An up-to-date, self-contained introduction to the theory and applications of the finite element method This thoroughly revised classic engineering textbook offers a broad-based overview of the finite element method. Written by a world-renowned mechanical engineering researcher and author, the book shows, step-by-step, how to calculate numerical solutions to steady-state as well as time-dependent problems. You also get detailed problems with worked-out solutions and downloadable programs that can be used and modified for real-world situations. Special attention is paid to applications that are…mehr
An up-to-date, self-contained introduction to the theory and applications of the finite element method This thoroughly revised classic engineering textbook offers a broad-based overview of the finite element method. Written by a world-renowned mechanical engineering researcher and author, the book shows, step-by-step, how to calculate numerical solutions to steady-state as well as time-dependent problems. You also get detailed problems with worked-out solutions and downloadable programs that can be used and modified for real-world situations. Special attention is paid to applications that are important in bioengineering, fluid and thermal sciences, structural mechanics, and a host of applied sciences. Introduction to the Finite Element Method, Fourth Edition, covers: .Mathematical preliminaries and classical variational methods .1-D finite element models of second-order differential equations .Applications to 1-D heat transfer and fluid and solid mechanics problems .Finite element analysis of beams and circular plates .Plane trusses and frames .Eigenvalue and time-dependent problems in 1-D .Numerical integration and computer implementation in 1-D .Single-variable problems in two dimensions .2-D interpolation functions, numerical integration, and computer implementation in 2-D .Flows of viscous incompressible fluids .Plane elasticity .3-D finite element analysis
J. N. Reddy, Ph.D. is an ISI Highly Cited Researcher and the author of over 650 journal papers and 21 books. He is a Life Fellow and ASME Medalist of the American Society of Mechanical Engineers (ASME), and a Fellow of all major professional societies of engineering. He has also received top mechanics medals from various societies. Dr. Reddy is a Member of the U.S. National Academy of Engineering and Foreign Fellow of the Canadian Academy of Engineering, Indian National Academy of Engineering, and Brazilian National Academy of Engineering. >
Inhaltsangabe
1 General Introduction 1.1 Background 1.2 Mathematical Model Development 1.3 Numerical Simulations 1.4 The Finite Element Method 1.5 The Present Study 1.6 Summary Problems References for Additional Reading 2 Mathematical Preliminaries and Classical Variational Methods 2.1 General Introduction 2.2 Some Mathematical Concepts and Formulae 2.3 Energy and Virtual Work Principles 2.4 Integral Formulations of Differential Equations 2.5 Variational Methods 2.6 Equations of Continuum Mechanics 2.7 Summary Problems References for Additional Reading 3 1-D Finite Element Models of Second-Order Differential Equations 3.1 Introduction 3.2 Finite Element Analysis Steps 3.3 Finite Element Models of Discrete Systems 3.4 Finite Element Models of Continuous Systems 3.5 Axisymmetric Problems 3.6 Errors in Finite Element Analysis 3.7 Summary Problems References for Additional Reading 4 Applications to 1-D Heat Transfer and Fluid and Solid Mechanics Problems 4.1 Preliminary Comments 4.2 Heat Transfer 4.3 Fluid Mechanics 4.4 Solid and Structural Mechanics 4.5 Summary Problems References 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 Elements 5.4 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 Structures 6.4 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 Analysis 7.5 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 Problems References 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 Problems 9.6 Summary Problems References for Additional Reading 10 2-D Interpolation Functions, Numerical Integration, and Computer Implementation 10.1 Introduction 10.2 2-D Element Library 10.3 Numerical Integration 10.4 Modeling Considerations 10.5 Computer Implementation and FEM2D 10.6 Summary Problems References for Additional Reading 11 Flows of Viscous Incompressible Fluids 11.1 Introduction 11.2 Governing Equations 11.3 Velocity-Pressure Formulation 11.4 Penalty Function Formulation 11.5 Computational Aspects 11.6 Numerical Examples 11.7 Summary Problems References for Additional Reading 12 Plane Elasticity 12.1 Introduction 12.2 Governing Equations 12.3 Virtual Work and Weak Formulations 12.4 Finite Element Model 12.5 Elimination of Shear Locking in Linear Elements 12.6 Numerical Examples 12.7 Summary Problems References for Additional Reading 13 3-D Finite Element Analysis 13.1 Introduction 13.2 Heat Transfer 13.3 Flows of Viscous Incompressible Fluids 13.4 Elasticity 13.5 Element Interpolation Functions and Numerical Integration 13.6 Numerical Examples 13.7 Summary Problems References for Additional Reading Index
1 General Introduction 1.1 Background 1.2 Mathematical Model Development 1.3 Numerical Simulations 1.4 The Finite Element Method 1.5 The Present Study 1.6 Summary Problems References for Additional Reading 2 Mathematical Preliminaries and Classical Variational Methods 2.1 General Introduction 2.2 Some Mathematical Concepts and Formulae 2.3 Energy and Virtual Work Principles 2.4 Integral Formulations of Differential Equations 2.5 Variational Methods 2.6 Equations of Continuum Mechanics 2.7 Summary Problems References for Additional Reading 3 1-D Finite Element Models of Second-Order Differential Equations 3.1 Introduction 3.2 Finite Element Analysis Steps 3.3 Finite Element Models of Discrete Systems 3.4 Finite Element Models of Continuous Systems 3.5 Axisymmetric Problems 3.6 Errors in Finite Element Analysis 3.7 Summary Problems References for Additional Reading 4 Applications to 1-D Heat Transfer and Fluid and Solid Mechanics Problems 4.1 Preliminary Comments 4.2 Heat Transfer 4.3 Fluid Mechanics 4.4 Solid and Structural Mechanics 4.5 Summary Problems References 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 Elements 5.4 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 Structures 6.4 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 Analysis 7.5 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 Problems References 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 Problems 9.6 Summary Problems References for Additional Reading 10 2-D Interpolation Functions, Numerical Integration, and Computer Implementation 10.1 Introduction 10.2 2-D Element Library 10.3 Numerical Integration 10.4 Modeling Considerations 10.5 Computer Implementation and FEM2D 10.6 Summary Problems References for Additional Reading 11 Flows of Viscous Incompressible Fluids 11.1 Introduction 11.2 Governing Equations 11.3 Velocity-Pressure Formulation 11.4 Penalty Function Formulation 11.5 Computational Aspects 11.6 Numerical Examples 11.7 Summary Problems References for Additional Reading 12 Plane Elasticity 12.1 Introduction 12.2 Governing Equations 12.3 Virtual Work and Weak Formulations 12.4 Finite Element Model 12.5 Elimination of Shear Locking in Linear Elements 12.6 Numerical Examples 12.7 Summary Problems References for Additional Reading 13 3-D Finite Element Analysis 13.1 Introduction 13.2 Heat Transfer 13.3 Flows of Viscous Incompressible Fluids 13.4 Elasticity 13.5 Element Interpolation Functions and Numerical Integration 13.6 Numerical Examples 13.7 Summary Problems References for Additional Reading Index
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