bending
5.6 The general energy principle of elastic problem
Discussion

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

6.1 Classic method and finite element method based on trial function
6.2 Natural discretization and approximated discretization in finite element method
6.3 Basic steps in the finite element method
6.4 Comparison of classic method and finite element method
Discussion

7、Finite element analysis of bar and beam structures

7.1 Construction and MATLAB programming of bar element in local coordinate system
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 Beam element coordinate transformation
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 Two-dimensional 3-node triangular element and MATLAB programming
8.2 Two-dimensional 4-node rectangular element and MATLAB programming
8.3 Axisymmetric element
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
9.4Numerical 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

10.1Node number and storage bandwidth
10.2 Properties of shape function matrix and stiffness matrix
10.3 Treatment of boundary conditions and calculation of reaction forces
10.4 Requirements for construction and convergence of displacement function
10.5C0 element and C1 element
10.6 Patch test of element
10.7 Accuracy and property of numerical solutions of finite element analysis
10.8 Error and average processing of element stress calculation result
10.9 Error control and the accuracy improving method of h method and p method
Discussion

11、High-order and complex element

11.1 1D high-order element
11.2 2D high-order element
11.3 3D high-order element
11.4 Bending plate element based on thin plate theory
11.5 Sub-structure and super-element

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

12.1 Finite element analysis for structural vibration: basic principle
12.2 Case of finite element analysis for structural vibration
12.3 Finite element analysis for elastic-plastic problems: basic principle
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 Finite element analysis for heat transfer: basic principle
13.2 Case of finite element analysis for heat transfer
13.3 Finite element analysis for thermal stress problems: basic principle
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