حل كتاب Solutions Manual for An Introduction to The Finite Element Method – Third Edition

حل كتاب
Solutions Manual for An Introduction to The Finite Element Method – Third Edition
by
J. N. REDDY
Department of Mechanical Engineering
Texas A & M University
Table of Contents
Overview
A About the Author
B Dedication
C Preface to the Fourth Edition
D Preface to the Third Edition
E Preface to the Second Edition
F Preface to the First Edition
G Symbols and Conversion Factors
View sub-sections1 General Introduction
View sub-sections2 Mathematical Preliminaries and Classical Variational Methods
View sub-sections3 1-D Finite Element Models of Second-Order Differential Equations
View sub-sections4 Applications to 1-D Heat Transfer and Fluid and Solid Mechanics Problems
View sub-sections5 Finite Element Analysis of Beams and Circular Plates
View sub-sections6 Plane Trusses and Frames
View sub-sections7 Eigenvalue and Time-Dependent Problems in 1-D
View sub-sections8 Numerical Integration and Computer Implementation
View sub-sections9 Single-Variable Problems in Two Dimensions
View sub-sections10 2-D Interpolation Functions, Numerical Integration, and Computer Implementation
View sub-sections11 Flows of Viscous Incompressible Fluids
View sub-sections12 Plane Elasticity
View sub-sections13 3-D Finite Element Analysis
Overview
A About the Author
B Dedication
C Preface to the Fourth Edition
D Preface to the Third Edition
E Preface to the Second Edition
F Preface to the First Edition
G Symbols and Conversion Factors
View sub-sections1 General Introduction
1.0 CHAPTER PRELIMINARIES
1.1 Background
1.2 Mathematical Model Development
1.3 Numerical Simulations
View sub-sections1.4 The Finite Element Method
1.5 The Present Study
1.6 Summary
1.7 Problems
1.8 References for Additional Reading
View sub-sections2 Mathematical Preliminaries and Classical Variational Methods
2.0 CHAPTER PRELIMINARIES
View sub-sections2.1 General Introduction
View sub-sections2.2 Some Mathematical Concepts and Formulae
View sub-sections2.3 Energy and Virtual Work Principles
View sub-sections2.4 Integral Formulations of Differential Equations
View sub-sections2.5 Variational Methods
View sub-sections2.6 Equations of Continuum Mechanics
2.7 Summary
2.8 Problems
2.9 References for Additional Reading
View sub-sections3 1-D Finite Element Models of Second-Order Differential Equations
3.0 CHAPTER PRELIMINARIES
View sub-sections3.1 Introduction
View sub-sections3.2 Finite Element Analysis Steps
View sub-sections3.3 Finite Element Models of Discrete Systems
View sub-sections3.4 Finite Element Models of Continuous Systems
View sub-sections3.5 Axisymmetric Problems
View sub-sections3.6 Errors in Finite Element Analysis
3.7 Summary
3.8 Problems
3.9 References for Additional Reading
View sub-sections4 Applications to 1-D Heat Transfer and Fluid and Solid Mechanics Problems
4.0 CHAPTER PRELIMINARIES
4.1 Preliminary Comments
View sub-sections4.2 Heat Transfer
View sub-sections4.3 Fluid Mechanics
View sub-sections4.4 Solid and Structural Mechanics
4.5 Summary
4.6 Problems
4.7 References for Additional Reading
View sub-sections5 Finite Element Analysis of Beams and Circular Plates
5.0 CHAPTER PRELIMINARIES
5.1 Introduction
View sub-sections5.2 Euler–Bernoulli Beam Element
View sub-sections5.3 Timoshenko Beam Elements
View sub-sections5.4 Axisymmetric Bending of Circular Plates
5.5 Summary
5.6 Problems
5.7 References for Additional Reading
View sub-sections6 Plane Trusses and Frames
6.0 CHAPTER PRELIMINARIES
6.1 Introduction
View sub-sections6.2 Analysis of Trusses
View sub-sections6.3 Analysis of Plane Frame Structures
View sub-sections6.4 Inclusion of Constraint Conditions
6.5 Summary
6.6 Problems Free
6.7 References for Additional Reading
View sub-sections7 Eigenvalue and Time-Dependent Problems in 1-D
7.0 CHAPTER PRELIMINARIES
7.1 Introduction
View sub-sections7.2 Equations of Motion
View sub-sections7.3 Eigenvalue Problems
View sub-sections7.4 Transient Analysis
7.5 Summary
7.6 Problems
7.7 References for Additional Reading
View sub-sections8 Numerical Integration and Computer Implementation
8.0 CHAPTER PRELIMINARIES
8.1 Introduction
View sub-sections8.2 Numerical Integration
View sub-sections8.3 Computer Implementation
View sub-sections8.4 Applications of Program FEM1D
8.5 Summary
8.6 Problems
8.7 References for Additional Reading
View sub-sections9 Single-Variable Problems in Two Dimensions
9.0 CHAPTER PRELIMINARIES
9.1 Introduction
View sub-sections9.2 Boundary Value Problems
View sub-sections9.3 Modeling Considerations
View sub-sections9.4 Numerical Examples
View sub-sections9.5 Eigenvalue and Time-Dependent Problems
9.6 Summary
9.7 Problems
9.8 References for Additional Reading
View sub-sections10 2-D Interpolation Functions, Numerical Integration, and Computer Implementation
10.0 CHAPTER PRELIMINARIES
View sub-sections10.1 Introduction
View sub-sections10.2 2-D Element Library
View sub-sections10.3 Numerical Integration
View sub-sections10.4 Modeling Considerations
View sub-sections10.5 Computer Implementation and FEM2D
10.6 Summary
10.7 Problems
10.8 References for Additional Reading
View sub-sections11 Flows of Viscous Incompressible Fluids
11.0 CHAPTER PRELIMINARIES
11.1 Introduction
11.2 Governing Equations
View sub-sections11.3 Velocity–Pressure Formulation
View sub-sections11.4 Penalty Function Formulation
View sub-sections11.5 Computational Aspects
11.6 Numerical Examples
11.7 Summary
11.8 Problems
11.9 References for Additional Reading
View sub-sections12 Plane Elasticity
12.0 CHAPTER PRELIMINARIES
12.1 Introduction
View sub-sections12.2 Governing Equations
View sub-sections12.3 Virtual Work and Weak Formulations
View sub-sections12.4 Finite Element Model
View sub-sections12.5 Elimination of Shear Locking in Linear Elements
12.6 Numerical Examples
12.7 Summary
12.8 Problems
12.9 References for Additional Reading
View sub-sections13 3-D Finite Element Analysis
13.0 CHAPTER PRELIMINARIES
13.1 Introduction
View sub-sections13.2 Heat Transfer
View sub-sections13.3 Flows of Viscous Incompressible Fluids
View sub-sections13.4 Elasticity
View sub-sections13.5 Element Interpolation Functions and Numerical Integration
13.6 Numerical Examples
13.7 Summary
13.8 Problems
13.9 References for Additional Reading
Table of Contents
Contents
Finite Element Method
- Introduction to finite element analysis
- Brief history
- General Finite Element Method steps
3.1. Step 1: Discretize and Select the Element Types
3.2. Step 2: Select U Function (degrees of freedom)
3.3. Step 3: Determination of strain/displacement and stress/strain relationships
3.4. Step 4: Derive the Element Stiffness Matrix and Equations
3.5. Step 5: Assemble the Element Equations to get the Global or Total Equations, and then add Boundary Conditions
3.6. Step 6: Determine the Unknown Degrees of Freedom
3.7. Step 7: Solution for the Element Strains and Stresses
3.8. Step 8: Analyze the Result of finite element analysis - Application of FEM (finite element analysis)
4.1. Aerospace & FEA analysis
4.2. Naval & FEA analysis
4.3. Sports & FEA analysis - Benefits of Using the Finite Element Method
- Limitation of Finite Element Method
- FEM & FEA (Finite Element Analysis)
- FEM Software
8.1 Verification and Validation of FEA Results - Example of process FEM to FEA
9.1. Step 1: Modeling
9.2. Step 2: Choose the material of the structure
9.3. Step 3: Assemble the structure
9.4. Step 4: Choose the solution method
9.5. Step 5: Create boundary condition
9.6. Step 6: Choose the element type
9.7. Step 7: result
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