{"product_id":"introduction-to-the-explicit-finite-element-method-for-nonlinear-transient-dynamics-hardback-9780470572375","title":"Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics (Hardback) 9780470572375","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntroduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eShen R. Wu (Author), Lei Gu (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470572375, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 12 October 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e352 pages\u003cbr\u003e24.1 x 16.5 x 2.3 cm, 0.626 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eA systematic introduction to the theories and formulations of the explicit finite element method\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAs numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. \u003ci\u003eIntroduction to the Explicit Finite\u003c\/i\u003e \u003ci\u003eElement Method for Nonlinear Transient Dynamics\u003c\/i\u003e is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element.\u003c\/p\u003e \u003cp\u003eThe authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections:\u003c\/p\u003e \u003cp\u003e• \u003cb\u003eFundamentals\u003c\/b\u003e explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory\u003c\/p\u003e \u003cp\u003e• \u003cb\u003eElement Technology\u003c\/b\u003e discusses four-node, three-node, eight-node, and two-node element theories\u003c\/p\u003e \u003cp\u003e• \u003cb\u003eMaterial Models\u003c\/b\u003e outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage\u003c\/p\u003e \u003cp\u003e• \u003cb\u003eContact and Constraint Conditions\u003c\/b\u003e covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions\u003c\/p\u003e \u003cp\u003eThroughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntroduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics\u003c\/i\u003e is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Fundamentals 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Era of Simulation and Computer Aided Engineering 3\u003c\/p\u003e \u003cp\u003e1.1.1 A World of Simulation 3\u003c\/p\u003e \u003cp\u003e1.1.2 Evolution of Explicit Finite Element Method 4\u003c\/p\u003e \u003cp\u003e1.1.3 Computer Aided Engineering (CAE)—Opportunities and Challenges 5\u003c\/p\u003e \u003cp\u003e1.2 Preliminaries 6\u003c\/p\u003e \u003cp\u003e1.2.1 Notations 6\u003c\/p\u003e \u003cp\u003e1.2.2 Constitutive Relations of Elasticity 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Framework of Explicit Finite Element Method for Nonlinear Transient Dynamics 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Transient Structural Dynamics 11\u003c\/p\u003e \u003cp\u003e2.2 Variational Principles for Transient Dynamics 13\u003c\/p\u003e \u003cp\u003e2.2.1 Hamilton’s Principle 13\u003c\/p\u003e \u003cp\u003e2.2.2 Galerkin Method 15\u003c\/p\u003e \u003cp\u003e2.3 Finite Element Equations and the Explicit Procedures 15\u003c\/p\u003e \u003cp\u003e2.3.1 Discretization in Space by Finite Element 16\u003c\/p\u003e \u003cp\u003e2.3.2 System of Semidiscretization 19\u003c\/p\u003e \u003cp\u003e2.3.3 Discretization in Time by Finite Difference 19\u003c\/p\u003e \u003cp\u003e2.3.4 Procedure of the Explicit Finite Element Method 20\u003c\/p\u003e \u003cp\u003e2.4 Main Features of the Explicit Finite Element Method 21\u003c\/p\u003e \u003cp\u003e2.4.1 Stability Condition and Time Step Size 22\u003c\/p\u003e \u003cp\u003e2.4.2 Diagonal Mass Matrix 23\u003c\/p\u003e \u003cp\u003e2.4.3 Corotational Stress 24\u003c\/p\u003e \u003cp\u003e2.5 Assessment of Explicit Finite Element Method 24\u003c\/p\u003e \u003cp\u003e2.5.1 About the Solution of the Elastodynamics 24\u003c\/p\u003e \u003cp\u003e2.5.2 A Priori Error Estimate of Explicit Finite Element Method for Elastodynamics 25\u003c\/p\u003e \u003cp\u003e2.5.3 About the Diagonal Mass Matrix 30\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Element Technology 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Four-Node Shell Element (Reissner–Mindlin Plate Theory) 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Fundamentals of Plates and Shells 40\u003c\/p\u003e \u003cp\u003e3.1.1 Characteristics of Thin-walled Structures 40\u003c\/p\u003e \u003cp\u003e3.1.2 Resultant Equations 42\u003c\/p\u003e \u003cp\u003e3.1.3 Applications to Linear Elasticity 44\u003c\/p\u003e \u003cp\u003e3.1.4 Kirchhoff–Love Theory 46\u003c\/p\u003e \u003cp\u003e3.1.5 Reissner–Mindlin Plate Theory 47\u003c\/p\u003e \u003cp\u003e3.2 Linear Theory of R-M Plate 47\u003c\/p\u003e \u003cp\u003e3.2.1 Helmholtz Decomposition for R-M Plate 48\u003c\/p\u003e \u003cp\u003e3.2.2 Load Scaling for Static Problem of R-M Plate 48\u003c\/p\u003e \u003cp\u003e3.2.3 Load Scaling and Mass Scaling for Dynamic Problem of R-M Plate 49\u003c\/p\u003e \u003cp\u003e3.2.4 Relation between R-M Theory and K-L Theory 50\u003c\/p\u003e \u003cp\u003e3.3 Interpolation for Four-node R-M Plate Element 52\u003c\/p\u003e \u003cp\u003e3.3.1 Variational Equations for R-M Plate 52\u003c\/p\u003e \u003cp\u003e3.3.2 Bilinear Interpolations 52\u003c\/p\u003e \u003cp\u003e3.3.3 Shear Locking Issues of R-M Plate Element 55\u003c\/p\u003e \u003cp\u003e3.4 Reduced Integration and Selective Reduced Integration 56\u003c\/p\u003e \u003cp\u003e3.4.1 Reduced Integration 56\u003c\/p\u003e \u003cp\u003e3.4.2 Selective Reduced Integration 57\u003c\/p\u003e \u003cp\u003e3.4.3 Nonlinear Application of Selective Reduced Integration—Hughes–Liu Element 58\u003c\/p\u003e \u003cp\u003e3.5 Perturbation Hourglass Control—Belytschko–Tsay Element 60\u003c\/p\u003e \u003cp\u003e3.5.1 Concept of Hourglass Control 61\u003c\/p\u003e \u003cp\u003e3.5.2 Four-node Belytschko–Tsay Shell Element—Perturbation Hourglass Control 63\u003c\/p\u003e \u003cp\u003e3.5.3 Improvement of Belytschko–Tsay Shell Element 68\u003c\/p\u003e \u003cp\u003e3.5.4 About Convergence of Element using Reduced Integration 70\u003c\/p\u003e \u003cp\u003e3.6 Physical Hourglass Control—Belytschko–Leviathan (QPH) Element 71\u003c\/p\u003e \u003cp\u003e3.6.1 Constant and Nonconstant Contributions 71\u003c\/p\u003e \u003cp\u003e3.6.2 Projection of Shear Strain 72\u003c\/p\u003e \u003cp\u003e3.6.3 Physical Hourglass Control by One-point Integration 73\u003c\/p\u003e \u003cp\u003e3.6.4 Drill Projection 74\u003c\/p\u003e \u003cp\u003e3.6.5 Improvement of B-L (QPH) Element 76\u003c\/p\u003e \u003cp\u003e3.7 Shear Projection Method—Bathe–Dvorkin Element 76\u003c\/p\u003e \u003cp\u003e3.7.1 Projection of Transverse Shear Strain 76\u003c\/p\u003e \u003cp\u003e3.7.2 Convergence of B-D Element 78\u003c\/p\u003e \u003cp\u003e3.8 Assessment of Four-node R-M Plate Element 80\u003c\/p\u003e \u003cp\u003e3.8.1 Evaluations with Warped Mesh and Reduced Thickness 80\u003c\/p\u003e \u003cp\u003e3.8.2 About the Locking-free Low Order Four-node R-M Plate Element 85\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Three-Node Shell Element (Reissner–Mindlin Plate Theory) 88\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Fundamentals of a Three-node \u003ci\u003eC\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e Element 89\u003c\/p\u003e \u003cp\u003e4.1.1 Transformation and Jacobian 89\u003c\/p\u003e \u003cp\u003e4.1.2 Numerical Quadrature for In-plane Integration 91\u003c\/p\u003e \u003cp\u003e4.1.3 Shear Locking with \u003ci\u003eC\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e Triangular Element 91\u003c\/p\u003e \u003cp\u003e4.2 Decomposition Method for \u003ci\u003eC\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e Triangular Element with One-point Integration 92\u003c\/p\u003e \u003cp\u003e4.2.1 A \u003ci\u003eC\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e Element with Decomposition of Deflection 92\u003c\/p\u003e \u003cp\u003e4.2.2 A \u003ci\u003eC\u003c\/i\u003e\u003csup\u003e0\u003c\/sup\u003e Element with Decomposition of Rotations 96\u003c\/p\u003e \u003cp\u003e4.3 Discrete Kirchhoff Triangular Element 97\u003c\/p\u003e \u003cp\u003e4.4 Assessment of Three-node R-M Plate Element 102\u003c\/p\u003e \u003cp\u003e4.4.1 Evaluations with Warped Mesh and Reduced Thickness 102\u003c\/p\u003e \u003cp\u003e4.4.2 About the Locking-free Low Order Three-node R-M Plate Element 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Eight-Node Solid Element 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Trilinear Interpolation for the Eight-node Hexahedron Element 107\u003c\/p\u003e \u003cp\u003e5.2 Locking Issues of the Eight-node Solid Element 111\u003c\/p\u003e \u003cp\u003e5.3 One-point Reduced Integration and the Perturbed Hourglass Control 113\u003c\/p\u003e \u003cp\u003e5.4 Assumed Strain Method and Selective\/Reduced Integration 115\u003c\/p\u003e \u003cp\u003e5.5 Assumed Deviatoric Strain 118\u003c\/p\u003e \u003cp\u003e5.6 An Enhanced Assumed Strain Method 118\u003c\/p\u003e \u003cp\u003e5.7 Taylor Expansion of Assumed Strain about the Element Center 120\u003c\/p\u003e \u003cp\u003e5.8 Evaluation of Eight-node Solid Element 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Two-Node Element 128\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Truss and Rod Element 128\u003c\/p\u003e \u003cp\u003e6.2 Timoshenko Beam Element 129\u003c\/p\u003e \u003cp\u003e6.3 Spring Element 131\u003c\/p\u003e \u003cp\u003e6.3.1 One Degree of Freedom Spring Element 131\u003c\/p\u003e \u003cp\u003e6.3.2 Six Degrees of Freedom Spring Element 132\u003c\/p\u003e \u003cp\u003e6.3.3 Three-node Spring Element 133\u003c\/p\u003e \u003cp\u003e6.4 Spot Weld Element 134\u003c\/p\u003e \u003cp\u003e6.4.1 Description of Spot Weld Separation 134\u003c\/p\u003e \u003cp\u003e6.4.2 Failure Criterion 135\u003c\/p\u003e \u003cp\u003e6.4.3 Finite Element Representation of Spot Weld 137\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Material Models 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Material Model of Plasticity 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Fundamentals of Plasticity 142\u003c\/p\u003e \u003cp\u003e7.1.1 Tensile Test 142\u003c\/p\u003e \u003cp\u003e7.1.2 Hardening 144\u003c\/p\u003e \u003cp\u003e7.1.3 Yield Surface 145\u003c\/p\u003e \u003cp\u003e7.1.4 Normality Condition 150\u003c\/p\u003e \u003cp\u003e7.1.5 Strain Rate Effect\/Viscoplasticity 152\u003c\/p\u003e \u003cp\u003e7.2 Constitutive Equations 153\u003c\/p\u003e \u003cp\u003e7.2.1 Relations between Stress Increments and Strain Increments 153\u003c\/p\u003e \u003cp\u003e7.2.2 Constitutive Equations for Mises Criterion 157\u003c\/p\u003e \u003cp\u003e7.2.3 Application to Kinematic Hardening 158\u003c\/p\u003e \u003cp\u003e7.3 Software Implementation 159\u003c\/p\u003e \u003cp\u003e7.3.1 Explicit Finite Element Procedure with Plasticity 160\u003c\/p\u003e \u003cp\u003e7.3.2 Normal (Radial) Return Scheme 160\u003c\/p\u003e \u003cp\u003e7.3.3 A Generalized Plane Stress Model 163\u003c\/p\u003e \u003cp\u003e7.3.4 Stress Resultant Approach 164\u003c\/p\u003e \u003cp\u003e7.4 Evaluation of Shell Elements with Plastic Deformation 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Continuum Mechanics Model of Ductile Damage 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Concept of Damage Mechanics 175\u003c\/p\u003e \u003cp\u003e8.2 Gurson’s Model 177\u003c\/p\u003e \u003cp\u003e8.2.1 Damage Variables and Yield Function 178\u003c\/p\u003e \u003cp\u003e8.2.2 Constitutive Equation and Damage Growth 179\u003c\/p\u003e \u003cp\u003e8.3 Chow’s Isotropic Model of Continuum Damage Mechanics 180\u003c\/p\u003e \u003cp\u003e8.3.1 Damage Effect Tensor 181\u003c\/p\u003e \u003cp\u003e8.3.2 Yield Function and Constitutive Equation 183\u003c\/p\u003e \u003cp\u003e8.3.3 Damage Growth 185\u003c\/p\u003e \u003cp\u003e8.3.4 Application to Plates and Shells 187\u003c\/p\u003e \u003cp\u003e8.3.5 Determination of Parameters 188\u003c\/p\u003e \u003cp\u003e8.4 Chow’s Anisotropic Model of Continuum Damage Mechanics 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Models of Nonlinear Materials 192\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Viscoelasticity 192\u003c\/p\u003e \u003cp\u003e9.1.1 Spring–Damper Model 192\u003c\/p\u003e \u003cp\u003e9.1.2 A General Three-dimensional Viscoelasticity Model 196\u003c\/p\u003e \u003cp\u003e9.2 Polymer and Engineering Plastics 197\u003c\/p\u003e \u003cp\u003e9.2.1 Fundamental Mechanical Properties of Polymer Materials 197\u003c\/p\u003e \u003cp\u003e9.2.2 A Temperature, Strain Rate, and Pressure Dependent Constitutive Relation 198\u003c\/p\u003e \u003cp\u003e9.2.3 A Nonlinear Viscoelastic Model of Polymer Materials 199\u003c\/p\u003e \u003cp\u003e9.3 Rubber 200\u003c\/p\u003e \u003cp\u003e9.3.1 Mooney–Rivlin Model of Rubber Material 200\u003c\/p\u003e \u003cp\u003e9.3.2 Blatz–Ko Model 202\u003c\/p\u003e \u003cp\u003e9.3.3 Ogden Model 203\u003c\/p\u003e \u003cp\u003e9.4 Foam 203\u003c\/p\u003e \u003cp\u003e9.4.1 A Cap Model Combining Volumetric Plasticity and Pressure Dependent Deviatoric Plasticity 205\u003c\/p\u003e \u003cp\u003e9.4.2 A Model Consisting of Polymer Skeleton and Air 205\u003c\/p\u003e \u003cp\u003e9.4.3 A Phenomenological Uniaxial Model 207\u003c\/p\u003e \u003cp\u003e9.4.4 Hysteresis Behavior 208\u003c\/p\u003e \u003cp\u003e9.4.5 Dynamic Behavior 209\u003c\/p\u003e \u003cp\u003e9.5 Honeycomb 209\u003c\/p\u003e \u003cp\u003e9.5.1 Structure of Hexagonal Honeycomb 210\u003c\/p\u003e \u003cp\u003e9.5.2 Critical Buckling Load 210\u003c\/p\u003e \u003cp\u003e9.5.3 A Phenomenological Material Model of Honeycomb 211\u003c\/p\u003e \u003cp\u003e9.5.4 Behavior of Honeycomb under Complex Loading Conditions 213\u003c\/p\u003e \u003cp\u003e9.6 Laminated Glazing 214\u003c\/p\u003e \u003cp\u003e9.6.1 Application of J-integral 214\u003c\/p\u003e \u003cp\u003e9.6.2 Application of Anisotropic Damage Model 215\u003c\/p\u003e \u003cp\u003e9.6.3 A Simplified Model with Shell Element for the Laminated Glass 216\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Contact and Constraint Conditions 219\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Three-Dimensional Surface Contact 221\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Examples of Contact Problems 221\u003c\/p\u003e \u003cp\u003e10.1.1 Uniformly Loaded String with a Flat Rigid Obstacle 222\u003c\/p\u003e \u003cp\u003e10.1.2 Hertz Contact Problem 225\u003c\/p\u003e \u003cp\u003e10.1.3 Elastic Impact of Two Balls 226\u003c\/p\u003e \u003cp\u003e10.1.4 Impact of an Elastic Rod on the Flat Rigid Obstacle 228\u003c\/p\u003e \u003cp\u003e10.1.5 Impact of a Vibrating String to the Flat Rigid Obstacle 231\u003c\/p\u003e \u003cp\u003e10.2 Description of Contact Conditions 233\u003c\/p\u003e \u003cp\u003e10.2.1 Contact with a Smooth Rigid Obstacle—Signorini’s Problem 233\u003c\/p\u003e \u003cp\u003e10.2.2 Contact between Two Smooth Deformable Bodies 237\u003c\/p\u003e \u003cp\u003e10.2.3 Coulomb’s Law of Friction 240\u003c\/p\u003e \u003cp\u003e10.2.4 Conditions for “In Contact” 242\u003c\/p\u003e \u003cp\u003e10.2.5 Domain Contact 242\u003c\/p\u003e \u003cp\u003e10.3 Variational Principle for the Dynamic Contact Problem 243\u003c\/p\u003e \u003cp\u003e10.3.1 Variational Formulation for Frictionless Dynamic Contact Problem 243\u003c\/p\u003e \u003cp\u003e10.3.2 Variational Formulation for Frictional Dynamic Contact Problem 247\u003c\/p\u003e \u003cp\u003e10.3.3 Variational Formulation for Domain Contact 250\u003c\/p\u003e \u003cp\u003e10.4 Penalty Method and the Regularization of Variational Inequality 252\u003c\/p\u003e \u003cp\u003e10.4.1 Concept of Penalty Method 252\u003c\/p\u003e \u003cp\u003e10.4.2 Penalty Method for Nonlinear Dynamic Contact Problem 256\u003c\/p\u003e \u003cp\u003e10.4.3 Explicit Finite Element Procedure with Penalty Method for Dynamic Contact 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Numerical Procedures for Three-Dimensional Surface Contact 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 A Contact Algorithm with Slave Node Searching Master Segment 262\u003c\/p\u003e \u003cp\u003e11.1.1 Global Search 263\u003c\/p\u003e \u003cp\u003e11.1.2 Bucket Sorting Method 264\u003c\/p\u003e \u003cp\u003e11.1.3 Local Search 266\u003c\/p\u003e \u003cp\u003e11.1.4 Penalty Contact Force 268\u003c\/p\u003e \u003cp\u003e11.2 A Contact Algorithm with Master Segment Searching Slave Node 272\u003c\/p\u003e \u003cp\u003e11.2.1 Global Search with Bucket Sorting Based on Segment’s Capture Box 272\u003c\/p\u003e \u003cp\u003e11.2.2 Local Search with the Projection of Slave Point 273\u003c\/p\u003e \u003cp\u003e11.3 Method of Contact Territory and Defense Node 273\u003c\/p\u003e \u003cp\u003e11.3.1 Global Search with Bucket Sorting Based on Segment’s Territory 274\u003c\/p\u003e \u003cp\u003e11.3.2 Local Search in the Territory 274\u003c\/p\u003e \u003cp\u003e11.3.3 Defense Node and Contact Force 275\u003c\/p\u003e \u003cp\u003e11.4 Pinball Contact Algorithm 277\u003c\/p\u003e \u003cp\u003e11.4.1 The Pinball Hierarchy 277\u003c\/p\u003e \u003cp\u003e11.4.2 Penalty Contact Force 278\u003c\/p\u003e \u003cp\u003e11.5 Edge (Line Segment) Contact 279\u003c\/p\u003e \u003cp\u003e11.5.1 Search for Line Contact 279\u003c\/p\u003e \u003cp\u003e11.5.2 Penalty Contact Force of Edge-to-Edge Contact 281\u003c\/p\u003e \u003cp\u003e11.6 Evaluation of Contact Algorithm with Penalty Method 282\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Kinematic Constraint Conditions 289\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Rigid Wall 289\u003c\/p\u003e \u003cp\u003e12.1.1 A Stationary Flat Rigid Wall 290\u003c\/p\u003e \u003cp\u003e12.1.2 A Moving Flat Rigid Wall 291\u003c\/p\u003e \u003cp\u003e12.1.3 Rigid Wall with a Curved Surface 293\u003c\/p\u003e \u003cp\u003e12.2 Rigid Body 296\u003c\/p\u003e \u003cp\u003e12.3 Explicit Finite Element Procedure with Constraint Conditions 298\u003c\/p\u003e \u003cp\u003e12.4 Application Examples with Constraint Conditions 300\u003c\/p\u003e \u003cp\u003eReferences 305\u003c\/p\u003e \u003cp\u003eIndex 325\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand 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