Finite Element Analysis and the Basics of CAE Technology

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Features: This book systematically introduces the finite element method and basic knowledge related to CAE technology, covering topics such as the theoretical foundation of the finite element method, algorithmic techniques, mesh partitioning techniques, graphical post-processing techniques, and several technical issues in CAE software applications. It also provides a brief introduction to some of the important CAE software both domestically and internationally. This book can be used by researchers and developers in mechanics, engineering structural analysis, computational mathematics, and CAE software engineering, as well as engineering technicians in related fields. It can also serve as a textbook or reference book for relevant majors in universities.
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Table of Contents
Chapter 1 Introduction
1.1 Basic Concepts of CAE
1.2 History of CAE Development
1.3 CAE Analysis Process and Content
1.4 Key Technical Indicators of CAE Products
1.5 Finite Element Mesh Partitioning in CAE Software
1.6 Post-processing Systems in CAE Software
Chapter 2 Basic Theories and Methods of Finite Element Analysis
2.1 Introduction
2.2 Theoretical Foundation of Elasticity in Finite Element Analysis
2.2.1 Basic Governing Equations of Elasticity
2.2.2 Variational Principle Foundation of Finite Element Analysis
2.2.3 Displacement Mode Finite Element Method: Element Displacement and Shape Functions
2.2.4 Examples of Specific Expressions of Element Matrices and Vectors
2.3 Finite Element Method for Dynamics Analysis
2.3.1 Basic Equations of Dynamic Finite Element Analysis
2.3.2 Mass Matrix and Damping Matrix in Dynamics Analysis
2.3.3 Eigenvalue Problems in Dynamics
2.3.4 Dynamics Analysis Based on Frequency Domain
2.3.5 Methods for Reducing Degrees of Freedom in Dynamic Systems
2.4 Nonlinear Finite Element Analysis
2.4.1 Material Nonlinear Finite Element Analysis
2.4.2 Analysis of Material Nonlinear Problems Related to Time
2.4.3 Finite Element Analysis of Geometric Nonlinear Problems
2.4.4 Structural Buckling and Stability Analysis
2.4.5 Finite Element Analysis of Contact Problems
2.5 Finite Element Method for Heat Conduction Analysis
2.5.1 Basic Equations of Heat Conduction Analysis
2.5.2 Finite Element Method for Solving Heat Conduction Equations
2.5.3 Finite Element Method for Nonlinear Heat Conduction Analysis
2.5.4 Finite Element Analysis of Heat Conduction with Phase Change
2.6 Finite Element Analysis for Electromagnetic Problems
2.6.1 Basic Governing Equations for Electromagnetic Problem Analysis
2.6.2 Finite Element Equations for Electromagnetic Field Analysis
2.6.3 Two-Dimensional Static Electromagnetic Field Finite Element Analysis
2.6.4 Two-Dimensional Transient Eddy Current Field Finite Element Analysis
2.6.5 Finite Element Equations for Three-Dimensional Transient Eddy Current Field
2.6.6 Electromagnetic Energy Storage Calculation
2.6.7 Electromagnetic Force Calculation
2.7 Finite Element Method for General Field Problems
Chapter 3 Several Methods and Key Technologies in the Implementation of Finite Element Method
3.1 Matrix Assembly and Formation of the Overall Equation
3.1.1 Coordinate Transformation of Element Stiffness Matrix
3.1.2 Formation of the Overall Equilibrium Equation and Matrix Assembly
3.1.3 Optimization of Node Numbering
3.2 Treatment of Boundary Conditions and Solution of the Overall Equation
3.2.1 Treatment of Boundary Conditions
3.2.2 Solution of the Overall Equation
3.3 Commonly Used Elements in Finite Element Analysis
3.3.1 Spatial Truss Element
3.3.2 Spatial Beam Element
3.3.3 Plane Three-Node Triangular Element
3.3.4 Annular Element for Axisymmetric Problem Analysis
3.3.5 Plane Rectangular Element
3.3.6 Spatial Tetrahedral Element
3.3.7 Plane Isoparametric Element
3.3.8 Spatial Isoparametric Element
3.3.9 Rectangular Plate Element
3.3.10 Triangular Plate Element
3.3.11 Rectangular Plate Shell Element
3.3.12 Four-Node Thick Shell Element
3.4 Several Solution Methods for Dynamics Problems
3.4.1 Solution Methods for Eigenvalue Problems
3.4.2 Mode Superposition Method for Solving Vibration Response
3.4.3 Time-Domain Integration Method for Solving Vibration Response
3.5 Several Solution Techniques for Heat Conduction Analysis
3.5.1 Element Construction for Heat Conduction Analysis
3.5.2 Solution Algorithm for Steady-State Heat Conduction Finite Element Analysis
3.5.3 Solution Algorithm for Unsteady-State Heat Conduction Finite Element Analysis
3.6 Basic Algorithms for Nonlinear Finite Element Analysis
3.6.1 Direct Iteration Method
3.6.2 Newton-Raphson Method
3.6.3 Modified Newton-Raphson Method
3.6.4 Incremental Method
3.6.5 Arc-Length Method
Chapter 4 Pre-Processing System of Finite Element Analysis
4.1 Finite Element Modeling
4.1.1 Finite Element Model
4.1.2 Geometric Modeling
4.1.3 Mesh Generation
4.1.4 Physical Modeling
4.2 Methods for Generating Finite Element Mesh
4.2.1 Overview of Finite Element Mesh Generation Methods
4.2.2 Fully Automatic Mesh Partitioning of Arbitrary Plane Regions Based on AFT Method
4.2.3 Delaunay Triangulation Method
4.2.4 Constrained Delaunay Triangulation Method
4.2.5 Mapping Method
4.2.6 Automatic Generation of Three-Dimensional Finite Element Mesh Based on Improved Octree Method
4.3 Several Research Fields in Finite Element Mesh Generation
4.3.1 Methods for Generating Finite Element Mesh on Complex Three-Dimensional Composite Surfaces
4.3.2 Closed Surface Partitioning Method
4.3.3 Mesh Quality Optimization
4.3.4 Case Studies of Mesh Partitioning for Composite Surfaces
4.3.5 Hexahedral Mesh Generation
4.3.6 Parallel Algorithms for Mesh Generation
4.3.7 Overview of Adaptive Mesh Generation Methods
4.4 Secondary Development of AutoCAD and CAD/CAE Integration
4.4.1 Comparison of Several Commonly Used Development Tools for AutoCAD Secondary Development
4.4.2 ADS
4.4.3 ObjectARX
4.4.4 MCADAPI
4.4.5 CAD/CAE Integration Method Based on Extended Entity Data
4.4.6 Finite Element Modeling Software AutoFEM
4.4.7 Main Functions and Characteristics of the AutoFEM System
Chapter 5 Post-Processing System of CAE Software
5.1 Introduction
5.2 Main Functions of Finite Element Post-Processing System
5.3 Data Management of Post-Processing System
5.3.1 Characteristics of Data Management in Post-Processing System
5.3.2 Management of Structural Model Data
5.3.3 Management of Computational Result Data
5.4 Selection of Graphical Engine for Post-Processing System
5.4.1 Introduction to OpenGL
5.4.2 Basic Concepts of OpenGL
5.4.3 Features of OpenGL
5.4.4 Composition of OpenGL
5.4.5 Basic Drawing of OpenGL
5.5 Implementation of Graphical Processing Functions in Finite Element Post-Processing System
5.5.1 Implementation of Graphical Geometric Transformation Functions
5.5.2 Drawing of Mesh Graphs
5.5.3 Drawing of Hidden Line Graphs
5.5.4 Drawing of Color Cloud Graphs
5.5.5 Drawing of Contour Line Graphs
5.5.6 Drawing of Deformation Graphs
5.5.7 Drawing of Animation Graphs
5.5.8 Drawing of Beam Element-Related Graphs
5.5.9 Display of Various Identifiers
5.5.10 Introduction to Volume Rendering Graphs
5.5.11 Direct Volume Rendering Algorithm Based on Scan Surfaces
5.5.12 Volume Rendering Algorithm Flow
5.5.13 Basic Principles of Vector Field Graphs
5.5.14 Data Space Transformation of Vector Field Graphs
5.5.15 Algorithm Flow and Key Points of Vector Field Graphs
Chapter 6 Application of CAE Software
6.1 Selection and Use of CAE Software
6.1.1 Selection of CAE Software
6.1.2 Operation Process of CAE Software
6.2 Issues to Note When Using CAE Software
6.2.1 Sources of Errors in Structural Analysis Using CAE Software
6.2.2 Determining the Functional Requirements of CAE Software Based on the Mechanical Behavior of Structures
6.2.3 Issues to Note in Structural Modeling
6.2.4 Treatment of Internal Connections and Boundary Conditions in Structural Modeling
6.2.5 Issues to Note When Using the Pre-Processing and Post-Processing of CAE Software
6.3 Introduction to Some CAE Software
6.3.1 Introduction to Some CAE Finite Element Analysis Software Abroad
6.3.2 Introduction to Analysis Functions of Some Finite Element Analysis Software Abroad
6.3.3 Introduction to Domestic Structural Finite Element Analysis and Optimization Design Software JIFEX
References