Introduction to the Finite Element Method 4E

Inbunden, Engelska, 2018

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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

Produktinformation

Utgivningsdatum2018-11-16
Mått210 x 261 x 45 mm
Vikt1 646 g
FormatInbunden
SpråkEngelska
Antal sidor816
Upplaga4
FörlagMcGraw-Hill Education
ISBN9781259861901

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Teknik: allmänt inom Naturvetenskap och teknik

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 Reading3 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 Reading5 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 Reading8 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 Reading11 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 Reading12 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