| Description |
1 online resource (xxii, 682 pages) : illustrations |
| Contents |
Part 1. Linear Static Analysis -- 1. Fundamental Concepts; A Simple One-Dimensional Boundary-Value Problem -- 1.1. Introductory Remarks and Preliminaries -- 1.2. Strong, or Classical, Form of the Problem -- 1.3. Weak, or Variational, Form of the Problem -- 1.4. Eqivalence of Strong and Weak Forms; Natural Boundary Conditions -- 1.5. Galerkin's Approximation Method -- 1.6. Matrix Equations; Stiffness Matrix K -- 1.7. Examples: 1 and 2 Degrees of Freedom -- 1.8. Piecewise Linear Finite Element Space -- 1.9. Properties of K -- 1.10. Mathematical Analysis -- 1.11. Interlude: Gauss Elimination; Hand-calculation Version -- 1.12. The Element Point of View -- 1.13. Element Stiffness Matrix and Force Vector -- 1.14. Assembly of Global Stiffness Matrix and Force Vector; LM Array -- 1.15. Explicit Computation of Element Stiffness Matrix and Force Vector -- 1.16. Exercise: Bernoulli-Euler Beam Theory and Hermite Cubics -- Appendix 1.I. An Elementary Discussion of Continuity, Differentiability, and Smoothness -- 2. Formulation of Two- and Three-Dimensional Boundary-Value Problems -- 2.1. Introductory Remarks -- 2.2. Preliminaries -- 2.3. Classical Linear Heat Conduction: Strong and Weak Forms; Equivalence -- 2.4. Heat Conduction: Galerkin Formulation; Symmetry and Positive-definiteness of K -- 2.5. Heat Conduction: Element Stiffness Matrix and Force Vector -- 2.6. Heat Conduction: Data Processing Arrays ID, IEN, and LM -- 2.7. Classical Linear Elastostatics: Strong and Weak Forms; Equivalence -- 2.8. Elastostatics: Galerkin Formulation, Symmetry, and Positive-definiteness of K -- 2.9. Elastostatics: Element Stiffness Matrix and Force Vector -- 2.10. Elastostatics: Data Processing Arrays ID, IEN, and LM -- 2.11. Summary of Important Equations for Problems Considered in Chapters 1 and 2 -- 2.12. Axisymmetric Formulations and Additional Exercises -- 3. Isoparametric Elements and Elementary Programming Concepts -- 3.1. Preliminary Concepts -- 3.2. Bilinear Quadrilateral Element -- 3.3. Isoparametric Elements -- 3.4. Linear Triangular Element; An Example of "Degeneration" -- 3.5. Trilinear Hexahedral Element -- 3.6. Higher-order Elements; Lagrange Polynomials -- 3.7. Elements with Variable Numbers of Nodes -- 3.8. Numerical Integration; Gaussian Quadrature -- 3.9. Derivatives of Shape Functions and Shape Function Subroutines -- 3.10. Element Stiffness Formulation -- 3.11. Additional Exercises -- Appendix 3.I. Triangular and Tetrahedral Elements -- Appendix 3. II. Methodology for Developing Special Shape Functions with Application to Singularities -- 4. Mixed and Penalty Methods, Reduced and Selective Integration, and Sundry Variational Crimes -- 4.1. "Best Approximation" and Error Estimates: Why the standard FEM usually works and why sometimes it does not -- 4.2. Incompressible Elasticity and Stokes Flow -- 4.2.1. Prelude to Mixed and Penalty Methods -- 4.3. A Mixed Formulation of Compressible Elasticity Capable of Representing the Incompressible Limit -- 4.3.1. Strong Form -- 4.3.2. Weak Form -- 4.3.3. Galerkin Formulation -- 4.3.4. Matrix Problem -- 4.3.5. Definition of Element Arrays -- 4.3.6. Illustration of a Fundamental Difficulty -- 4.3.7. Constraint Counts -- 4.3.8. Discontinuous Pressure Elements -- 4.3.9. Continuous Pressure Elements -- 4.4. Penalty Formulation: Reduced and Selective Integration Techniques; Equivalence with Mixed Methods -- 4.4.1. Pressure Smoothing -- 4.5. An Extension of Reduced and Selective Integration Techniques -- 4.5.1. Axisymmetry and Anisotropy: Prelude to Nonlinear Analysis -- 4.5.2. Strain Projection: The B-approach -- 4.6. The Patch Test; Rank Deficiency -- 4.7. Nonconforming Elements -- 4.8. Hourglass Stiffness -- 4.9. Additional Exercises and Projects -- Appendix 4.I. Mathematical Preliminaries -- 4.I.1. Basic Properties of Linear Spaces -- 4.I.2. Sobolev Norms -- 4.I.3. Approximation Properties of Finite Element Spaces in Sobolev Norms -- 4.I.4. Hypotheses on a(., .) -- Appendix 4. II. Advanced Topics in the Theory of Mixed and Penalty Methods: Pressure Modes and Error Estimates / David S. Malkus -- 4. II.1. Pressure Modes, Spurious and Otherwise -- 4. II.2. Existence and Uniqueness of Solutions in the Presence of Modes -- 4. II.3. Two Sides of Pressure Modes -- 4. II.4. Pressure Modes in the Penalty Formulation -- 4. II.5. The Big Picture -- 4. II.6. Error Estimates and Pressure Smoothing -- 5. The C[superscript 0]-Approach to Plates and Beams -- 5.1. Introduction -- 5.2. Reissner-Mindlin Plate Theory -- 5.2.1. Main Assumptions -- 5.2.2. Constitutive Equation -- 5.2.3. Strain-displacement Equations -- 5.2.4. Summary of Plate Theory Notations -- 5.2.5. Variational Equation -- 5.2.6. Strong Form -- 5.2.7. Weak Form -- 5.2.8. Matrix Formulation -- 5.2.9. Finite Element Stiffness Matrix and Load Vector -- 5.3. Plate-bending Elements -- 5.3.1. Some Convergence Criteria -- 5.3.2. Shear Constraints and Locking -- 5.3.3. Boundary Conditions -- 5.3.4. Reduced and Selective Integration Lagrange Plate Elements -- 5.3.5. Equivalence with Mixed Methods -- 5.3.6. Rank Deficiency -- 5.3.7. The Heterosis Element -- 5.3.8. T1: A Correct-rank, Four-node Bilinear Element -- 5.3.9. The Linear Triangle -- 5.3.10. The Discrete Kirchhoff Approach -- 5.3.11. Discussion of Some Quadrilateral Bending Elements -- 5.4. Beams and Frames -- 5.4.1. Main Assumptions -- 5.4.2. Constitutive Equation -- 5.4.3. Strain-displacement Equations -- 5.4.4. Definitions of Quantities Appearing in the Theory -- 5.4.5. Variational Equation -- 5.4.6. Strong Form -- 5.4.7. Weak Form -- 5.4.8. Matrix Formulation of the Variational Equation -- 5.4.9. Finite Element Stiffness Matrix and Load Vector -- 5.4.10. Representation of Stiffness and Load in Global Coordinates -- 5.5. Reduced Integration Beam Elements -- The C[superscript 0]-Approach to Curved Structural Elements -- 6.1. Introduction -- 6.2. Doubly Curved Shells in Three Dimensions -- 6.2.1. Geometry -- 6.2.2. Lamina Coordinate Systems -- 6.2.3. Fiber Coordinate Systems -- 6.2.4. Kinematics -- 6.2.5. Reduced Constitutive Equation -- 6.2.6. Strain-displacement Matrix -- 6.2.7. Stiffness Matrix -- 6.2.8. External Force Vector -- 6.2.9. Fiber Numerical Integration -- 6.2.10. Stress Resultants -- 6.2.11. Shell Elements -- 6.2.12. Some References to the Recent Literature -- 6.2.13. Simplifications: Shells as an Assembly of Flat Elements -- 6.3. Shells of Revolution; Rings and Tubes in Two Dimensions -- 6.3.1. Geometric and Kinematic Descriptions -- 6.3.2. Reduced Constitutive Equations -- 6.3.3. Strain-displacement Matrix -- 6.3.4. Stiffness Matrix -- 6.3.5. External Force Vector -- 6.3.6. Stress Resultants -- 6.3.7. Boundary Conditions -- 6.3.8. Shell Elements -- Part 2. Linear Dynamic Analysis -- 7. Formulation of Parabolic, Hyperbolic, and Elliptic-Elgenvalue Problems -- 7.1. Parabolic Case: Heat Equation -- 7.2. Hyperbolic Case: Elastodynamics and Structural Dynamics -- 7.3. Eigenvalue Problems: Frequency Analysis and Buckling -- 7.3.1. Standard Error Estimates -- 7.3.2. Alternative Definitions of the Mass Matrix; Lumped and Higher-order Mass -- 7.3.3. Estimation of Eigenvalues -- Appendix 7.I. Error Estimates for Semidiscrete Galerkin Approximations -- 8. Algorithms for Parabolic Problems -- 8.1. One-step Algorithms for the Semidiscrete Heat Equation: Generalized Trapezoidal Method -- 8.2. Analysis of the Generalized Trapezoidal Method -- 8.2.1. Modal Reduction to SDOF Form -- 8.2.2. Stability -- 8.2.3. Convergence -- 8.2.4. An Alternative Approach to Stability: The Energy Method -- 8.2.5. Additional Exercises -- 8.3. Elementary Finite Difference Equations for the One-dimensional Heat Equation; the von Neumann Method of Stability Analysis -- 8.4. Element-by-element (EBE) Implicit Methods -- 8.5. Modal Analysis -- 9. Algorithms for Hyperbolic and Parabolic-Hyperbolic Problems -- 9.1. One-step Algorithms for the Semidiscrete Equation of Motion -- 9.1.1. The Newmark Method -- 9.1.2. Analysis -- 9.1.3 |
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Measures of Accuracy: Numerical Dissipation and Dispersion -- 9.1.4. Matched Methods -- 9.1.5. Additional Exercises -- 9.2. Summary of Time-step Estimates for Some Simple Finite Elements |
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9.3. Linear Multistep (LMS) Methods -- 9.3.1. LMS Methods for First-order Equations -- 9.3.2. LMS Methods for Second-order Equations -- 9.3.3. Survey of Some Commonly Used Algorithms in Structural Dynamics -- 9.3.4. Some Recently Developed Algorithms for Structural Dynamics -- 9.4. Algorithms Based upon Operator Splitting and Mesh Partitions -- 9.4.1. Stability via the Energy Method -- 9.4.2. Predictor/Multicorrector Algorithms -- 9.5. Mass Matrices for Shell Elements -- 10. Solution Techniques for Eigenvalue Problems -- 10.1. The Generalized Eigenproblem -- 10.2. Static Condensation -- 10.3. Discrete Rayleigh-Ritz Reduction -- 10.4. Irons-Guyan Reduction -- 10.5. Subspace Iteration -- 10.5.1. Spectrum Slicing -- 10.5.2. Inverse Iteration -- 10.6. The Lanczos Algorithm for Solution of Large Generalized Eigenproblems / Bahram Nour-Omid -- 10.6.1. Introduction -- 10.6.2. Spectral Transformation -- 10.6.3. Conditions for Real Eigenvalues -- 10.6.4. The Rayleigh-Ritz Approximation -- 10.6.5. Derivation of the Lanczos Algorithm -- 10.6.6. Reduction to Tridiagonal Form -- 10.6.7. Convergence Criterion for Eigenvalues -- 10.6.8. Loss of Orthogonality -- 10.6.9. Restoring Orthogonality -- 11. Dlearn -- A Linear Static and Dynamic Finite Element Analysis Program / Thomas J.R. Hughes, Robert M. Ferencz and Arthur M. Raefsky -- 11.1. Introduction -- 11.2. Description of Coding Techniques Used in DLEARN -- 11.2.1. Compacted Column Storage Scheme -- 11.2.2. Crout Elimination -- 11.2.3. Dynamic Storage Allocation -- 11.3. Program Structure -- 11.3.1. Global Control -- 11.3.2. Initialization Phase -- 11.3.3. Solution Phase -- 11.4. Adding an Element to DLEARN -- 11.5. DLEARN User's Manual -- 11.5.1. Remarks for the New User -- 11.5.2. Input Instructions -- 11.5.3. Examples -- 1. Planar Truss -- 2. Static Analysis of a Plane Strain Cantilever Beam -- 3. Dynamic Analysis of a Plane Strain Cantilever Beam -- 4. Implicit-explicit Dynamic Analysis of a Rod -- 11.5.4. Subroutine Index for Program Listing |
| Summary |
Directed toward students without in-depth mathematical training, this text cultivates comprehensive skills in linear static and dynamic finite element methodology. Included are a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories derived directly from three-dimensional elasticity theory. Solution guide available upon request |
| Notes |
Reprint. Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1987. The author has corrected minor errors in the text and deleted the sections of Chapters 10 and 11 that are no longer necessary |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Finite element method.
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Boundary value problems.
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TECHNOLOGY & ENGINEERING -- Civil -- General.
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TECHNOLOGY & ENGINEERING -- Engineering (General)
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TECHNOLOGY & ENGINEERING -- Reference.
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Boundary value problems
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Finite element method
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Método dos elementos finitos.
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Diferenças finitas.
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| Form |
Electronic book
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| LC no. |
00038414 |
| ISBN |
9780486135021 |
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0486135020 |
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9781621985884 |
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1621985881 |
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