Introduction to the explicit finite element method for nonlinear transient dynamics

This text specifically addresses the explicit finite element method for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method as well as programing a code without extensively reading the more general finite element books.

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Bibliographic Details
Main Authors Wu, Shen R, Gu, Lei
Format eBook Book
LanguageEnglish
Published Hoboken, NJ WILEY 2012
Wiley
John Wiley & Sons, Incorporated
Wiley-Blackwell
John Wiley & Sons
Edition1
Subjects
Finite element method
Finite Mathematics
Mathematics
MATHEMATICS / Mathematical Analysis. bisacsh
Numerical analysis
Online AccessGet full text
ISBN1118382099
9781118382097
9780470572375
047057237X
9781118382011
1118382013
DOI10.1002/9781118382011

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Table of Contents:
  • Introduction to the explicit finite element method for nonlinear transient dynamics -- Contents -- Preface -- Part I: Fundamentals -- Chapter 1: Introduction -- Chapter 2: Framework of Explicit Finite Element Method for Nonlinear Transient Dynamics -- Part II: Element Technology -- Chapter 3: Four-Node Shell Element (Reissner–Mindlin Plate Theory) -- Chapter 4: Three-Node Shell Element (Reissner–Mindlin Plate Theory) -- Chapter 5: Eight-Node Solid Element -- Chapter 6: Two-Node Element -- Part III: Material Models -- Chapter 7: Material Model of Plasticity -- Chapter 8: Continuum Mechanics Model of Ductile Damage -- Chapter 9: Models of Nonlinear Materials -- Part IV: Contact and Constraint Conditions -- Chapter 10: Three-Dimensional Surface Contact -- Chapter 11: Numerical Procedures for Three-Dimensional Surface Contact -- Chapter 12: Kinematic Constraint Conditions -- References -- Index.
  • Intro -- INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS -- CONTENTS -- PREFACE -- PART I FUNDAMENTALS -- 1 INTRODUCTION -- 1.1 Era of Simulation and Computer Aided Engineering -- 1.1.1 A World of Simulation -- 1.1.2 Evolution of Explicit Finite Element Method -- 1.1.3 Computer Aided Engineering (CAE)-Opportunities and Challenges -- 1.2 Preliminaries -- 1.2.1 Notations -- 1.2.2 Constitutive Relations of Elasticity -- 2 FRAMEWORK OF EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS -- 2.1 Transient Structural Dynamics -- 2.2 Variational Principles for Transient Dynamics -- 2.2.1 Hamilton's Principle -- 2.2.2 Galerkin Method -- 2.3 Finite Element Equations and the Explicit Procedures -- 2.3.1 Discretization in Space by Finite Element -- 2.3.2 System of Semidiscretization -- 2.3.3 Discretization in Time by Finite Difference -- 2.3.4 Procedure of the Explicit Finite Element Method -- 2.4 Main Features of the Explicit Finite Element Method -- 2.4.1 Stability Condition and Time Step Size -- 2.4.2 Diagonal Mass Matrix -- 2.4.3 Corotational Stress -- 2.5 Assessment of Explicit Finite Element Method -- 2.5.1 About the Solution of the Elastodynamics -- 2.5.2 A Priori Error Estimate of Explicit Finite Element Method for Elastodynamics -- 2.5.3 About the Diagonal Mass Matrix -- PART II ELEMENT TECHNOLOGY -- 3 FOUR-NODE SHELL ELEMENT (REISSNER-MINDLIN PLATE THEORY) -- 3.1 Fundamentals of Plates and Shells -- 3.1.1 Characteristics of Thin-walled Structures -- 3.1.2 Resultant Equations -- 3.1.3 Applications to Linear Elasticity -- 3.1.4 Kirchhoff-Love Theory -- 3.1.5 Reissner-Mindlin Plate Theory -- 3.2 Linear Theory of R-M Plate -- 3.2.1 Helmholtz Decomposition for R-M Plate -- 3.2.2 Load Scaling for Static Problem of R-M Plate -- 3.2.3 Load Scaling and Mass Scaling for Dynamic Problem of R-M Plate
  • 4.4.1 Evaluations with Warped Mesh and Reduced Thickness -- 4.4.2 About the Locking-free Low Order Three-node R-M Plate Element -- 5 EIGHT-NODE SOLID ELEMENT -- 5.1 Trilinear Interpolation for the Eight-node Hexahedron Element -- 5.2 Locking Issues of the Eight-node Solid Element -- 5.3 One-point Reduced Integration and the Perturbed Hourglass Control -- 5.4 Assumed Strain Method and Selective/Reduced Integration -- 5.5 Assumed Deviatoric Strain -- 5.6 An Enhanced Assumed Strain Method -- 5.7 Taylor Expansion of Assumed Strain about the Element Center -- 5.8 Evaluation of Eight-node Solid Element -- 6 TWO-NODE ELEMENT -- 6.1 Truss and Rod Element -- 6.2 Timoshenko Beam Element -- 6.3 Spring Element -- 6.3.1 One Degree of Freedom Spring Element -- 6.3.2 Six Degrees of Freedom Spring Element -- 6.3.3 Three-node Spring Element -- 6.4 Spot Weld Element -- 6.4.1 Description of Spot Weld Separation -- 6.4.2 Failure Criterion -- 6.4.3 Finite Element Representation of Spot Weld -- PART III MATERIAL MODELS -- 7 MATERIAL MODEL OF PLASTICITY -- 7.1 Fundamentals of Plasticity -- 7.1.1 Tensile Test -- 7.1.2 Hardening -- 7.1.3 Yield Surface -- 7.1.4 Normality Condition -- 7.1.5 Strain Rate Effect/Viscoplasticity -- 7.2 Constitutive Equations -- 7.2.1 Relations between Stress Increments and Strain Increments -- 7.2.2 Constitutive Equations for Mises Criterion -- 7.2.3 Application to Kinematic Hardening -- 7.3 Software Implementation -- 7.3.1 Explicit Finite Element Procedure with Plasticity -- 7.3.2 Normal (Radial) Return Scheme -- 7.3.3 A Generalized Plane Stress Model -- 7.3.4 Stress Resultant Approach -- 7.4 Evaluation of Shell Elements with Plastic Deformation -- 8 CONTINUUM MECHANICS MODEL OF DUCTILE DAMAGE -- 8.1 Concept of Damage Mechanics -- 8.2 Gurson's Model -- 8.2.1 Damage Variables and Yield Function -- 8.2.2 Constitutive Equation and Damage Growth
  • 8.3 Chow's Isotropic Model of Continuum Damage Mechanics -- 8.3.1 Damage Effect Tensor -- 8.3.2 Yield Function and Constitutive Equation -- 8.3.3 Damage Growth -- 8.3.4 Application to Plates and Shells -- 8.3.5 Determination of Parameters -- 8.4 Chow's Anisotropic Model of Continuum Damage Mechanics -- 9 MODELS OF NONLINEAR MATERIALS -- 9.1 Viscoelasticity -- 9.1.1 Spring-Damper Model -- 9.1.2 A General Three-dimensional Viscoelasticity Model -- 9.2 Polymer and Engineering Plastics -- 9.2.1 Fundamental Mechanical Properties of Polymer Materials -- 9.2.2 A Temperature, Strain Rate, and Pressure Dependent Constitutive Relation -- 9.2.3 A Nonlinear Viscoelastic Model of Polymer Materials -- 9.3 Rubber -- 9.3.1 Mooney-Rivlin Model of Rubber Material -- 9.3.2 Blatz-Ko Model -- 9.3.3 Ogden Model -- 9.4 Foam -- 9.4.1 A Cap Model Combining Volumetric Plasticity and Pressure Dependent Deviatoric Plasticity -- 9.4.2 A Model Consisting of Polymer Skeleton and Air -- 9.4.3 A Phenomenological Uniaxial Model -- 9.4.4 Hysteresis Behavior -- 9.4.5 Dynamic Behavior -- 9.5 Honeycomb -- 9.5.1 Structure of Hexagonal Honeycomb -- 9.5.2 Critical Buckling Load -- 9.5.3 A Phenomenological Material Model of Honeycomb -- 9.5.4 Behavior of Honeycomb under Complex Loading Conditions -- 9.6 Laminated Glazing -- 9.6.1 Application of J-integral -- 9.6.2 Application of Anisotropic Damage Model -- 9.6.3 A Simplified Model with Shell Element for the Laminated Glass -- PART IV CONTACT AND CONSTRAINT CONDITIONS -- 10 THREE-DIMENSIONAL SURFACE CONTACT -- 10.1 Examples of Contact Problems -- 10.1.1 Uniformly Loaded String with a Flat Rigid Obstacle -- 10.1.2 Hertz Contact Problem -- 10.1.3 Elastic Impact of Two Balls -- 10.1.4 Impact of an Elastic Rod on the Flat Rigid Obstacle -- 10.1.5 Impact of a Vibrating String to the Flat Rigid Obstacle -- 10.2 Description of Contact Conditions
  • 10.2.1 Contact with a Smooth Rigid Obstacle-Signorini's Problem -- 10.2.2 Contact between Two Smooth Deformable Bodies -- 10.2.3 Coulomb's Law of Friction -- 10.2.4 Conditions for "In Contact" -- 10.2.5 Domain Contact -- 10.3 Variational Principle for the Dynamic Contact Problem -- 10.3.1 Variational Formulation for Frictionless Dynamic Contact Problem -- 10.3.2 Variational Formulation for Frictional Dynamic Contact Problem -- 10.3.3 Variational Formulation for Domain Contact -- 10.4 Penalty Method and the Regularization of Variational Inequality -- 10.4.1 Concept of Penalty Method -- 10.4.2 Penalty Method for Nonlinear Dynamic Contact Problem -- 10.4.3 Explicit Finite Element Procedure with Penalty Method for Dynamic Contact -- 11 NUMERICAL PROCEDURES FOR THREE-DIMENSIONAL SURFACE CONTACT -- 11.1 A Contact Algorithm with Slave Node Searching Master Segment -- 11.1.1 Global Search -- 11.1.2 Bucket Sorting Method -- 11.1.3 Local Search -- 11.1.4 Penalty Contact Force -- 11.2 A Contact Algorithm with Master Segment Searching Slave Node -- 11.2.1 Global Search with Bucket Sorting Based on Segment's Capture Box -- 11.2.2 Local Search with the Projection of Slave Point -- 11.3 Method of Contact Territory and Defense Node -- 11.3.1 Global Search with Bucket Sorting Based on Segment's Territory -- 11.3.2 Local Search in the Territory -- 11.3.3 Defense Node and Contact Force -- 11.4 Pinball Contact Algorithm -- 11.4.1 The Pinball Hierarchy -- 11.4.2 Penalty Contact Force -- 11.5 Edge (Line Segment) Contact -- 11.5.1 Search for Line Contact -- 11.5.2 Penalty Contact Force of Edge-to-Edge Contact -- 11.6 Evaluation of Contact Algorithm with Penalty Method -- 12 KINEMATIC CONSTRAINT CONDITIONS -- 12.1 Rigid Wall -- 12.1.1 A Stationary Flat Rigid Wall -- 12.1.2 A Moving Flat Rigid Wall -- 12.1.3 Rigid Wall with a Curved Surface -- 12.2 Rigid Body
  • 3.2.4 Relation between R-M Theory and K-L Theory -- 3.3 Interpolation for Four-node R-M Plate Element -- 3.3.1 Variational Equations for R-M Plate -- 3.3.2 Bilinear Interpolations -- 3.3.3 Shear Locking Issues of R-M Plate Element -- 3.4 Reduced Integration and Selective Reduced Integration -- 3.4.1 Reduced Integration -- 3.4.2 Selective Reduced Integration -- 3.4.3 Nonlinear Application of Selective Reduced Integration-Hughes-Liu Element -- 3.5 Perturbation Hourglass Control-Belytschko-Tsay Element -- 3.5.1 Concept of Hourglass Control -- 3.5.2 Four-node Belytschko-Tsay Shell Element-Perturbation Hourglass Control -- 3.5.3 Improvement of Belytschko-Tsay Shell Element -- 3.5.4 About Convergence of Element using Reduced Integration -- 3.6 Physical Hourglass Control-Belytschko-Leviathan (QPH) Element -- 3.6.1 Constant and Nonconstant Contributions -- 3.6.2 Projection of Shear Strain -- 3.6.3 Physical Hourglass Control by One-point Integration -- 3.6.4 Drill Projection -- 3.6.5 Improvement of B-L (QPH) Element -- 3.7 Shear Projection Method-Bathe-Dvorkin Element -- 3.7.1 Projection of Transverse Shear Strain -- 3.7.2 Convergence of B-D Element -- 3.8 Assessment of Four-node R-M Plate Element -- 3.8.1 Evaluations with Warped Mesh and Reduced Thickness -- 3.8.2 About the Locking-free Low Order Four-node R-M Plate Element -- 4 THREE-NODE SHELL ELEMENT (REISSNER-MINDLIN PLATE THEORY) -- 4.1 Fundamentals of a Three-node C0 Element -- 4.1.1 Transformation and Jacobian -- 4.1.2 Numerical Quadrature for In-plane Integration -- 4.1.3 Shear Locking with C0 Triangular Element -- 4.2 Decomposition Method for C0 Triangular Element with One-point Integration -- 4.2.1 A C0 Element with Decomposition of Deflection -- 4.2.2 A C0 Element with Decomposition of Rotations -- 4.3 Discrete Kirchhoff Triangular Element -- 4.4 Assessment of Three-node R-M Plate Element
  • 12.3 Explicit Finite Element Procedure with Constraint Conditions