{"product_id":"the-finite-element-method-for-threedimensional-thermomechanical-applications-9780470857526","title":"The Finite Element Method for ThreeDimensional","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eOffers basic and advanced methods for using the finite element method for three dimensional, industrial problems. This book covers cyclic symmetry, rigid body motion, and nonlinear multiple point constraints.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eNomenclature xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Displacements, Strain, Stress and Energy 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Reference State 1\u003c\/p\u003e \u003cp\u003e1.2 The Spatial State 4\u003c\/p\u003e \u003cp\u003e1.3 Strain Measures 9\u003c\/p\u003e \u003cp\u003e1.4 Principal Strains 13\u003c\/p\u003e \u003cp\u003e1.5 Velocity 19\u003c\/p\u003e \u003cp\u003e1.6 Objective Tensors 22\u003c\/p\u003e \u003cp\u003e1.7 Balance Laws 25\u003c\/p\u003e \u003cp\u003e1.7.1 Conservation of mass 25\u003c\/p\u003e \u003cp\u003e1.7.2 Conservation of momentum 25\u003c\/p\u003e \u003cp\u003e1.7.3 Conservation of angular momentum 26\u003c\/p\u003e \u003cp\u003e1.7.4 Conservation of energy 26\u003c\/p\u003e \u003cp\u003e1.7.5 Entropy inequality 27\u003c\/p\u003e \u003cp\u003e1.7.6 Closure 28\u003c\/p\u003e \u003cp\u003e1.8 Localization of the Balance Laws 28\u003c\/p\u003e \u003cp\u003e1.8.1 Conservation of mass 28\u003c\/p\u003e \u003cp\u003e1.8.2 Conservation of momentum 29\u003c\/p\u003e \u003cp\u003e1.8.3 Conservation of angular momentum 31\u003c\/p\u003e \u003cp\u003e1.8.4 Conservation of energy 31\u003c\/p\u003e \u003cp\u003e1.8.5 Entropy inequality 31\u003c\/p\u003e \u003cp\u003e1.9 The Stress Tensor 31\u003c\/p\u003e \u003cp\u003e1.10 The Balance Laws in Material Coordinates 34\u003c\/p\u003e \u003cp\u003e1.10.1 Conservation of mass 35\u003c\/p\u003e \u003cp\u003e1.10.2 Conservation of momentum 35\u003c\/p\u003e \u003cp\u003e1.10.3 Conservation of angular momentum 37\u003c\/p\u003e \u003cp\u003e1.10.4 Conservation of energy 37\u003c\/p\u003e \u003cp\u003e1.10.5 Entropy inequality 37\u003c\/p\u003e \u003cp\u003e1.11 The Weak Form of the Balance of Momentum 38\u003c\/p\u003e \u003cp\u003e1.11.1 Formulation of the boundary conditions (material coordinates) 38\u003c\/p\u003e \u003cp\u003e1.11.2 Deriving the weak form from the strong form (material coordinates) 39\u003c\/p\u003e \u003cp\u003e1.11.3 Deriving the strong form from the weak form (material coordinates) 41\u003c\/p\u003e \u003cp\u003e1.11.4 The weak form in spatial coordinates 41\u003c\/p\u003e \u003cp\u003e1.12 The Weak Form of the Energy Balance 42\u003c\/p\u003e \u003cp\u003e1.13 Constitutive Equations 43\u003c\/p\u003e \u003cp\u003e1.13.1 Summary of the balance equations 43\u003c\/p\u003e \u003cp\u003e1.13.2 Development of the constitutive theory 44\u003c\/p\u003e \u003cp\u003e1.14 Elastic Materials 47\u003c\/p\u003e \u003cp\u003e1.14.1 General form 47\u003c\/p\u003e \u003cp\u003e1.14.2 Linear elastic materials 49\u003c\/p\u003e \u003cp\u003e1.14.3 Isotropic linear elastic materials 52\u003c\/p\u003e \u003cp\u003e1.14.4 Linearizing the strains 54\u003c\/p\u003e \u003cp\u003e1.14.5 Isotropic elastic materials 58\u003c\/p\u003e \u003cp\u003e1.15 Fluids 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Linear Mechanical Applications 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 General Equations 63\u003c\/p\u003e \u003cp\u003e2.2 The Shape Functions 67\u003c\/p\u003e \u003cp\u003e2.2.1 The 8-node brick element 68\u003c\/p\u003e \u003cp\u003e2.2.2 The 20-node brick element 69\u003c\/p\u003e \u003cp\u003e2.2.3 The 4-node tetrahedral element 71\u003c\/p\u003e \u003cp\u003e2.2.4 The 10-node tetrahedral element 72\u003c\/p\u003e \u003cp\u003e2.2.5 The 6-node wedge element 73\u003c\/p\u003e \u003cp\u003e2.2.6 The 15-node wedge element 73\u003c\/p\u003e \u003cp\u003e2.3 Numerical Integration 75\u003c\/p\u003e \u003cp\u003e2.3.1 Hexahedral elements 76\u003c\/p\u003e \u003cp\u003e2.3.2 Tetrahedral elements 78\u003c\/p\u003e \u003cp\u003e2.3.3 Wedge elements 78\u003c\/p\u003e \u003cp\u003e2.3.4 Integration over a surface in three-dimensional space 81\u003c\/p\u003e \u003cp\u003e2.4 Extrapolation of Integration Point Values to the Nodes 82\u003c\/p\u003e \u003cp\u003e2.4.1 The 8-node hexahedral element 83\u003c\/p\u003e \u003cp\u003e2.4.2 The 20-node hexahedral element 84\u003c\/p\u003e \u003cp\u003e2.4.3 The tetrahedral elements 86\u003c\/p\u003e \u003cp\u003e2.4.4 The wedge elements 86\u003c\/p\u003e \u003cp\u003e2.5 Problematic Element Behavior 86\u003c\/p\u003e \u003cp\u003e2.5.1 Shear locking 87\u003c\/p\u003e \u003cp\u003e2.5.2 Volumetric locking 87\u003c\/p\u003e \u003cp\u003e2.5.3 Hourglassing 90\u003c\/p\u003e \u003cp\u003e2.6 Linear Constraints 91\u003c\/p\u003e \u003cp\u003e2.6.1 Inclusion in the global system of equations 91\u003c\/p\u003e \u003cp\u003e2.6.2 Forces induced by linear constraints 96\u003c\/p\u003e \u003cp\u003e2.7 Transformations 97\u003c\/p\u003e \u003cp\u003e2.8 Loading 103\u003c\/p\u003e \u003cp\u003e2.8.1 Centrifugal loading 103\u003c\/p\u003e \u003cp\u003e2.8.2 Temperature loading 104\u003c\/p\u003e \u003cp\u003e2.9 Modal Analysis 106\u003c\/p\u003e \u003cp\u003e2.9.1 Frequency calculation 106\u003c\/p\u003e \u003cp\u003e2.9.2 Linear dynamic analysis 108\u003c\/p\u003e \u003cp\u003e2.9.3 Buckling 112\u003c\/p\u003e \u003cp\u003e2.10 Cyclic Symmetry 114\u003c\/p\u003e \u003cp\u003e2.11 Dynamics: The α-Method 120\u003c\/p\u003e \u003cp\u003e2.11.1 Implicit formulation 120\u003c\/p\u003e \u003cp\u003e2.11.2 Extension to nonlinear applications 123\u003c\/p\u003e \u003cp\u003e2.11.3 Consistency and accuracy of the implicit formulation 126\u003c\/p\u003e \u003cp\u003e2.11.4 Stability of the implicit scheme 130\u003c\/p\u003e \u003cp\u003e2.11.5 Explicit formulation 136\u003c\/p\u003e \u003cp\u003e2.11.6 The consistent mass matrix 138\u003c\/p\u003e \u003cp\u003e2.11.7 Lumped mass matrix 140\u003c\/p\u003e \u003cp\u003e2.11.8 Spherical shell subject to a suddenly applied uniform pressure 141\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Geometric Nonlinear Effects 143\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 General Equations 143\u003c\/p\u003e \u003cp\u003e3.2 Application to a Snapping-through Plate 148\u003c\/p\u003e \u003cp\u003e3.3 Solution-dependent Loading 150\u003c\/p\u003e \u003cp\u003e3.3.1 Centrifugal forces 150\u003c\/p\u003e \u003cp\u003e3.3.2 Traction forces 151\u003c\/p\u003e \u003cp\u003e3.3.3 Example: a beam subject to hydrostatic pressure 154\u003c\/p\u003e \u003cp\u003e3.4 Nonlinear Multiple Point Constraints 154\u003c\/p\u003e \u003cp\u003e3.5 Rigid Body Motion 155\u003c\/p\u003e \u003cp\u003e3.5.1 Large rotations 155\u003c\/p\u003e \u003cp\u003e3.5.2 Rigid body formulation 159\u003c\/p\u003e \u003cp\u003e3.5.3 Beam and shell elements 162\u003c\/p\u003e \u003cp\u003e3.6 Mean Rotation 167\u003c\/p\u003e \u003cp\u003e3.7 Kinematic Constraints 171\u003c\/p\u003e \u003cp\u003e3.7.1 Points on a straight line 171\u003c\/p\u003e \u003cp\u003e3.7.2 Points in a plane 173\u003c\/p\u003e \u003cp\u003e3.8 Incompressibility Constraint 174\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Hyperelastic Materials 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Polyconvexity of the Stored-energy Function 177\u003c\/p\u003e \u003cp\u003e4.1.1 Physical requirements 177\u003c\/p\u003e \u003cp\u003e4.1.2 Convexity 180\u003c\/p\u003e \u003cp\u003e4.1.3 Polyconvexity 184\u003c\/p\u003e \u003cp\u003e4.1.4 Suitable stored-energy functions 189\u003c\/p\u003e \u003cp\u003e4.2 Isotropic Hyperelastic Materials 190\u003c\/p\u003e \u003cp\u003e4.2.1 Polynomial form 191\u003c\/p\u003e \u003cp\u003e4.2.2 Arruda–Boyce form 193\u003c\/p\u003e \u003cp\u003e4.2.3 The Ogden form 194\u003c\/p\u003e \u003cp\u003e4.2.4 Elastomeric foam behavior 195\u003c\/p\u003e \u003cp\u003e4.3 Nonhomogeneous Shear Experiment 196\u003c\/p\u003e \u003cp\u003e4.4 Derivatives of Invariants and Principal Stretches 199\u003c\/p\u003e \u003cp\u003e4.4.1 Derivatives of the invariants 199\u003c\/p\u003e \u003cp\u003e4.4.2 Derivatives of the principal stretches 200\u003c\/p\u003e \u003cp\u003e4.4.3 Expressions for the stress and stiffness for three equal eigenvalues 206\u003c\/p\u003e \u003cp\u003e4.5 Tangent Stiffness Matrix at Zero Deformation 209\u003c\/p\u003e \u003cp\u003e4.5.1 Polynomial form 210\u003c\/p\u003e \u003cp\u003e4.5.2 Arruda–Boyce form 211\u003c\/p\u003e \u003cp\u003e4.5.3 Ogden form 211\u003c\/p\u003e \u003cp\u003e4.5.4 Elastomeric foam behavior 211\u003c\/p\u003e \u003cp\u003e4.5.5 Closure 212\u003c\/p\u003e \u003cp\u003e4.6 Inflation of a Balloon 212\u003c\/p\u003e \u003cp\u003e4.7 Anisotropic Hyperelasticity 216\u003c\/p\u003e \u003cp\u003e4.7.1 Transversely isotropic materials 217\u003c\/p\u003e \u003cp\u003e4.7.2 Fiber-reinforced material 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Infinitesimal Strain Plasticity 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 225\u003c\/p\u003e \u003cp\u003e5.2 The General Framework of Plasticity 225\u003c\/p\u003e \u003cp\u003e5.2.1 Theoretical derivation 225\u003c\/p\u003e \u003cp\u003e5.2.2 Numerical implementation 232\u003c\/p\u003e \u003cp\u003e5.3 Three-dimensional Single Surface Viscoplasticity 235\u003c\/p\u003e \u003cp\u003e5.3.1 Theoretical derivation 235\u003c\/p\u003e \u003cp\u003e5.3.2 Numerical procedure 239\u003c\/p\u003e \u003cp\u003e5.3.3 Determination of the consistent elastoplastic tangent matrix 242\u003c\/p\u003e \u003cp\u003e5.4 Three-dimensional Multisurface Viscoplasticity: the Cailletaud Single Crystal Model 244\u003c\/p\u003e \u003cp\u003e5.4.1 Theoretical considerations 244\u003c\/p\u003e \u003cp\u003e5.4.2 Numerical aspects 248\u003c\/p\u003e \u003cp\u003e5.4.3 Stress update algorithm 249\u003c\/p\u003e \u003cp\u003e5.4.4 Determination of the consistent elastoplastic tangent matrix 259\u003c\/p\u003e \u003cp\u003e5.4.5 Tensile test on an anisotropic material 260\u003c\/p\u003e \u003cp\u003e5.5 Anisotropic Elasticity with a von Mises–type Yield Surface 262\u003c\/p\u003e \u003cp\u003e5.5.1 Basic equations 262\u003c\/p\u003e \u003cp\u003e5.5.2 Numerical procedure 263\u003c\/p\u003e \u003cp\u003e5.5.3 Special case: isotropic elasticity 270\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Finite Strain Elastoplasticity 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Multiplicative Decomposition of the Deformation Gradient 273\u003c\/p\u003e \u003cp\u003e6.2 Deriving the Flow Rule 275\u003c\/p\u003e \u003cp\u003e6.2.1 Arguments of the free-energy function and yield condition 275\u003c\/p\u003e \u003cp\u003e6.2.2 Principle of maximum plastic dissipation 276\u003c\/p\u003e \u003cp\u003e6.2.3 Uncoupled volumetric\/deviatoric response 278\u003c\/p\u003e \u003cp\u003e6.3 Isotropic Hyperelasticity with a von Mises–type Yield Surface 279\u003c\/p\u003e \u003cp\u003e6.3.1 Uncoupled isotropic hyperelastic model 279\u003c\/p\u003e \u003cp\u003e6.3.2 Yield surface and derivation of the flow rule 280\u003c\/p\u003e \u003cp\u003e6.4 Extensions 284\u003c\/p\u003e \u003cp\u003e6.4.1 Kinematic hardening 284\u003c\/p\u003e \u003cp\u003e6.4.2 Viscoplastic behavior 285\u003c\/p\u003e \u003cp\u003e6.5 Summary of the Equations 287\u003c\/p\u003e \u003cp\u003e6.6 Stress Update Algorithm 287\u003c\/p\u003e \u003cp\u003e6.6.1 Derivation 287\u003c\/p\u003e \u003cp\u003e6.6.2 Summary 291\u003c\/p\u003e \u003cp\u003e6.6.3 Expansion of a thick-walled cylinder 293\u003c\/p\u003e \u003cp\u003e6.7 Derivation of Consistent Elastoplastic Moduli 294\u003c\/p\u003e \u003cp\u003e6.7.1 The volumetric stress 295\u003c\/p\u003e \u003cp\u003e6.7.2 Trial stress 295\u003c\/p\u003e \u003cp\u003e6.7.3 Plastic correction 296\u003c\/p\u003e \u003cp\u003e6.8 Isochoric Plastic Deformation 300\u003c\/p\u003e \u003cp\u003e6.9 Burst Calculation of a Compressor 302\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Heat Transfer 305\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 305\u003c\/p\u003e \u003cp\u003e7.2 The Governing Equations 305\u003c\/p\u003e \u003cp\u003e7.3 Weak Form of the Energy Equation 307\u003c\/p\u003e \u003cp\u003e7.4 Finite Element Procedure 309\u003c\/p\u003e \u003cp\u003e7.5 Time Discretization and Linearization of the Governing Equation 310\u003c\/p\u003e \u003cp\u003e7.6 Forced Fluid Convection 312\u003c\/p\u003e \u003cp\u003e7.7 Cavity Radiation 317\u003c\/p\u003e \u003cp\u003e7.7.1 Governing equations 317\u003c\/p\u003e \u003cp\u003e7.7.2 Numerical aspects 324\u003c\/p\u003e \u003cp\u003eReferences 329\u003c\/p\u003e \u003cp\u003eIndex 335\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402444710231,"sku":"9780470857526","price":93.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470857526.jpg?v=1730480419","url":"https:\/\/bookcurl.com\/products\/the-finite-element-method-for-threedimensional-thermomechanical-applications-9780470857526","provider":"Book Curl","version":"1.0","type":"link"}