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Introduction to the finite element method J. N. Reddy

By: Material type: TextTextPublication details: Chennai: McGraw-Hill Education, 2019.Edition: 4Description: 782pISBN:
  • 9789390385270
DDC classification:
  • 620.001 RED
Contents:
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
Summary: This authoritative and thoroughly revised, classic mechanical engineering textbook offers a broad-based overview and applications of the finite element method. This revision updates and expands the already large number of problems and worked-out examples and brings the technical coverage in line with current practices. Readers will get details on non-traditional applications in bioengineering, fluid, and thermal sciences, in addition to solid and structural mechanics. Written by a recognized mechanical engineering expert, An Introduction to the Finite Element Method, Fourth Edition, teaches, step-by-step, how to determine numerical solutions to equilibrium as well as time-dependent problems from fluid and thermal sciences and structural mechanics. Beginning with differential equations, the book presents a self-contained approach to the construction of weak forms, interpolation theory, finite element equations and their solution, and computer implementation. The author provides a solutions manual as well as computer programs that are available for download.
List(s) this item appears in: New Arrivals (June 2024) | NEW ARRIVALS
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Item type Current library Collection Call number Status Date due Barcode
Books Books IIITDM Kurnool MECHANICAL ENGINEERING Non-fiction 620.001 RED (Browse shelf(Opens below)) Available 0006743
Books Books IIITDM Kurnool MECHANICAL ENGINEERING Non-fiction 620.001 RED (Browse shelf(Opens below)) Available 0006744
Books Books IIITDM Kurnool MECHANICAL ENGINEERING Non-fiction 620.001 RED (Browse shelf(Opens below)) Available 0006745
Books Books IIITDM Kurnool MECHANICAL ENGINEERING Non-fiction 620.001 RED (Browse shelf(Opens below)) Available 0006746
Reference Reference IIITDM Kurnool SCIENCES Reference 620.001 RED (Browse shelf(Opens below)) Not For Loan 0005651
Books Books IIITDM Kurnool SCIENCES Non-fiction 620.001 RED (Browse shelf(Opens below)) Available 0005652
Books Books IIITDM Kurnool SCIENCES Non-fiction 620.001 RED (Browse shelf(Opens below)) Available 0005653

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

This authoritative and thoroughly revised, classic mechanical engineering textbook
offers a broad-based overview and applications of the finite element method. This
revision updates and expands the already large number of problems and worked-out
examples and brings the technical coverage in line with current practices. Readers will
get details on non-traditional applications in bioengineering, fluid, and thermal
sciences, in addition to solid and structural mechanics.
Written by a recognized mechanical engineering expert, An Introduction to the Finite
Element Method, Fourth Edition, teaches, step-by-step, how to determine numerical
solutions to equilibrium as well as time-dependent problems from fluid and thermal
sciences and structural mechanics. Beginning with differential equations, the book
presents a self-contained approach to the construction of weak forms, interpolation
theory, finite element equations and their solution, and computer implementation. The
author provides a solutions manual as well as computer programs that are available
for download.

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