Finite Element Method for Three Dimensional Thermomechanical - Application

Informationen zum Autor Guido Dhondt obtained his civil engineering degree at the Catholic University of Leuven, Belgium (1983), going on to undertake a Ph.D. in Civil Engineering at Princeton University, USA (1987).  Presently, he works in the field of fracture mechanics and finite element analysis at MTU Aero Engines, Germany.  He is one of the authors of the free software finite element program CalculiX. Klappentext The Finite Element Method for Three-Dimensional Thermomechanical Applications offers basic and advanced methods for using the finite element method for three-dimensional, industrial problems.* Covers cyclic symmetry, rigid body motion, and nonlinear multiple point constraints.* Offers advanced material formulations, including large strain multiplicative viscoplasticity, anisotropic hyperelastic materials and single crystals.* All methods are implemented using the finite element software CalculiX, which is freely available (GNU General Public License applies). Zusammenfassung Offers 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. Inhaltsverzeichnis Preface xiii Nomenclature xv 1 Displacements, Strain, Stress and Energy 1 1.1 The Reference State 1 1.2 The Spatial State 4 1.3 Strain Measures 9 1.4 Principal Strains 13 1.5 Velocity 19 1.6 Objective Tensors 22 1.7 Balance Laws 25 1.7.1 Conservation of mass 25 1.7.2 Conservation of momentum 25 1.7.3 Conservation of angular momentum 26 1.7.4 Conservation of energy 26 1.7.5 Entropy inequality 27 1.7.6 Closure 28 1.8 Localization of the Balance Laws 28 1.8.1 Conservation of mass 28 1.8.2 Conservation of momentum 29 1.8.3 Conservation of angular momentum 31 1.8.4 Conservation of energy 31 1.8.5 Entropy inequality 31 1.9 The Stress Tensor 31 1.10 The Balance Laws in Material Coordinates 34 1.10.1 Conservation of mass 35 1.10.2 Conservation of momentum 35 1.10.3 Conservation of angular momentum 37 1.10.4 Conservation of energy 37 1.10.5 Entropy inequality 37 1.11 The Weak Form of the Balance of Momentum 38 1.11.1 Formulation of the boundary conditions (material coordinates) 38 1.11.2 Deriving the weak form from the strong form (material coordinates) 39 1.11.3 Deriving the strong form from the weak form (material coordinates) 41 1.11.4 The weak form in spatial coordinates 41 1.12 The Weak Form of the Energy Balance 42 1.13 Constitutive Equations 43 1.13.1 Summary of the balance equations 43 1.13.2 Development of the constitutive theory 44 1.14 Elastic Materials 47 1.14.1 General form 47 1.14.2 Linear elastic materials 49 1.14.3 Isotropic linear elastic materials 52 1.14.4 Linearizing the strains 54 1.14.5 Isotropic elastic materials 58 1.15 Fluids 59 2 Linear Mechanical Applications 63 2.1 General Equations 63 2.2 The Shape Functions 67 2.2.1 The 8-node brick element 68 2.2.2 The 20-node brick element 69 2.2.3 The 4-node tetrahedral element 71 2.2.4 The 10-node tetrahedral element 72 2.2.5 The 6-node wedge element 73 2.2.6 The 15-node wedge element 73 2.3 Numerical Integration 75 2.3.1 Hexahedral elements 76 2.3.2 Tetrahedral elements 78 2.3.3 Wedge elements 78 2.3.4 Integration over a surface in three-dimensional space 81 2.4 Extrapolation of Integration Point Values to the Nodes 82 2.4.1 The 8-node hexahedral element 83 2.4.2 The 20-node hexahedral element 84 2.4.3 The tetrahedral elements 86 2.4.4 The wedge elements 86 ...

List of contents

Preface.
 
Nomenclature.
 
1 Displacements, Strain, Stress and Energy.
 
1.1 The Reference State.
 
1.2 The Spatial State.
 
1.3 Strain Measures.
 
1.4 Principal Strains.
 
1.5 Velocity.
 
1.6 Objective Tensors.
 
1.7 Balance Laws.
 
1.8 Localization of the Balance Laws.
 
1.9 The Stress Tensor.
 
1.10 The Balance Laws in Material Coordinates.
 
1.11 The Weak Form of the Balance of Momentum.
 
1.12 The Weak Form of the Energy Balance.
 
1.13 Constitutive Equations.
 
1.14 Elastic Materials.
 
1.15 Fluids.
 
2 Linear Mechanical Applications.
 
2.1 General Equations.
 
2.2 The Shape Functions.
 
2.3 Numerical Integration.
 
2.4 Extrapolation of Integration Point Values to the Nodes.
 
2.5 Problematic Element Behavior.
 
2.6 Linear Constraints.
 
2.7 Transformations.
 
2.8 Loading.
 
2.9 Modal Analysis.
 
2.10 Cyclic Symmetry.
 
2.11 Dynamics: The ±-Method.
 
3 Geometric Nonlinear Effects.
 
3.1 General Equations.
 
3.2 Application to a Snapping-through Plate.
 
3.3 Solution-dependent Loading.
 
3.4 Nonlinear Multiple Point Constraints.
 
3.5 Rigid Body Motion.
 
3.6 Mean Rotation.
 
3.7 Kinematic Constraints.
 
3.8 Incompressibility Constraint.
 
4 Hyperelastic Materials.
 
4.1 Polyconvexity of the Stored-energy Function.
 
4.2 Isotropic Hyperelastic Materials.
 
4.3 Nonhomogeneous Shear Experiment.
 
4.4 Derivatives of Invariants and Principal Stretches.
 
4.5 Tangent Stiffness Matrix at Zero Deformation.
 
4.6 Inflation of a Balloon.
 
4.7 Anisotropic Hyperelasticity.
 
5 Infinitesimal Strain Plasticity.
 
5.1 Introduction.
 
5.2 The General Framework of Plasticity.
 
5.3 Three-dimensional Single Surface Viscoplasticity.
 
5.4 Three-dimensional Multisurface Viscoplasticity: the Cailletaud Single Crystal Model.
 
5.5 Anisotropic Elasticity with a von Mises-type Yield Surface.
 
6 Finite Strain Elastoplasticity.
 
6.1 Multiplicative Decomposition of the Deformation Gradient.
 
6.2 Deriving the Flow Rule.
 
6.3 Isotropic Hyperelasticity with a von Mises-type Yield Surface.
 
6.4 Extensions.
 
6.5 Summary of the Equations.
 
6.6 Stress Update Algorithm.
 
6.7 Derivation of Consistent Elastoplastic Moduli.
 
6.8 Isochoric Plastic Deformation.
 
6.9 Burst Calculation of a Compressor.
 
7 Heat Transfer.
 
7.1 Introduction.
 
7.2 The Governing Equations.
 
7.3 Weak Form of the Energy Equation.
 
7.4 Finite Element Procedure.
 
7.5 Time Discretization and Linearization of the Governing Equation.
 
7.6 Forced Fluid Convection.
 
7.7 Cavity Radiation.
 
References.
 
Index.

Product details

• Authors: G Dhondt, Guido Dhondt, Guido (Munich Dhondt, Dhondt Guido, Guido Dhondt
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 07.05.2004
• EAN: 9780470857526
• ISBN: 978-0-470-85752-6
• No. of pages: 362
• Subjects: Natural sciences, medicine, IT, technology > Technology > Mechanical engineering, production engineering; Maschinenbau, Thermodynamik, Thermodynamics, Mechanical Engineering, Solid Mechanics, Festkörpermechanik, Aeronautic & Aerospace Engineering, Luft- u. Raumfahrttechnik, Finite-Element-Methode