The Finite Element Method and Applications in Engineering Using ANSYS®

Description

The Finite Element Method and Applications with ANSYS(R) provides the reader with theoretical and practical knowledge of the finite element method and with the skills required to analyze engineering problems with ANSYS(R), a commercially available FEA program. This self-contained, introductory text minimizes the need for additional reference material, covering the fundamental topics in finite element methods as well as advanced topics concerning modeling and analysis with ANSYS(R). These topics are introduced through extensive examples from various engineering disciplines, presented in a step-by-step fashion. The book focuses on the use of ANSYS(R) through both the Graphics User Interface (GUI) and the ANSYS(R) Parametric Design Language (APDL). The text details more than 40 example problems, with solutions demonstrated in a step-by-step fashion, primarily through the use of GUI and, to a lesser extent, APDL. Furthermore, it includes a CD-ROM with the "input" files for the example problems so that readers can regenerate them on their own computers, as well as the colored figures and screen shots. Students, researchers, and practicing engineers will find this an essential reference for use in predicting and simulating the physical behavior of complex engineering systems using ANSYS(R). 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