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An introduction to nonlinear finite element analysis : with applications to heat transfer, fluid mechanics, and solid mechanics /
The development of realistic mathematical models that govern the response of systems or processes is strongly connected to the ability to translate them into meaningful discrete models that allow for a systematic evaluation of various parameters of the systems and processes. The second edition of th...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Oxford University Press,
[2014]
|
| Edición: | Second edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Machine-generated contents note: 1. General Introduction and Mathematical Preliminaries
- 1.1. General Comments
- 1.2. Mathematical Models
- 1.3. Numerical Simulations
- 1.4. The Finite Element Method
- 1.5. Non-linear Analysis
- 1.5.1. Introduction
- 1.5.2. Classification of Non-linearities
- 1.6. Review of Vectors and Tensors
- 1.6.1. Preliminary Comments
- 1.6.2. Definition of a Physical Vector
- 1.6.2.1. Vector addition
- 1.6.2.2. Multiplication of a vector by a scalar
- 1.6.3. Scalar and Vector Products
- 1.6.3.1. Scalar product (or "dot" product)
- 1.6.3.2. Vector product
- 1.6.3.3. Plane area as a vector
- 1.6.3.4. Linear independence of vectors
- 1.6.3.5. Components of a vector
- 1.6.4. Summation Convention and Kronecker Delta and Permutation Symbol
- 1.6.4.1. Summation convention
- 1.6.4.2. Kronecker delta symbol
- 1.6.4.3. The permutation symbol
- 1.6.5. Tensors and their Matri.
- Note continued: 6.7.4.2. Fully-discretized equations
- 6.7.5. Stability and Accuracy
- 6.7.5.1. Preliminary comments
- 6.7.5.2. Stability criteria
- 6.7.6. Computer Implementation
- 6.7.7. Numerical Examples
- 6.8. Summary
- Problems
- 7. Non-linear Bending of Elastic Plates
- 7.1. Introduction
- 7.2. The Classical Plate Theory
- 7.2.1. Assumptions of the Kinematics
- 7.2.2. Displacement and Strain Fields
- 7.3. Weak Formulation of the CPT
- 7.3.1. Virtual Work Statement
- 7.3.2. Weak Forms
- 7.3.3. Equilibrium Equations
- 7.3.4. Boundary Conditions
- 7.3.4.1. The Kirchhoff free-edge condition
- 7.3.4.2. Typical edge conditions
- 7.3.5. Stress Resultant-Deflection Relations
- 7.4. Finite Element Models of the CPT
- 7.4.1. General Formulation
- 7.4.2. Tangent Stiffness Coefficients
- 7.4.3. Non-Conforming and Conforming Plate Elements
- 7.5. Computer Implementation of the CPT Elements
- 7.5.1. General Remarks
- 7.5.2. Programming Aspects
- 7.5.3. Post-Computation of Stresses
- 7.6. Numerical Examples using the CPT Elements
- 7.6.1. Preliminary Comments
- 7.6.2. Results of Linear Analysis
- 7.6.3. Results of Non-linear Analysis
- 7.7. The First-Order Shear Deformation Plate Theory
- 7.7.1. Introduction
- 7.7.2. Displacement Field
- 7.7.3. Weak Forms using the Principle of Virtual Displacements
- 7.7.4. Governing Equations
- 7.8. Finite Element Models of the FSDT
- 7.8.1. Weak Forms
- 7.8.2. The Finite Element Model
- 7.8.3. Tangent Stiffness Coefficients
- 7.8.4. Shear and Membrane Locking
- 7.9. Computer Implementation and Numerical Results of the FSDT Elements
- 7.9.1. Computer Implementation
- 7.9.2. Results of Linear Analysis
- 7.9.3. Results of Non-linear Analysis
- 7.10. Transient Analysis of the FSDT
- 7.10.1. Equations of Motion
- 7.10.2. The Finite Element Model
- 7.10.3. Time Approximation
- 7.10.4. Numerical Examples
- 7.11. Summary
- Problems
- 8. Non-linear Bending of Elastic Shells
- 8.1. Introduction
- 8.2. Governing Equations
- 8.2.1. Geometric Description
- 8.2.2. General Strain-Displacement Relations
- 8.2.3. Stress Resultants
- 8.2.4. Displacement and Strain Fields
- 8.2.5. Equations of Equilibrium
- 8.2.6. Shell Constitutive Relations
- 8.3. Finite Element Formulation
- 8.3.1. Weak Forms
- 8.3.2. Finite Element Model
- 8.3.3. Linear Analysis
- 8.3.4. Non-linear Analysis
- 8.4. Summary
- Problems
- 9. Finite Element Formulations of Solid Continua
- 9.1. Introduction
- 9.1.1. Background
- 9.1.2. Summary of Definitions and Concepts from Continuum Mechanics
- 9.1.3. Energetically-Conjugate Stresses and Strains
- 9.2. Various Strain and Stress Measures
- 9.2.1. Introduction
- 9.2.2. Notation
- 9.2.3. Conservation of Mass
- 9.2.4. Green-Lagrange Strain Tensors
- 9.2.4.1. Green-Lagrange strain increment tensor
- 9.2.4.2. Updated Green-Lagrange strain tensor
- 9.2.5. Euler-Almansi Strain Tensor
- 9.2.6. Relationships Between Various Stress Tensors
- 9.2.7. Constitutive Equations
- 9.3. Total Lagrangian and Updated Lagrangian Formulations
- 9.3.1. Principle of Virtual Displacements
- 9.3.2. Total Lagrangian Formulation
- 9.3.2.1. Weak form
- 9.3.2.2. Incremental decompositions
- 9.3.2.3. Linearization
- 9.3.3. Updated Lagrangian Formulation
- 9.3.3.1. Weak form
- 9.3.3.2. Incremental decompositions
- 9.3.3.3. Linearization
- 9.3.4. Some Remarks on the Formulations
- 9.4. Finite Element Models of 2-D Continua
- 9.4.1. Introduction
- 9.4.2. Total Lagrangian Formulation
- 9.4.3. Updated Lagrangian Formulation
- 9.4.4. Computer Implementation
- 9.4.5. A Numerical Example
- 9.5. Conventional Continuum Shell Finite Element
- 9.5.1. Introduction
- 9.5.2. Incremental Equations of Motion
- 9.5.3. Finite Element Model of a Continuum
- 9.5.4. Shell Finite Element
- 9.5.5. Numerical Examples
- 9.5.5.1. Simply-supported orthotropic plate under uniform load
- 9.5.5.2. Four-layer (0°/907/907deg;/0°) clamped plate under uniform load
- 9.5.5.3. Cylindrical shell roof under self-weight
- 9.5.5.4. Simply-supported spherical shell under point bad
- 9.5.5.5. Shallow cylindrical shell under point load
- 9.6. A Refined Continuum Shell Finite Element
- 9.6.1. Backgound
- 9.6.2. Representation of Shell Mid-Surface
- 9.6.3. Displacement and Strain Fields
- 9.6.4. Constitutive Relations
- 9.6.4.1. Isotropic and functionally-graded shells
- 9.6.4.2. Laminated composite shells
- 9.6.5. The Principle of Virtual Displacements and its Discretization
- 9.6.6. The Spectral/hp Basis Functions
- 9.6.7. Finite Element Model and Solution of Non-linear Equations
- 9.6.7.1. The Newton procedure
- 9.6.7.2. The cylindrical arc-length procedure
- 9.6.7.3. Element-level static condensation and assembly of elements
- 9.6.8. Numerical Examples
- 9.6.8.1. A cantilevered plate strip under an end transverse load
- 9.6.8.2. Post-buckling of a plate strip under axial compressive load
- 9.6.8.3. An annular plate with a slit under an end transverse load
- 9.6.8.4. A cylindrical panel subjected to a point load
- 9.6.8.5. Pull-out of an open-ended cylindrical shell
- 9.6.8.6. A pinched half-cylindrical shell
- 9.6.8.7. A pinched cylinder with rigid diaphragms
- 9.6.8.8. A pinched hemisphere with an 18° hole
- 9.6.8.9. A pinched composite hyperboloidal shell
- 9.7. Summary
- Problems
- 10. Weak-Form Finite Element Models of Flows of Viscous Incompressible Fluids
- 10.1. Introduction
- 10.2. Governing Equations
- 10.2.1. Introduction
- 10.2.2. Equation of Mass Continuity
- 10.2.3. Equations of Motion
- 10.2.4. Energy Equation
- 10.2.5. Constitutive Equations
- 10.2.6. Boundary Conditions
- 10.3. Summary of Governing Equations
- 10.3.1. Vector Form
- 10.3.2. Cartesian Component Form
- 10.4. Velocity-Pressure Finite Element Model
- 10.4.1. Weak Forms
- 10.4.2. Semi-discrete Finite Element Model
- 10.4.3. Fully-Discretized Finite Element Model
- 10.5. Penalty Finite Element Models
- 10.5.1. Introduction
- 10.5.2. Penalty Function Method
- 10.5.3. Reduced Integration Penalty Model
- 10.5.4. Consistent Penalty Model
- 10.6. Computational Aspects
- 10.6.1. Properties of the Finite Element Equations
- 10.6.2. Choice of Elements
- 10.6.3. Evaluation of Element Matrices in Penalty Models
- 10.6.4. Post-Computation of Pressure and Stresses
- 10.7. Computer Implementation
- 10.7.1. Mixed Model
- 10.7.2. Penalty Model
- 10.7.3. Transient Analysis
- 10.8. Numerical Examples
- 10.8.1. Preliminary Comments
- 10.8.2. Linear Problems
- 10.8.3. Non-linear Problems
- 10.8.4. Transient Analysis
- 10.9. Non-Newtonian Fluids
- 10.9.1. Introduction
- 10.9.2. Governing Equations in Cylindrical Coordinates
- 10.9.3. Power-Law Fluids
- 10.9.4. White-Metzner Fluids
- 10.9.5. Numerical Examples
- 10.10. Coupled Fluid Flow and Heat Transfer
- 10.10.1. Finite Element Models
- 10.10.2. Numerical Examples
- 10.10.2.1. Heated cavity
- 10.10.2.2. Solar receiver
- 10.11. Summary
- Problems
- 11. Least-Squares Finite Element Models of Flows of Viscous Incompressible Fluids
- 11.1. Introduction
- 11.2. Least-Squares Finite Element Formulation
- 11.2.1. The Navier-Stokes Equations of Incompressible Fluids
- 11.2.2. Numerical Examples
- 11.2.2.1. Low Reynolds number flow past a circular cylinder
- 11.2.2.2. Steady flow over a backward facing step
- 11.2.2.3. Lid-driven cavity flow
- 11.3. A Least-Squares Finite Element Model with Enhanced Element-Level Mass Conservation
- 11.3.1. Introduction
- 11.3.2. Unsteady Flows
- 11.3.2.1. The velocity-pressure-vorticity first-order system
- 11.3.2.2. Temporal discretization
- 11.3.2.3. The standard L2-norm based Least-Squares model
- 11.3.2.4. A modified L2-norm based Least-Squares model with improved element-level mass conservation
- 11.3.3. Numerical Examples: verification Problems
- 11.3.3.1. Steady Kovasznay flow
- 11.3.3.2. Steady flow in a 1 X 2 rectangular cavity
- 11.3.3.3. Steady flow past a large cylinder in a narrow channel
- 11.3.3.4. Unsteady flow
- past a circular cylinder
- 11.3.3.5. Unsteady flow past a large cylinder in a narrow channel
- 11.4. Summary and Future Direction
- Problems
- Appendix 1 Solution Procedures for Linear Equations
- A1.1. Introduction
- A1.2. Direct Methods
- A1.2.1. Preliminary Comments
- A1.2.2. Symmetric Solver
- A1.2.3. Unsymmetric Solver
- A1.3. Iterative Methods
- Appendix 2 Solution Procedures for Non-linear Equations
- A2.1. Introduction
- A2.2. The Picard Iteration Method
- A2.3. The Newton Iteration Method
- A2.4. The Riks and Modified Risk Methods.