Finite Element Method for Engineers, 4th revised edition [235909]

£100.00

A useful balance of theory, applications, and real-world examples, "The Finite Element Method for Engineers, Fourth Edition" presents a clear, easy-to-understand explanation of finite element fundamentals, and enables readers to use the method in research and in solving practical, real-life problems. It develops the basic finite element method mathematical formulation, beginning with physical considerations, proceeding to the well-established variation approach, and placing a strong emphasis on the versatile method of weighted residuals, which has shown itself to be important in nonstructural applications. The authors demonstrate the tremendous power of the finite element method to solve problems that classical methods cannot handle, including elasticity problems, general field problems, heat transfer problems, and fluid mechanics problems. They supply practical information on boundary conditions and mesh generation, and they offer a fresh perspective on finite element analysis with an overview of the current state of finite element optimal design. Supplemented with numerous real-world problems and examples taken directly from the authors' experience in industry and research, "The Finite Element Method for Engineers, Fourth Edition" gives readers the real insight needed to apply the method to challenging problems and to reason out solutions that cannot be found in any textbook.

Contents: PREFACE. PART I. 1. Meet the Finite Element Method. 1.1 What Is the Finite Element Method? 1.2 How the Finite Element Method Works. 1.3 A Brief History of the Method. 1.4 Range of Applications. 1.5 Commercial Finite Element Software. 1.6 The Future of the Finite Element Method. References. 2. The Direct Approach: A Physical Interpretation. 2.1 Introduction. 2.2 Defining Elements and Their Properties. 2.2.1 Linear Spring Systems. 2.2.2 Flow Systems. 2.2.3 Simple Elements from Structural Mechanics. 2.2.4 Coordinate Transformations. 2.3 Assembling the Parts. 2.3.1 Assembly Rules Derived from an Example. 2.3.2 General Assembly Procedure. 2.3.3 Features of the Assembled Matrix. 2.3.4 Introducing Boundary Conditions. 2.4 Solver Technology. 2.4.1 Linear Direct Solvers. 2.4.2 Iterative Solvers. 2.4.3 Eigensolvers. 2.4.4 Nonlinear Equation Solvers. 2.5 Closure. References. Problems. 3. The Mathematical Approach: A Variational Interpretation. 3.1 Introduction. 3.2 Continuum Problems. 3.2.1 Introduction. 3.2.2 Problem Statement. 3.2.3 Classification of Differential Equations. 3.3 Some Methods for Solving Continuum Problems. 3.3.1 An Overview. 3.3.2 The Variational Approach. 3.3.3 The Ritz Method. 3.4 The Finite Element Method. 3.4.1 Relation to the Ritz Method. 3.4.2 Generalizing the Definition of an Element. 3.4.3 Example of a Piecewise Approximation. 3.4.4 Element Equations from a Variational Principle. 3.4.5 Requirements for Interpolation Functions. 3.4.6 Domain Discretization. 3.4.7 Example of a Complete Finite Element Solution. 3.5 Closure. References. Problems. 4. The Mathematical Approach: A Generalized Interpretation. 4.1 Introduction. 4.2 Deriving Finite Element Equations from the Method of Weighted Residuals. 4.2.1 Example: One--Dimensional Poisson Equation. 4.2.2 Example: Two--Dimensional Heat Conduction. 4.2.3 Example: Time--Dependent Heat Conduction. 4.3 Closure. References. Problems. 5. Elements and Interpolation Functions. 5.1 Introduction. 5.2 Basic Element Shapes. 5.3 Terminology and Preliminary Considerations. 5.3.1 Types of Notes. 5.3.2 Degrees of Freedom. 5.3.3 Interpolation Functions--Polynomials. 5.4 Generalized Coordinates and the Order of the Polynomial. 5.4.1 Generalized Coordinates. 5.4.2 Geometric Isotropy. 5.4.3 Deriving Interpolation Functions. 5.5 Natural Coordinates. 5.5.1 Natural Coordinates in One Dimension. 5.5.2 Natural Coordinates in Two Dimensions. 5.5.3 Natural Coordinates in Three Dimensions. 5.6 Interpolation Concepts in One Dimension. 5.6.1 Lagrange Polynomials. 5.6.2 Hermite Polynomials. 5.7 Internal Nodes--Condensation /Substructuring. 5.8 Two--Dimensional Elements. 5.8.1 Elements for C 0 Problems. 5.8.2 Elements for C 1 Problems. 5.9 Three--Dimensional Elements. 5.9.1 Elements forC 0 Problems. 5.9.2 Elements for C 1 Problems. 5.10 Isoparametric Elements for C 0 Problems. 5.10.1 Coordinate Transformation. 5.10.2 Evaluation of Element Matrices. 5.10.3 Example of Isoparametric Element Matrix Evaluation. 5.11 Numerical Integration. 5.11.1 Newton--Cotes. 5.11.2 Gauss--Legendre. 5.11.3 Numerical Example for Element Matrix Evaluation. 5.12 Closure. References. Problems. PART II. 6. Elasticity Problems. 6.1 Introduction. 6.2 General Formulation for Three--Dimensional Problems. 6.2.1 Problem Statement. 6.2.2 The Variational Method. 6.2.3 The Galerkin Method. 6.2.4 The System Equations. 6.3 Application to Plane Stress and Plane Strain. 6.3.1 Displacement Model for a Triangular Element. 6.3.2 Element Stiffness Matrix for a Triangle. 6.3.3 Element Force Vectors for a Triangle. 6.4 Application to Axisymmetric Stress Analysis. 6.4.1 Displacement Model for Triangular Toroid. 6.4.2 Element Stiffness Matrix for Triangular Toroid. 6.4.3 Element Force Vectors for Triangular Toroid. 6.5 Application to Plate--Bending Problems. 6.5.1 Requirements for the Displacement Interpolation Functions. 6.5.2 Rectangular Plate--Bending Elements. 6.6 Three--Dimensional Problems. 6.6.1 Introduction. 6.6.2 Formulation for the Linear Tetrahedral Element. 6.6.3 Higher--Order Elements. 6.7 Introduction to Structural Dynamics. 6.7.1 Formulation of Equations. 6.7.2 Free Undamped Vibrations. 6.7.3 Finding Transient Motion via Mode Superposition. 6.7.4 Finding Transient Motion via Recurrence Relations. 6.8 Closure. References. Problems. 7. General Field Problems. 7.1 Introduction. 7.2 Equilibrium Problems. 7.2.1 Quasi--Harmonic Equations. 7.2.2 Boundary Conditions. 7.2.3 Variational Principle. 7.2.4 Element Equations. 7.2.5 Element Equations in Two Dimensions. 7.3 Eigenvalue Problems. 7.3.1 Helmholtz Equations. 7.3.2 Variational Principle. 7.3.3 Element Equations. 7.3.4 Examples. 7.3.5 Sample Problem. 7.4 Propagation Problems. 7.4.1 General Time--Dependent Field Problems. 7.4.2 Finite Element Equations. 7.4.3 Element Equations in One Space Dimension. 7.5 Solving the Discretized Time--Dependent Equations. 7.5.1 Solution Methods for First--Order Equations. 7.5.2 Finding TransientResponse viaModeSuperposition. 7.5.3 Finding Transient Response via Recurrence Relations. 7.5.4 Oscillation and Stability of Transient Response. 7.5.5 Algorithm Order. 7.5.6 Sample Problem. 7.6 Closure. References. Problems. 8. Heat Transfer Problems. 8.1 Introduction. 8.2 Conduction. 8.2.1 Problem Statement. 8.2.2 Finite Element Formulation. 8.2.3 Element Equations. 8.2.4 Linear Steady--State and Transient Solutions. 8.2.5 Nonlinear Steady--State Solutions. 8.2.6 Nonlinear Transient Solutions. 8.3 Conduction with Surface Radiation. 8.3.1 Problem Statement. 8.3.2 Element Equations with Radiation. 8.3.3 Steady--State Solutions. 8.3.4 Transient Solutions. 8.4 Convective--Diffusion Equation 8.4.1 Problem Statement. 8.4.2 Finite Element Formulation. 8.4.3 One--Dimensional Problem. 8.4.4 Two--Dimensional Solutions. 8.5 Free and Forced Convection. 8.5.1 Problem Statement. 8.5.2 Finite Element Formulation. 8.5.3 Solution Techniques. 8.5.4 Free--Convection Example. 8.5.5 Forced Convection. 8.6 Closure. References. Problems. 9. Fluid Mechanics Problems. 9.1 Introduction. 9.2 Inviscid Incompressible Flow. 9.2.1 Problem Statement. 9.2.2 Finite Element Formulation. 9.2.3 Velocity Component Smoothing. 9.2.4 Example with Unstructured Mesh. 9.2.5 The Kutta Condition. 9.3 Viscous Incompressible Flow without Inertia. 9.3.1 Problem Statement. 9.3.2 Stream Function Formulation. 9.3.3 Velocity and Pressure Formulation. 9.4 Viscous Incompressible Flow with Inertia. 9.4.1 Mixed Velocity and Pressure Formulation. 9.4.2 Penalty Function Formulation. 9.4.3 Equal--Order Velocity and Pressure Formulation. 9.5 Compressible Flow. 9.5.1 Problem Statement. 9.5.2 Low--Speed Flow with Variable Density. 9.5.3 High--Speed Flow. 9.6 Closure. References. Problems. 10. Boundary Conditions, Mesh Generation, and Other Practical Considerations. 10.1 Introduction. 10.2 Physical Singularities. 10.3 Benchmark Problems. 10.4 Symmetry. 10.4.1 Definition of Types of Symmetry. 10.4.2 Antisymmetry. 10.4.3 A Complex Loading Example: Two Aces of Symmetry. 10.4.4 Axisymmetry and Rotational Symmetry. 10.4.5 The Torsion Problem. 10.4.6 Heat Transfer. 10.5 Dimensional Analysis. 10.6 Mesh Generation. 10.6.1 Mapped Meshing. 10.6.2 Free Meshing. 10.6.3 Mesh Topology Cleanup and Mesh Smoothing. 10.6.4 Mesh Refinement Methods. 10.6.5 Error Indicators. 10.6.6 Adaptive Remeshing, 535 10.6.7 p and h /p Methods, 537 10.7 Lumped Mass versus Consistent Mass, 541 10.8 Modeling Fasteners. 10.9 Connecting Rod Analysis. 10.10 Crankshaft and Flywheel Analysis. 10.11 Disc Brake Analysis. 10.11.1 An Automotive Brake Primer. 10.11.2 Rotor Analysis Using Rotational Symmetry. 10.11.3 Rotor Coning Analysis Using Axisymmetry. 10.11.4 Simulating Friction. 10.11.5 Hot Spotting. 10.12 Closure. References. Problems. 11. Finite Elements in Design. 11.1 Introduction. 11.2 Design Optimization. 11.2.1 The Optimization Problem. 11.2.2 Practical Aspects of Numerical Optimization. 11.2.3 Optimization Algorithms. 11.2.4 Software Packages for Optimal Design. 11.3 Finite Element--Based Optimal Design. 11.3.1 Design Parameterization. 11.3.2 Structural Optimization. 11.3.3 Topology Optimization. 11.3.4 Approximation Techniques. 11.3.5 Multidisciplinary Design Optimization. 11.4 Design Sensitivity Analysis. 11.4.1 Finite Difference Approximations. 11.4.2 Analytical Methods for Design Sensitivity Analysis. 11.4.3 Design Sensitivities for Eigenproblems. 11.4.4 Semianalytical Approach. 11.4.5 Other Advancements in Design Sensitivity Analysis. 11.5 Examples of Design Sensitivity Analysis. 11.5.1 Numerical Example: Steady--State Equilibrium Analysis. 11.5.2 Numerical Example: Eigenvalue and Eigenvector Analysis. 11.5.3 Sensitivity Analysis for Steady--State Conduction in a Solid. 11.5.4 Numerical Example for Steady--State Conduction in a Solid. 11.6 Case Study: Finite Element--Based Design. 11.7 Closure. References. Problems. Appendix A: Matrices. A.1 Definitions. A.2 Special Types of Square Matrices. A.3 Matrix Operations. A.4 Special Matrix Products. A.4.1 Product of a Square Matrix and a Column Matrix. A.4.2 Product of a Row Matrix and a Square Matrix. A.4.3 Product of a Row Matrix and a Column Matrix. A.4.4 Product of the Identity Matrix and Any Other Matrix. A.5 Matrix Transpose. A.6 Quadratic Forms. A.7 Matrix Inverse. A.8 Matrix Partitioning. A.9 The Calculus of Matrices. A.9.1 Differentiation of a Matrix. A.9.2 Integration of a Matrix. A.9.3 Differentiation of a Quadratic Functional. A.10 Norms. Appendix B: Variational Calculus. B.1 Introduction. B.2 Calculus--The Minima of a Function. B.2.1 Definitions. B.2.2 Functions of One Variable. B.2.3 Functions of Two or More Variables. B.3 Variational Calculus--The Minima of Functionals. B.3.1 Definitions. B.3.2 Functionals of One Variable. B.3.3 More General Functionals. References. Appendix C: Basic Equations from Linear Elasticity Theory. C.1 Introduction. C.2 Stress Components. C.3 Strain Components. C.4 Generalized Hooke's Law (Constitutive Equations). C.5 Static Equilibrium Equations. C.6 Compatibility Conditions. C.7 Differential Equations for Displacements. C.8 Minimum Potential Energy Principle. C.9 Plane Strain and Plane Stress. C.10 Thermal Effects. C.11 Thin--Plate Bending. References. Appendix D: Basic Equations from Fluid Mechanics. D.1 Introduction. D.2 Definitions and Concepts. D.3 Laws of Motion. D.3.1 Differential Continuity Equation. D.3.2 Differential Momentum Equation (Navier--Stokes Equations). D.3.3 Thermal Energy Equation. D.3.4 Conservative Form of Equations. D.3.5 Supplementary Equations. D.3.6 Problem Statement. D.4 Stream Functions and Vorticity. D.5 Potential Flow. D.6 Viscous Incompressible Flow. D.6.1 Primitive Variable Formulation. D.6.2 Vorticity and Stream Function Formulation. D.7 Boundary Layer Flow. References. Appendix E: Basic Equations from Heat Transfer. E.1 Introduction. E.2 Conduction. E.2.1 Heat Conduction Equation. E.2.2 Boundary Conditions. E.2.3 Nondimensional Parameters. E.3 Convection. E.3.1 Convection Equations. E.3.2 Boundary Conditions. E.3.3 Nondimensional Parameters. E.4 Radiation. E.4.1 Surface Radiation. E.4.2 Radiation Exchange between Surfaces. E.5 Heat Transfer Units. References. Index.

Finite Element Method for Engineers, 4th revised edition

Author:	Huebner, Kenneth H.\|Dewhirst, Donald
Date Published:	2001
Document Type:	Books
Format:	Hardback
ISBN:	0471370789
ISBN13:	9780471370789
Pages:	744
Publisher:	John Wiley & Sons

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