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Computational Continuum Mechanics, 3rd Edition

Book Description

An updated and expanded edition of the popular guide to basic continuum mechanics and computational techniques  

This updated third edition of the popular reference covers state-of-the-art computational techniques for basic continuum mechanics modeling of both small and large deformations. Approaches to developing complex models are described in detail, and numerous examples are presented demonstrating how computational algorithms can be developed using basic continuum mechanics approaches. 

The integration of geometry and analysis for the study of the motion and behaviors of materials under varying conditions is an increasingly popular approach in continuum mechanics, and absolute nodal coordinate formulation (ANCF) is rapidly emerging as the best way to achieve that integration. At the same time, simulation software is undergoing significant changes which will lead to the seamless fusion of CAD, finite element, and multibody system computer codes in one computational environment. Computational Continuum Mechanics, Third Edition is the only book to provide in-depth coverage of the formulations required to achieve this integration.

  • Provides detailed coverage of the absolute nodal coordinate formulation (ANCF), a popular new approach to the integration of geometry and analysis
  • Provides detailed coverage of the floating frame of reference (FFR) formulation, a popular well-established approach for solving small deformation problems
  • Supplies numerous examples of how complex models have been developed to solve an array of real-world problems
  • Covers modeling of both small and large deformations in detail
  • Demonstrates how to develop computational algorithms using basic continuum mechanics approaches 

Computational Continuum Mechanics, Third Edition is designed to function equally well as a text for advanced undergraduates and first-year graduate students and as a working reference for researchers, practicing engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.

Table of Contents

  1. COVER
  2. TITLE PAGE
  3. COPYRIGHT
  4. PREFACE
  5. CHAPTER 1: INTRODUCTION
    1. 1.1 MATRICES
    2. 1.2 VECTORS
    3. 1.3 SUMMATION CONVENTION
    4. 1.4 CARTESIAN TENSORS
    5. 1.5 POLAR DECOMPOSITION THEOREM
    6. 1.6 D'ALEMBERT'S PRINCIPLE
    7. 1.7 VIRTUAL WORK PRINCIPLE
    8. 1.8 APPROXIMATION METHODS
    9. 1.9 DISCRETE EQUATIONS
    10. 1.10 MOMENTUM, WORK, AND ENERGY
    11. 1.11 PARAMETER CHANGE AND COORDINATE TRANSFORMATION
    12. PROBLEMS
  6. CHAPTER 2: KINEMATICS
    1. 2.1 MOTION DESCRIPTION
    2. 2.2 STRAIN COMPONENTS
    3. 2.3 OTHER DEFORMATION MEASURES
    4. 2.4 DECOMPOSITION OF DISPLACEMENT
    5. 2.5 VELOCITY AND ACCELERATION
    6. 2.6 COORDINATE TRANSFORMATION
    7. 2.7 OBJECTIVITY
    8. 2.8 CHANGE OF VOLUME AND AREA
    9. 2.9 CONTINUITY EQUATION
    10. 2.10 REYNOLDS' TRANSPORT THEOREM
    11. 2.11 EXAMPLES OF DEFORMATION
    12. 2.12 GEOMETRY CONCEPTS
    13. PROBLEMS
  7. CHAPTER 3: FORCES AND STRESSES
    1. 3.1 EQUILIBRIUM OF FORCES
    2. 3.2 TRANSFORMATION OF STRESSES
    3. 3.3 EQUATIONS OF EQUILIBRIUM
    4. 3.4 SYMMETRY OF THE CAUCHY STRESS TENSOR
    5. 3.5 VIRTUAL WORK OF THE FORCES
    6. 3.6 DEVIATORIC STRESSES
    7. 3.7 STRESS OBJECTIVITY
    8. 3.8 ENERGY BALANCE
    9. PROBLEMS
  8. CHAPTER 4: CONSTITUTIVE EQUATIONS
    1. 4.1 GENERALIZED HOOKE'S LAW
    2. 4.2 ANISOTROPIC LINEARLY ELASTIC MATERIALS
    3. 4.3 MATERIAL SYMMETRY
    4. 4.4 HOMOGENEOUS ISOTROPIC MATERIAL
    5. 4.5 PRINCIPAL STRAIN INVARIANTS
    6. 4.6 SPECIAL MATERIAL MODELS FOR LARGE DEFORMATIONS
    7. 4.7 LINEAR VISCOELASTICITY
    8. 4.8 NONLINEAR VISCOELASTICITY
    9. 4.9 A SIMPLE VISCOELASTIC MODEL FOR ISOTROPIC MATERIALS
    10. 4.10 FLUID CONSTITUTIVE EQUATIONS
    11. 4.11 NAVIER–STOKES EQUATIONS
    12. PROBLEMS
  9. CHAPTER 5: FINITE ELEMENT FORMULATION: LARGE-DEFORMATION, LARGE-ROTATION PROBLEM
    1. 5.1 DISPLACEMENT FIELD
    2. 5.2 ELEMENT CONNECTIVITY
    3. 5.3 INERTIA AND ELASTIC FORCES
    4. 5.4 EQUATIONS OF MOTION
    5. 5.5 NUMERICAL EVALUATION OF THE ELASTIC FORCES
    6. 5.6 FINITE ELEMENTS AND GEOMETRY
    7. 5.7 TWO-DIMENSIONAL EULER–BERNOULLI BEAM ELEMENT
    8. 5.8 TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM ELEMENT
    9. 5.9 THREE-DIMENSIONAL CABLE ELEMENT
    10. 5.10 THREE-DIMENSIONAL BEAM ELEMENT
    11. 5.11 THIN-PLATE ELEMENT
    12. 5.12 HIGHER-ORDER PLATE ELEMENT
    13. 5.13 BRICK ELEMENT
    14. 5.14 ELEMENT PERFORMANCE
    15. 5.15 OTHER FINITE ELEMENT FORMULATIONS
    16. 5.16 UPDATED LAGRANGIAN AND EULERIAN FORMULATIONS
    17. 5.17 CONCLUDING REMARKS
    18. PROBLEMS
  10. CHAPTER 6: FINITE ELEMENT FORMULATION: SMALL-DEFORMATION, LARGE-ROTATION PROBLEM
    1. 6.1 BACKGROUND
    2. 6.2 ROTATION AND ANGULAR VELOCITY
    3. 6.3 FLOATING FRAME OF REFERENCE (FFR)
    4. 6.4 INTERMEDIATE ELEMENT COORDINATE SYSTEM
    5. 6.5 CONNECTIVITY AND REFERENCE CONDITIONS
    6. 6.6 KINEMATIC EQUATIONS
    7. 6.7 FORMULATION OF THE INERTIA FORCES
    8. 6.8 ELASTIC FORCES
    9. 6.9 EQUATIONS OF MOTION
    10. 6.10 COORDINATE REDUCTION
    11. 6.11 INTEGRATION OF FINITE ELEMENT AND MULTIBODY SYSTEM ALGORITHMS
    12. PROBLEMS
  11. CHAPTER 7: COMPUTATIONAL GEOMETRY AND FINITE ELEMENT ANALYSIS
    1. 7.1 GEOMETRY AND FINITE ELEMENT METHOD
    2. 7.2 ANCF GEOMETRY
    3. 7.3 BEZIER GEOMETRY
    4. 7.4 B-SPLINE CURVE REPRESENTATION
    5. 7.5 CONVERSION OF B-SPLINE GEOMETRY TO ANCF GEOMETRY
    6. 7.6 ANCF AND B-SPLINE SURFACES
    7. 7.7 STRUCTURAL AND NONSTRUCTURAL DISCONTINUITIES
    8. PROBLEMS
  12. CHAPTER 8: PLASTICITY FORMULATIONS
    1. 8.1 ONE-DIMENSIONAL PROBLEM
    2. 8.2 LOADING AND UNLOADING CONDITIONS
    3. 8.3 SOLUTION OF THE PLASTICITY EQUATIONS
    4. 8.4 GENERALIZATION OF THE PLASTICITY THEORY: SMALL STRAINS
    5. 8.5 J2 FLOW THEORY WITH ISOTROPIC/KINEMATIC HARDENING
    6. 8.6 NONLINEAR FORMULATION FOR HYPERELASTIC–PLASTIC MATERIALS
    7. 8.7 HYPERELASTIC–PLASTIC J2 FLOW THEORY
    8. PROBLEMS
  13. REFERENCES
  14. INDEX
  15. End User License Agreement