The Finite Element Method and Applications in Engineering Using ANSYS®

Preface
Contents
List of Problems Solved
Chapter-1
Introduction
1.1 Concept
1.2 Nodes
1.3 Elements
1.4 Direct Approach
1.4.1 Linear Spring
1.4.2 Heat Flow
1.4.3 Assembly of the Global System of Equations
1.4.4 Solution of the Global System of Equations
1.4.5 Boundary Conditions
Chapter-2
Fundamentals of ANSYS
2.1 Useful Definitions
2.2 Before an ANSYS Session
2.2.1 Analysis Discipline
2.2.1.1 Structural Analysis
2.2.1.2 Thermal Analysis
2.2.1.3 Degrees of Freedom
2.2.2 Time Dependence
2.2.3 Nonlinearity
2.2.3.1 Geometric Nonlinearity
2.2.3.2 Material Nonlinearity
2.2.3.3 Changing-status Nonlinearity
2.2.4 Practical Modeling Considerations
2.2.4.1 Symmetry Conditions
2.2.4.2 Mesh Density
2.3 Organization of ANSYS Software
2.4 ANSYS Analysis Approach
2.4.1 ANSYS Preprocessor
2.4.2 ANSYS Solution Processor
2.4.3 ANSYS General Postprocessor
2.4.4 ANSYS Time History Postprocessor
2.5 ANSYS File Structure
2.5.1 Database File
2.5.2 Log File
2.6 Error File
2.6.1 Results Files
2.7 Description of ANSYS Menus and Windows
2.7.1 Utility Menu
2.7.2 Main Menu
2.7.3 Toolbar
2.7.4 Input Field
2.7.5 Graphics Window
2.7.6 Output Window
2.8 Using the ANSYS Help System
2.8.1 Help Contents
2.8.2 Help Index
2.8.3 Search in Help
2.8.4 Verification Manual
Chapter-3
Fundamentals of Discretization
3.1 Local and Global Numbering
3.2 Approximation Functions
3.3 Coordinate Systems
3.3.1 Generalized Coordinates
3.3.2 Global Coordinates
3.3.3 Local Coordinates
3.3.4 Natural Coordinates
3.3.4.1 Natural Coordinates in One Dimension
3.3.4.2 Natural Coordinates in Two Dimensions
3.4 Shape Functions
3.4.1 Linear Line Element with Two Nodes
3.4.1.1 Global Coordinate
3.4.1.2 Centroidal Coordinate
3.4.2 Quadratic Line Element with Three Nodes: Centroidal Coordinate
3.4.3 Linear Triangular Element with Three Nodes: Global Coordinate
3.4.4 Quadratic Triangular Element with Six Nodes
3.4.5 Linear Quadrilateral Element with Four Nodes: Centroidal Coordinate
3.5 Isoparametric Elements: Curved Boundaries
3.6 Numerical Evaluation of Integrals
3.6.1 Line Integrals
3.6.2 Triangular Area Integrals
3.6.3 Quadrilateral Area Integrals
3.7 Problems
Chapter 4
ANSYS Preprocessor
4.1 Fundamentals of Modeling
4.2 Modeling Operations
4.2.1 Title
4.2.2 Elements
4.2.3 Real Constants
4.2.4 Material Properties
4.2.5 Element Attributes
4.2.6 Interaction with the Graphics Window: Picking Entities
4.2.7 Coordinate Systems
4.2.7.1 Global Coordinate Systems
4.2.7.2 Local Coordinate Systems
4.2.8 Working Plane
4.3 Solid Modeling
4.3.1 Bottom-up Approach: Entities
4.3.1.1 Keypoints
4.3.1.2 Lines
4.3.1.3 Areas
4.3.1.4 Volumes
4.3.2 Top-Down Approach: Primitives
4.3.2.1 Area Primitives
4.3.2.2 Volume Primitives
4.4 Boolean Operators
4.4.1 Adding
4.4.2 Subtracting
4.4.3 Overlap
4.4.4 Gluing
4.4.5 Dividing
4.5 Additional Operations
4.5.1 Extrusion
4.5.2 Moving and Copying
4.5.3 Keeping/Deleting Original Entities
4.5.4 Listing Entities
4.5.5 Deleting Entities
4.6 Viewing a Model
4.6.1 Plotting: Pan, Zoom, and Rotate Functions
4.6.2 Plotting/Listing Entities
4.6.3 Numbers in the Graphics Window
4.7 Meshing
4.7.1 Automatic Meshing
4.7.1.1 Specifying Mesh Density Globally
4.7.1.2 Specifying Number of Element Edges on Specific Lines
4.7.1.3 Smart Sizing
4.7.1.4 Mapped Meshing
4.7.2 Manipulation of the Mesh
4.7.2.1 Changing Element Attributes
4.7.2.2 Clearing and Deleting Mesh
4.7.2.3 Numbering Controls
4.8 Selecting and Components
4.8.1 Selecting Operations
4.8.2 Components
Chapter-5
ANSYS Solution and Postprocessing
5.1 Overview
5.2 Solution
5.2.1 Analysis Options/Solution Controls
5.2.2 Boundary Conditions
5.2.3 Initial Conditions
5.2.4 Body Loads
5.2.5 Solution in Single and Multiple Load Steps
5.2.6 Failure to Obtain Solution
5.3 Postprocessing
5.3.1 General Postprocessor
5.3.2 Time History Postprocessor
5.3.3 Read Results
5.3.4 Plot Results
5.3.5 Element Tables
5.3.6 List Results
5.4 Example: One-dimensional Transient Heat Transfer
Chapter-6
Finite Element Equations
6.1 Method of Weighted Residuals
6.1.1 Example: One-Dimensional Differential Equation with Line Elements
6.1.2 Example: Two-Dimensional Differential Equation with Linear Triangular Elements
6.1.2.1 Galerkin’s Method
6.1.2.2 ANSYS Solution
6.1.3 Example: Two-Dimensional Differential Equation with Linear Quadrilateral Elements
6.1.3.1 Galerkin’s Method
6.1.3.2 ANSYS Solution
6.2 Principle of Minimum Potential Energy
6.2.1 Example: One-Dimensional Analysis with Line Elements
6.2.2 Two-Dimensional Structural Analysis
6.2.2.1 Plane Stress Conditions
6.2.2.2 Plane Strain Conditions
6.2.2.3 Finite Element Equations with Linear Triangular Elements
6.2.2.4 Example of a Plane Stress Analysis with Linear Triangular Elements
6.2.2.5 ANSYS Solution
6.2.2.6 Example of a Plane Stress Analysis with Linear Quadrilateral Isoparametric Elements
6.3 Problems
Chapter-7
Use of Commands in ANSYS
7.1 Basic ANSYS Commands
7.1.1 Operators and Functions
7.1.2 Defining Parameters
7.2 A Typical Input File
7.3 Selecting Operations
7.4 Extracting Information from ANSYS
7.5 Programming with ANSYS
7.5.1 DO Loops
7.5.2 IF Statements
7.5.3 /OUTPUT and *VWRITE Commands
7.6 Macro Files
7.7 Useful Resources
7.7.1 Using the Log File for Programming
7.7.2 Using the Verification Problems for Programming
Chapter-8
Linear Structural Analysis
8.1 Static Analysis
8.1.1 Trusses
8.1.1.1 Elongation of a Bar Under its Own Weight Using Truss Elements
8.1.1.2 Analysis of a Truss Structure with Symmetry
8.1.2 Beams
8.1.2.1 Analysis of a Slit Ring
8.1.3 Three-Dimensional Problems
8.1.4 Two-Dimensional Idealizations
8.1.4.1 Plane Stress
8.1.4.2 Plane Strain
8.1.4.3 Axisymmetric
8.1.5 Plates and Shells
8.1.5.1 Static Analysis of a Bracket
8.1.5.2 Analysis of a Circular Plate Pushed Down by a Piston Head
8.1.5.3 Analysis of an Axisymmetric Shell with Internal Pressure
8.1.5.4 Analysis of a Layered Composite Plate
8.2 Linear Buckling Analysis
8.3 Thermomechanical Analysis
8.4 Fracture Mechanics Analysis
8.5 Dynamic Analysis
8.5.1 Modal Analysis
8.5.1.1 Modal Analysis of a Bracket
8.5.1.2 Vibration of an Automobile Suspension
8.5.2 Harmonic Analysis
8.5.2.1 Harmonic Analysis of a Bracket
8.5.2.2 Harmonic Analysis of a Guitar String
8.5.3 Transient Analysis
8.5.3.1 Dynamic Analysis of a Bracket
8.5.3.2 Impact Loading on a Beam
8.5.3.3 Dynamic Analysis of a 4-bar Linkage
Chapter 9
Linear Analysis of Field Problems
9.1 Heat Transfer Problems
9.1.1 Steady-state Analysis
9.1.1.1 Analysis of a Tank/Pipe Assembly
9.1.1.2 Analysis of a Window Assembly
9.1.2 Transient Analysis
9.1.2.1 Transient Thermomechanical Analysis of an Electronic Package
9.1.2.2 Transient Thermomechanical Analysis of a Welded Joint
9.1.3 Radiation Analysis
9.2 Moisture Diffusion
Chapter-10
Nonlinear Structural Analysis
10.1 Geometric Nonlinearity
10.1.1 Large Deformation Analysis of a Plate
10.1.2 Post-buckling Analysis of a Plate with a Hole
10.2 Material Nonlinearity
10.2.1 Plastic Deformation of an Aluminum Sphere
10.2.2 Plastic Deformation of an Aluminum Cylinder
10.2.3 Stress Analysis of a Reinforced Viscoelastic Cylinder
10.2.4 Viscoplasticity Analysis of a Eutectic Solder Cylinder
10.2.5 Combined Plasticity and Creep
10.3 Contact
10.3.1 Contact Analysis of a Block Dropping on a Beam
10.3.2 Simulation of a Nano-Indentation Test
Chapter-11
Advanced Topics in ANSYS
11.1 Coupled Degrees of Freedom
11.2 Constraint Equations
11.3 Submodeling
11.4 Substructuring: Superelements
11.4.1 Generation Pass
11.4.1.1 Model Generation
11.4.1.2 Superelement Generation
11.4.2 Use Pass
11.4.3 Expansion Pass
11.5 Interacting with External Files
11.5.1 Reading an Input File
11.5.2 Writing Data to External ASCII Files
11.5.2.1 The /OUTPUT Command
11.5.2.2 The *CFOPEN and *CFCLOSE Commands
11.5.2.3 The *VWRITE Command
11.5.3 Executing an External File
11.5.4 Modifying ANSYS Results
11.6 Modifying the ANSYS GUI
11.6.1 GUI Development Demonstration
11.6.2 GUI Modification for Obtaining a Random Load Profile
11.6.3 Function Block for Selecting Elements Using a Pick Menu
Erratum to: The Finite Element Method and Applications in Engineering Using ANSYS
References
Index