Finite Elements for Engineers with Ansys Applications

Höfundur: Mohamed S. Gadala (Útgáfa: 0)
Finite Elements for Engineers with Ansys Applications

Kaup valmöguleikar

The finite element method (FEM) is indispensable in modeling and simulation in various engineering and physical systems, including structural analysis, stress, strain, fluid mechanics, heat transfer, dynamics, eigenproblems, design optimization, sound propagation, electromagnetics, and coupled field problems. This textbook integrates basic theory with real-life, design-oriented problems using ANSYS, the most commonly used computational software in the field.

For students as well as practicing engineers and designers, each chapter is highly illustrated and presented in a step-by-step manner. Fundamental concepts are presented in detail with reference to easy to understand worked examples that clearly introduce the method before progressing to more advanced content. Included are step-by-step solutions for project type problems using modelling software, special chapters for modelling and the use of ANSYS and Workbench programs, and extensive sets of problems and projects round out each chapter.

Nánar um bókina

Útgefandi
Cambridge University Press
ISBN
9781316998052
Print ISBN
9781107194083
Format
ePub
Útgáfa
0
Höfundar
Mohamed S. Gadala
Tungumál
English
Útgefið
2020-07-09
Prent takmörkun á líftíma
10
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • Cover
  • Half title
  • Title page
  • Imprints page
  • Contents
  • Preface
  • 1 Finite Element Concepts
  • Chapter Roadmap
  • 1.1 General Solution of Continuum Problems
  • 1.2 What is the Finite Element Method?
  • 1.3 Basic Concepts and Definitions
  • • Elements
  • • Element types and shapes
  • • Element assumptions, shape or approximation functions
  • • Element characteristic equations
  • • Nodes
  • • Nodal and global degrees of freedom (DOFs)
  • • Assembly
  • • Solution and rigid body motion
  • • CPU time
  • • Boundary conditions
  • 1.4 Element Types and Degrees of Freedom (DOFs)
  • 1.4.1 Truss Elements
  • 1.4.2 Beam Elements
  • 1.4.3 Two-Dimensional Elements
  • 1.4.4 Three-Dimensional Shell Elements
  • 1.4.5 Three-Dimensional Solid Elements
  • 1.5 General Procedures for Finite Element Analysis
  • 1.5.1 Basic Procedures in Finite Element Analysis
  • 1. Discretization of the Continuum: Modeling and Preprocessing
  • 2. Element Characteristic Equations
  • 3. Assembly of Global Equations
  • 4. Solution of Global Equations
  • 5. Postprocessing (Calculation of Other Solution Quantities)
  • 1.5.2 Phases of Finite Element Analysis in Commercial Programs
  • 1. Preprocessing Phase
  • 2. Solution or Processing Phase
  • 3. Postprocessing Phase
  • 1.6 Brief History of the Development of the FE Method
  • 1.6.1 Ancient Roots of the FE Method
  • 1.6.2 History of the Development of the FE Method
  • 1.6.3 History of the Development of Computers and FE Software Programs
  • Early Software Development
  • The Law-of-the-Land (Moore’s) (Moore 1965 and Multi-Mechanics 2014)
  • The Pre-Personal-Computer Era (Multi-Mechanics 2014)
  • The Personal-Computer Era (Multi-Mechanics 2014)
  • 64 Bits and Parallelization (Multi-Mechanics 2014)
  • 1.6.4 Future Outlook and What’s Next?
  • 1.7 Finite Element Applications
  • 1.7.1 Various Types of Application
  • Problems
  • Multiple Choice Questions
  • 2 Detailed Procedures
  • Chapter Roadmap
  • 2.1 Element Characteristic Equations for Simple Elements
  • 2.1.1 Simple Truss Element – One DOF per node
  • 2.1.2 One-Dimensional Heat Transfer Element
  • 2.1.3 Pipe Flow Element
  • 2.1.4 Direct Current Flow Element
  • 2.1.5 Torsional Element
  • 2.2 Simple Beam Element
  • Case a: vi = 1.0, all other DOFs = 0
  • 2.3 Assembling of Global Equations
  • 2.4 Application of Boundary Conditions
  • 2.4.1 Rigid Body Motion
  • 2.4.2 Applying Boundary Conditions
  • 2.4.3 Application Example: Beam Element with a Hinge
  • 2.5 Coordinate Transformations and More Element Equations
  • 2.5.1 Coordinate Transformations
  • 2.5.2 General Two-Dimensional Truss Element
  • 2.5.3 General Two-Dimensional Beam Element
  • 2.5.4 Three-Dimensional Truss Element
  • 2.5.5 Three-Dimensional Beam Element
  • Problems
  • 3 Modeling Aspects
  • Chapter Roadmap
  • 3.1 The Modeling Process
  • 3.2 Geometric Modeling
  • Key Points
  • Line or Line Segment
  • Area or Patch
  • Volume or Hyperpatch
  • Boolean Operations
  • Theory of Parametric Cubic Geometry
  • 3.3 Discrete Element Types in FE Programs
  • 3.3.1 Concentrated Mass–Inertia Elements
  • 3.3.2 Spring and Damper Elements
  • 3.4 Problem Classification and Element Choice
  • 3.4.1 Truss and Beam Problems
  • Geometrical Types
  • Loading Conditions
  • Degrees of Freedom (DOFs)
  • Element Shapes
  • Application Examples
  • 3.4.2 Two-Dimensional Problems
  • (i) 2D Plane Stress Problems
  • Geometrical Type
  • Loading Conditions
  • Degrees of Freedom:
  • Element Shapes (refer to ):
  • Application Examples:
  • (ii) 2D Plane Strain Problems
  • Geometrical Type
  • Loading Conditions
  • Degrees of Freedom (DOFs):
  • Element Shapes (see ):
  • Application Examples
  • (iii) 2D Axisymmetric Problems
  • Geometrical Type
  • Loading Conditions
  • Degrees of Freedom (DOFs):
  • Element Shapes (refer to ):
  • Application Examples:
  • 3.4.3 Shell Problems
  • Geometrical Types
  • Loading Conditions
  • Degrees of Freedom (DOFs)
  • Element Shapes (see )
  • Application Examples
  • 3.4.4 Three-Dimensional Solid Problems
  • Geometrical Type
  • Loading Conditions
  • Degrees of Freedom (DOFs)
  • Element Shapes (see )
  • Application Examples
  • 3.5 Synopsis of Problem Classification and Element Choice
  • 3.6 Symmetry Considerations
  • 3.6.1 Planar Symmetry
  • 3.6.2 Axial Symmetry
  • 3.6.3 Cyclic Symmetry
  • 3.6.4 Symmetric Structure with Non-Symmetric Loading
  • 3.7 Boundary Conditions
  • 3.7.1 Eliminating Rigid Body Motion
  • 3.7.2 Modeling Supports
  • 3.8 Mesh Intensity and Transition
  • 3.9 Modeling with Different Element Types
  • 3.10 Lumped Load Vectors
  • 3.10.1 Lumped Load Methods
  • 3.10.2 Node-by-Node Lumping
  • 3.10.3 Element-by-Element Lumping
  • 3.11 Model Checking
  • 3.11.1 Checks Initiated by the Program
  • 3.11.2 Checks Performed by the User
  • 3.12 General Modeling Hints
  • Problems
  • 4 Linear Static Analysis Using Ansys/Workbench
  • Chapter Roadmap
  • 4.1 Introduction to the Ansys Program
  • 4.1.1 Operation Modes in Ansys
  • 4.1.2 Starting up Ansys
  • 4.1.3 Windows in Ansys
  • 4.1.4 Ansys Structure and Files
  • 4.2 Ansys Project 1: Analysis of a 2D Support Bracket
  • 4.2.1 Problem Description
  • 4.2.2 Create the Model Geometry
  • 1. Define the Rectangle ()
  • 2. Create a Triangle by Three Keypoints (, )
  • 3. Change the Plot Control and Replot
  • 4. Save the Database
  • 5. Add Areas ()
  • 6. Create the Pin Hole and the Slot ()
  • 7. Subtract Areas ()
  • 8. Create Line Fillet ()
  • 9. Create Fillet Area ()
  • 10. Subtract the Fillet Areas ()
  • 11. Save the Database as 2D-Bracket.db
  • 4.2.3 Generate the FE Model
  • 1. Set Preferences ()
  • 2. Define the Material Properties ()
  • 3. Define the Element Types and Options ()
  • 4. Define the Real Constants ()
  • 5. Mesh the Area ()
  • 6. Save the Database as mesh.db
  • 4.2.4 Solution Operation
  • 1. Apply the Displacement Constraints ()
  • 2. Apply the Pressure Load ()
  • 3. Solve ()
  • 4.2.5 Displaying the Results and Exiting Ansys
  • 1. Plot the Deformed Shape ()
  • 2. Plot the Von Mises Equivalent Stress and Other Results ()
  • 3. Get the Reactions at the Fixed Side ()
  • 4. Exit the Ansys Program ()
  • 4.2.6 Batch-Type Solution
  • 4.2.7 Mesh Sensitivity Analysis
  • 1. Mesh Sensitivity Analysis ()
  • 2. Simple Beam Theory Analysis ()
  • 4.3 Introduction to Workbench
  • 4.3.1 Layout of Program Menus
  • 4.3.2 Overview of the Geometry and the DesignModeler Capabilities
  • (i) 2D Sketching Mode
  • (ii) 3D Modeling
  • (iii) File Menu
  • (iv) Create Menu
  • (v) Concept Menu
  • (vi) Tools Menu
  • 4.4 Workbench Project 1: 2D Cantilever Bracket
  • 4.4.1 Create the Model Geometry ()
  • 1. Setting Units ()
  • 2. Setting View ()
  • 3. Making the Sketches ()
  • 4. Filleting (, )
  • 5. Making the Bracket ()
  • 4.4.2 Generate the FE Model
  • 1. Material Properties ()
  • 2. Meshing ()
  • 3. Boundary Condition and Loading ()
  • 4.4.3 Solution, Results and Mesh Refinement
  • 1. Solution and Results ()
  • 2. Mesh Refinement (-)
  • 3. Thick Bracket ()
  • 4.5 Workbench Project 2: 3D T-Junction Analysis
  • 4.5.1 Problem Description
  • 4.5.2 Creating the Geometry
  • 4.5.3 T-Junction FE Model and Solution
  • 5 Finite Element Formulations
  • Chapter Roadmap
  • 5.1 Overview
  • 5.2 Strong and Weak Forms of the Problem
  • 5.3 FE Virtual Work Formulations
  • 5.4 Principle of Minimum Potential Energy and the Rayleigh–Ritz Method
  • 5.5 Linear Elastic FE Analysis Using Virtual Work Principle
  • 5.6 Heat Conduction Analysis Using Virtual Work Principle
  • 5.7 Method of Weighted Residuals (MWRs)
  • 5.7.1 Overview of MWRs
  • 5.7.2 Various Weighted Residual Methods
  • Point and Subdomain Collocation Methods
  • Continuous Least Squares Method
  • Least Squares Collocation Method
  • Galerkin Methods
  • 5.8 Galerkin Formulation of 2D Linear Elasticity Problems
  • 5.9 Formulation of Heat Conduction Analysis
  • 5.9.1 Heat Conduction Analysis Using Variational Principles
  • 5.9.2 3D Heat Conduction Analysis Using the Galerkin Formulation
  • Problems
  • Project Type Problems
  • 6 Linear Static Analysis
  • Chapter Roadmap
  • 6.1 Linear Elastic Analysis Formulation
  • 6.1.1 Problem Formulation by the Virtual Work and Galerkin Principles
  • 6.1.2 Specialization to Two-Dimensional Problems
  • The Plane Stress Case
  • The Plane Strain Case
  • The Axisymmetric Case
  • 6.2 Application to General Three-Dimensional Solid Elements
  • 6.3 Development of Simple Beam Element
  • 6.4 Development of Two-Dimensional Elements
  • 6.4.1 Plane Stress or Strain Triangular Elements with Three Nodes
  • Shape Function and Stiffness Matrix
  • Body Forces and Traction Forces
  • 6.4.2 Plane Stress or Strain Rectangular Element with Four Nodes
  • 6.4.3 Axisymmetric Triangular Ring Element with Three Nodes
  • Shape Function and Stiffness Matrix
  • Body Forces and Traction Forces
  • 6.5 Development of Three-Dimensional Solid Elements
  • 6.5.1 Tetrahedron Element with Four Nodes
  • Shape Function and Stiffness Matrix
  • Body Forces and Traction Forces
  • 6.6 Thermal Stresses
  • 6.6.1 Constitutive Equations with Thermal Effect
  • Plane Stress Case
  • Plane Strain Case
  • Axisymmetric Case
  • 6.6.2 Element Equations with Thermal Effect
  • 6.7 Isoparametric Elements
  • 6.7.1 General Concepts and the Need for Isoparametric Elements
  • Modeling and Idealization of Curved Boundaries
  • Inversion of the [A] Matrix
  • The Need for an Easy Procedure to Program the Element Formulation
  • 6.7.2 Development of 1D Truss Element
  • 6.7.3 Development of 2D Quadrilateral Element with Four to Nine Nodes
  • Two-Dimensional Quadrilateral Element with Four Nodes
  • Two-Dimensional Quadrilateral Element with Four to Nine Nodes
  • 6.7.4 Development of 2D Triangular Element with Three to Six Nodes
  • 6.7.5 Development of 3D Hexahedral or Cubical Element with Eight to 20 Nodes
  • 6.7.6 Development of 3D Tetrahedral Elements
  • 6.8 Application of Multi-Point Linear Constraint Equations (MPCs)
  • 6.8.1 Types of Constraint
  • 6.8.2 Method of Substitution
  • 6.8.3 Lagrange Multiplier Method
  • 6.8.4 Penalty Method
  • Problems
  • 6.1 Linear Elastic Analysis Formulation
  • 6.3 Development of Simple Beam Element
  • 6.4 Development of Two-Dimensional Elements
  • 6.6 Thermal Stresses
  • 6.7 Isoparametric Elements and Shape Functions
  • 6.8 Application of Multi-Point Linear Constraint Equations (MPCs)
  • Multiple Choice Questions
  • 7 Conduction Heat Transfer Analysis
  • Chapter Roadmap
  • 7.1 General Background
  • 7.1.1 Basic Modes of Heat Transfer
  • (i) Conduction
  • (ii) Convection
  • (iii) Radiation
  • 7.1.2 The One-Dimensional Heat Conduction Equation
  • • Isotropic material with constant conductivity
  • • Isotropic material with no heat generation ( qB=0)
  • • Isotropic material and steady state conditions
  • • Isotropic material with steady state conditions and no heat generation
  • 7.1.3 Boundary Conditions
  • • Prescribed temperature
  • • Prescribed heat flow or flux
  • • No heat flow (adiabatic or natural boundary)
  • • Convection heat exchange
  • • Radiation
  • 7.1.4 Sources of Nonlinearity
  • 7.2 FE Formulation of the Heat Conduction Problem
  • 7.3 Solution of the Transient Heat Transfer Equations
  • 7.3.1 General Considerations
  • Implicit Integration Schemes
  • Explicit Integration Schemes
  • 7.3.2 Direction Integration Method
  • (i) Linearization of the General Equation
  • Linear steady state:
  • Nonlinear steady state:
  • Linear transient analysis:
  • Nonlinear transient analysis:
  • (ii) The α-Method
  • For linear steady state conditions:
  • For nonlinear steady state conditions:
  • For linear transient analysis:
  • For nonlinear transient analysis:
  • For explicit schemes:
  • (iii) General Solution Steps
  • Implicit Scheme
  • Explicit Scheme
  • (iv) Stability and Accuracy Considerations
  • (v) Accuracy of the α-Method
  • 7.4 Element Equations for Heat Transfer Analysis
  • 7.4.1 One-Dimensional Elements
  • 7.4.2 Two-Dimensional Elements
  • (i) Three-Node Plane Triangular Elements
  • (ii) Three-Node Axisymmetric Elements
  • (iii) Isoparametric Elements
  • 7.5 Ansys/Workbench Project: Square Plate with Prescribed Temperature Boundary Conditions
  • Problem Statement
  • Approach and Assumptions
  • Solution Steps
  • (1) Specifying the Physics Problem
  • (2) Engineering Data
  • Editing the engineering data:
  • (3) Ansys Design Modeler
  • Entering the DesignModeler (DM) window:
  • Creating a two-dimensional sketch:
  • Creating an area:
  • (4) Ansys Workbench Modeling
  • Selecting the material and specifying thickness:
  • Generating the mesh:
  • Applying boundary conditions:
  • (5) Ansys Workbench Solver
  • (6) Ansys Workbench PostProcessor
  • Temperature contour within the plate:
  • Temperature distribution along X = 0.5 in ()
  • (7) Comparison ()
  • Problems
  • Project-Type Problems
  • Appendices
  • Appendix A Matrices and Systems of Linear Equations
  • A.1 Definition and Basic Operations
  • A.1.1 Definition of Matrices
  • A.1.2 Basic Matrix Operations
  • Equality
  • Addition and Subtraction
  • Scalar Multiplication
  • Multiplication of Matrix with Vector
  • Multiplication of Two Matrices
  • A.1.3 General Matrix Operations
  • Algebraic Operations
  • Matrix Partioning
  • Determinant
  • A.1.4 Special Types of Matrices
  • Square Matrix:
  • Upper and Lower Triangular Matrices:
  • Singular Matrix:
  • Row and Column Matrices:
  • Zero Matrix:
  • Unit Matrix:
  • Diagonal Matrix:
  • Transpose of a Matrix:
  • Minor:
  • Cofactor:
  • Adjoint Matrix:
  • Orthogonal Matrix:
  • Symmetric Matrix:
  • Antisymmetric Matrix:
  • A.2 Matrix Inversion and Solution of System of Equations
  • A.2.1 Definitions
  • Positive Definite Matrix:
  • Inverse of a Matrix:
  • A.2.2 Methods of Matrix Inversion
  • (i) Cramer’s Rule
  • (ii) Gauss–Jordan and Gauss Elimination Methods
  • (iii)
  • (iv) Consistency and General Solution of a System of Equations
  • A.2.3 Matrix Decomposition and Its Use in Matrix Inversion
  • (i) LU and LDU Decomposition
  • (ii) Solving a System of Equations Using LU Decomposition
  • (iii) Cholesky Decomposition
  • (iv) Matrix Inversion by Cholesky Decomposition
  • A.3 Errors and Iterative Refinements
  • A.3.1 Ill-Conditioning and Round-off Errors
  • A.3.2 Partial and Full Pivot Searches
  • A.3.3 Iterative Refinement of the Solution
  • A.4 Vector and Matrix Norms
  • Use and General Properties
  • Common Norms for Vectors
  • Eigenvalues and Spectrum of a Matrix
  • Common Norms for a Square Matrix
  • Condition Number and Conditioning of a Matrix
  • Appendix B Vectors and Tensors
  • B.1 Indicial Notation
  • B.2 Vectors and Tensors
  • B.2.1 Definitions
  • B.2.2 Vector Operations
  • Addition and Subtraction
  • Scalar Multiplication
  • Dot or Scalar Product
  • The Kronecker Delta
  • Cross or Vector Product
  • Permutation Symbol
  • Triple Scalar Product
  • B.2.3 Tensor Operations
  • Addition and Subtraction, Zero and Identity Tensors
  • Scalar Multiplication
  • Tensor or Dyadic Product of Two Vectors
  • Dot Products of a Vector and Tensor
  • B.2.4 Change of Base for Vectors and Tensors
  • B.3 Vector and Tensor Calculus
  • B.3.1 Time Derivatives of Vectors and Tensors
  • B.3.2 Spatial Derivatives of Scalar, Vector and Tensor Functions
  • Gradient of a Scalar Function
  • Divergence, Curl and Gradient of a Vector
  • B.3.3 Gauss Divergence Theorem
  • ℜ is a scalar
  • ℜ is the product of two scalars
  • ℜ is a vector
  • ℜ is the product of a scalar and vector
  • ℜ is a tensor
  • B.4 Eigenvalues and Eigenvectors of a Second-Order Tensor
  • References
  • Index