Computational continuum mechanics
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...
| Otros Autores: | |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
Wiley
2018.
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| Edición: | Third edition |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009631512406719 |
Tabla de Contenidos:
- Cover
- Title Page
- Copyright
- Contents
- Preface
- Chapter 1 Introduction
- 1.1 Matrices
- Definitions
- Determinant
- Inverse and Orthogonality
- Matrix Operations
- 1.2 Vectors
- Dot Product
- Cross Product
- Dyadic Product
- Projection
- 1.3 Summation Convention
- Unit Dyads
- 1.4 Cartesian Tensors
- Double Product or Double Contraction
- Invariants of the Second-Order Tensor
- Symmetric Tensors
- Higher-Order Tensors
- 1.5 Polar Decomposition Theorem
- Other Decompositions
- 1.6 D'Alembert's Principle
- Particle Mechanics
- Rigid-Body Kinematics
- Application of D'Alembert's Principle
- Continuum Forces
- 1.7 Virtual Work Principle
- Relationship with D'Alembert's Principle
- 1.8 Approximation Methods
- 1.9 Discrete Equations
- 1.10 Momentum, Work, and Energy
- Linear and Angular Momentum
- Work and Energy
- 1.11 Parameter Change and Coordinate Transformation
- Change of Parameters
- Coordinate Transformation
- Deformation and Strains
- Position Vector Gradients and Rigid Body Kinematics
- Problems
- Chapter 2 Kinematics
- 2.1 Motion Description
- Line Elements
- Rigid-Body Motion
- Floating Frame of Reference (FFR)
- Displacement Vector Gradients
- 2.2 Strain Components
- Geometric Interpretation of the Strains
- Eulerian Strain Tensor
- 2.3 Other Deformation Measures
- Right and Left Cauchy-Green Deformation Tensors
- Infinitesimal Strain Tensor
- 2.4 Decomposition of Displacement
- Homogeneous Motion
- Nonhomogeneous Motion
- 2.5 Velocity and Acceleration
- Eulerian Description
- Rate of Deformation and Spin Tensors
- Rate of Change of the Green-Lagrange Strain
- 2.6 Coordinate Transformation
- Strain Transformation
- Gradients and Strains
- Principal Strains
- Strain Invariants
- 2.7 Objectivity
- 2.8 Change of Volume and Area
- Volume
- Area.
- 2.9 Continuity Equation
- 2.10 Reynolds' Transport Theorem
- 2.11 Examples of Deformation
- Planar Displacement
- Extension and Stretch
- Shear Deformation
- 2.12 Geometry Concepts
- Problems
- Chapter 3 Forces and Stresses
- 3.1 Equilibrium of Forces
- 3.2 Transformation of Stresses
- 3.3 Equations of Equilibrium
- 3.4 Symmetry of the cauchy Stress Tensor
- Principal Stresses
- 3.5 Virtual Work of the Forces
- Tensor Double Product (Contraction)
- Volume Change
- Virtual Work
- Other Stress Measures
- First and Second Piola-Kirchhoff Stress Tensors
- Notation and Procedure
- Surface Forces
- Total and Updated Lagrangian Formulations
- Physical Interpretation
- 3.6 Deviatoric Stresses
- 3.7 Stress Objectivity
- Stress Rate
- Truesdell Stress Rate o
- Oldroyd and Convective Stress Rates o and o
- Green-Naghdi Stress Rate
- Jaumann Stress Rate
- 3.8 Energy Balance
- Problems
- Chapter 4 Constitutive Equations
- 4.1 Generalized Hooke's Law
- 4.2 Anisotropic Linearly Elastic Materials
- 4.3 Material Symmetry
- Reflection
- Rotations
- 4.4 Homogeneous Isotropic Material
- Poisson Effect and Locking
- Stress and Strain Invariants
- Plane-Stress and Plane-Strain Problems
- Finite Dimensional Model
- Generalized Elastic Forces
- Homogeneous Displacement
- 4.5 Principal Strain Invariants
- 4.6 Special Material Models for Large Deformations
- Compressible Neo-Hookean Material Models
- Incompressible Mooney-Rivlin Materials
- Objectivity
- 4.7 Linear Viscoelasticity
- One-Dimensional Model
- Other Viscoelastic Models
- Generalization
- Elastic Energy and Dissipation
- Another Form of the Viscoelastic Equations
- Three-Dimensional Linear Viscoelasticity
- 4.8 Nonlinear Viscoelasticity
- Another Model
- 4.9 A Simple Viscoelastic Model for Isotropic Materials
- 4.10 Fluid Constitutive Equations.
- 4.11 Navier-Stokes Equations
- Problems
- Chapter 5 Finite Element Formulation: Large-Deformation, Large-Rotation Problem
- Small- and Large-Deformation Problems
- Absolute Nodal Coordinate Formulation (ANCF)
- Organization
- 5.1 Displacement Field
- Separation of Variables
- Modes of Displacement
- Nodal Coordinates
- 5.2 Element Connectivity
- 5.3 Inertia and Elastic Forces
- Inertia Forces
- Elastic Forces
- 5.4 Equations of Motion
- Curved Geometry
- 5.5 Numerical Evaluation of the Elastic Forces
- Gaussian Quadrature
- Generalization
- 5.6 Finite Elements and Geometry
- General Continuum Mechanics Approach and Classical Theories
- Gradient Vectors
- Locking Problems
- Theory of Curves
- Theory of Surfaces
- Surface Curvature
- 5.7 Two-Dimensional Euler-Bernoulli Beam Element
- Kinematics of the Element
- Formulation of the Element Elastic Forces
- Special Case
- 5.8 Two-Dimensional Shear Deformable Beam Element
- Formulation of the Elastic Forces
- 5.9 Three-Dimensional Cable Element
- 5.10 Three-Dimensional Beam Element
- 5.11 Thin-Plate Element
- 5.12 Higher-Order Plate Element
- 5.13 Brick Element
- 5.14 Element Performance
- Patch Test
- Locking Problem
- Reduced Integration
- 5.15 Other Finite Element Formulations
- Isoparametric Finite Elements
- Use of Infinitesimal Rotation Coordinates
- Use of Finite Rotation Coordinates
- 5.16 Updated Lagrangian and Eulerian Formulations
- 5.17 Concluding Remarks
- ANCF Finite Elements
- Constrained Motion
- ANCF Reference Node
- Deformation Modes
- Problems
- Chapter 6 Finite Element Formulation: Small-Deformation, Large-Rotation Problem
- 6.1 Background
- Rigid-Body Motion
- Translations
- 6.2 Rotation and Angular Velocity
- Identities
- General Displacement
- Illustrative Example
- Euler Angles Singularity.
- 6.3 Floating Frame of Reference (FFR)
- 6.4 Intermediate Element Coordinate System
- 6.5 Connectivity and Reference Conditions
- Connectivity Conditions
- Reference Conditions
- Rigid-Body and Reference Motion
- 6.6 Kinematic Equations
- 6.7 Formulation of the Inertia Forces
- Body Inertia Shape Integrals
- 6.8 Elastic Forces
- 6.9 Equations of Motion
- 6.10 Coordinate Reduction
- 6.11 Integration of Finite Element and Multibody System Algorithms
- Linear Theory of Elastodynamics
- Nodal and Modal Coordinates
- Numerical Evaluation of the Inertia Shape Integrals
- Scaling of the Modal Coordinates
- Limitations of the FFR Formulation
- Problems
- Chapter 7 Computational Geometry and Finite Element Analysis
- 7.1 Geometry and Finite Element Method
- Bezier Geometry
- B-Spline Geometry
- NURBS Geometry
- 7.2 Ancf Geometry
- ANCF Element Geometry
- Control-Point Representation
- 7.3 Bezier Geometry
- 7.4 B-Spline Curve Representation
- Control Points and Degree of Continuity
- Illustrative Example
- Knot Insertion
- Comparison with FE Formulations
- 7.5 Conversion of B-Spline Geometry to ANCF Geometry
- 7.6 ANCF and B-Spline Surfaces
- B-Spline Surfaces
- ANCF Surfaces
- 7.7 Structural and Nonstructural Discontinuities
- B-Spline Model
- ANCF Model
- Problems
- Chapter 8 Plasticity Formulations
- 8.1 One-Dimensional Problem
- 8.2 Loading and Unloading Conditions
- 8.3 Solution of the Plasticity Equations
- Numerical Solution
- Plasticity Equations
- Trial Step
- The Return Mapping Algorithm
- 8.4 Generalization of the Plasticity Theory: Small Strains
- Associative Plasticity
- Numerical Solution of the Plasticity Equations
- Explicit Solution
- Implicit Solution
- 8.5 J2 Flow Theory with Isotropic/Kinematic Hardening
- Nonlinear Isotropic/Kinematic Hardening.
- Return Mapping Algorithm for Nonlinear Isotropic/Kinematic Hardening
- Linear Kinematic/Isotropic Hardening
- 8.6 Nonlinear Formulation for Hyperelastic-Plastic Materials
- Multiplicative Decomposition
- Hyperelastic Potential
- Rate of Deformation Tensors
- Flow Rule and Hardening Law
- Numerical Solution
- Rate-Dependent Plasticity
- 8.7 Hyperelastic-Plastic J2 Flow Theory
- Problems
- References
- Index
- EULA.
