Introduction to the Finite Element Method 4E

1 General Introduction 1.1 Background1.2 Mathematical Model Development 1.3 Numerical Simulations 1.4 The Finite Element Method1.5 The Present Study 1.6 Summary Problems References for Additional Reading 
2 Mathematical Preliminaries and Classical Variational Methods2.1 General Introduction 2.2 Some Mathematical Concepts and Formulae2.3 Energy and Virtual Work Principles 2.4 Integral Formulations of Differential Equations2.5 Variational Methods2.6 Equations of Continuum Mechanics2.7 Summary Problems References for Additional Reading
3 1-D Finite Element Models of Second-Order Differential Equations3.1 Introduction 3.2 Finite Element Analysis Steps 3.3 Finite Element Models of Discrete Systems3.4 Finite Element Models of Continuous Systems3.5 Axisymmetric Problems3.6 Errors in Finite Element Analysis 3.7 Summary ProblemsReferences for Additional Reading 
4 Applications to 1-D Heat Transfer and Fluid and SolidMechanics Problems 4.1 Preliminary Comments 4.2 Heat Transfer 4.3 Fluid Mechanics4.4 Solid and Structural Mechanics 4.5 Summary ProblemsReferences for Additional Reading
5 Finite Element Analysis of Beams and Circular Plates 5.1 Introduction 5.2 Euler–Bernoulli Beam Element 5.3 Timoshenko Beam Elements5.4 Axisymmetric Bending of Circular Plates 5.5 Summary Problems References for Additional Reading 
6 Plane Trusses and Frames 6.1 Introduction 6.2 Analysis of Trusses 6.3 Analysis of Plane Frame Structures6.4 Inclusion of Constraint Conditions 6.5 Summary Problems References for Additional Reading 
7 Eigenvalue and Time-Dependent Problems in 1-D 7.1 Introduction 7.2 Equations of Motion 7.3 Eigenvalue Problems 7.4 Transient Analysis7.5 Summary Problems References for Additional Reading
8 Numerical Integration and Computer Implementation 8.1 Introduction 8.2 Numerical Integration 8.3 Computer Implementation 8.4 Applications of Program FEM1D 8.5 Summary ProblemsReferences for Additional Reading 
9 Single-Variable Problems in Two Dimensions 9.1 Introduction 9.2 Boundary Value Problems 9.3 Modeling Considerations 9.4 Numerical Examples 9.5 Eigenvalue and Time-Dependent Problems9.6 Summary Problems References for Additional Reading 
10 2-D Interpolation Functions, Numerical Integration, and Computer Implementation 10.1 Introduction 10.2 2-D Element Library10.3 Numerical Integration 10.4 Modeling Considerations 10.5 Computer Implementation and FEM2D10.6 SummaryProblemsReferences for Additional Reading
11 Flows of Viscous Incompressible Fluids11.1 Introduction11.2 Governing Equations11.3 Velocity–Pressure Formulation11.4 Penalty Function Formulation 11.5 Computational Aspects 11.6 Numerical Examples 11.7 Summary Problems References for Additional Reading
12 Plane Elasticity 12.1 Introduction12.2 Governing Equations 12.3 Virtual Work and Weak Formulations12.4 Finite Element Model 12.5 Elimination of Shear Locking in Linear Elements12.6 Numerical Examples 12.7 SummaryProblems References for Additional Reading 
13 3-D Finite Element Analysis 13.1 Introduction 13.2 Heat Transfer13.3 Flows of Viscous Incompressible Fluids 13.4 Elasticity 13.5 Element Interpolation Functions and Numerical Integration 13.6 Numerical Examples13.7 Summary ProblemsReferences for Additional Reading 
Index