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 |  موضوع: كتاب Practical Aspects of Finite Element Modelling of Polymer Processing الأربعاء 20 فبراير 2019, 9:00 pm | |
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أخوانى فى الله
أحضرت لكم كتاب
Practical Aspects of Finite Element Modelling of Polymer Processing
Vahid Nassehi
Chemical Engineering Dept., Loughborough University
ويتناول الموضوعات الأتية :
Contents
Preface xiii
1 THE BASIC EQUATIONS OF NON-NEWTONIAN
FLUID MECHANICS 1
1.1 Governing Equations of Non-Newtonian Fluid Mechanics 2
1.1.l Continuity 2
1.1.2 Equation of motion 2
1.1.3 Thermal energy equation 3
1.2 Classification of Inelastic Time-Independent Fluids
1.2.1 Newtonian fluids
1.2.2 Generalized Newtonian fluids
1.3 Inelastic Time-Dependent Fluids
1.4 Viscoelastic Fluids
1.4.1 Model (material) parameters used in viscoelastic constitutive
1.4.2 Differential constitutive equations for viscoelastic fluids
1.4.3 Single-integral constitutive equations for viscoelastic fluids
1.4.4 Viscometric approach - the (CEF) model
equations
References
2 WEIGHTED RESIDUAL FINITE ELEMENT
METHODS - AN OUTLINE
2.1 Finite Element 19
2.1.1 Interpolation models 20
2.1.2 Shape functions of commonly used finite elements 23
2.1.3 Non-standard elements 27
2.1.4 Local 29
2.1.S Order of continuity of finite elements 32
2.1.6 Convergence 33
2.1.7 Irregular and curved elements - isoparametric mapping 34
2.1.8 Numerical integration 38
2.1.9 Mesh refinement - h- and p-versions of the finite element method 40viii CONTENTS
2.2 Numerical Solution of Differential Equations by the Weighted
Residual Method
2.2.1 Weighted residual statements in the context of finite element
2.2.2 The standard Galerkin method
2.2.2* Galerkin finite element procedure - a worked example
2.2.3 Streamline upwind Petrov-Galerkin method
2.2.3* Application of upwinding - a worked example
2.2.4 Least-squares finite element method
2.2.5 Solution of time-dependent problems
discretizations
References
3 FINITE ELEMENT MODELLING OF POLYMERIC
FLOW PROCESSES
3.1 Solution of the Equations of Continuity and Motion
3.1.1 The U-V-P scheme
3.1.2 The U-V-P scheme based on the slightly compressible
continuity equation
3.1.3 Penalty schemes
3.1.4 Calculation of pressure in the penalty schemes - variational
recovery method
3.1.5 Application of Green’s theorem - weak formulations
3.1.6 Least-squares scheme
3.2 Modelling of Viscoelastic Flow
3.2.1 Outline of a decoupled scheme for the differential constitutive
models
Derivation of the working equations
models
3.2.2 Finite element schemes for the integral constitutive
3.2.3 Non-isothermal viscoelastic flow
3.3 Solution of the Energy Equation
3.4 Imposition of Boundary Conditions in Polymer Processing
Models
3.4.1 Velocity and surface force (stress) components
Inlet conditions
Line of symmetry
Solid walls
Exit conditions
3.4.2 Slip-wall boundary conditions
3.4.3 Temperature and thermal stresses (temperature gradients)
3.5 Free Surface and Moving Boundary Problems
3.5.1 VOF method in ‘Eulerian’ frameworks
3.5.2 VOF method in ‘Arbitrary Lagrangian-Eulerian’
3.5.3 VOF method in ‘Lagrangian’ frameworks
frameworks
References
108CONTENTS ix
4 WORKING EQUATIONS OF THE FINITE
ELEMENT SCHEMES
4.1 Modelling of Steady State Stokles Flow of a Generalized
Newtonian Fluid
4.1.1 Governing equations in two-dimensional Cartesian coordinate
4.1.2 Governing equations in two-dimensional polar coordinate
4.1.3 Governing equations in axisymmetric coordinate systems
4.1.4 Working equations of the L[-V-P scheme in Cartesian
4.1.5 Working equations of the W V - P scheme in polar coordinate
4.1.6 Working equations of the WV-P scheme in axisymmetric
4.1.7 Working equations of the continuous penalty scheme in
4.1.8 Working equations of the continuous penalty scheme in polar
4.1.9 Working equations of the continuous penalty scheme in
4.1.10 Working equations of the discrete penalty scheme in Cartesian
4.1.11 Working equations of the least-squares scheme in Cartesian
systems
systems
coordinate systems
systems
coordinate systems
Cartesian coordinate systems
coordinate systems
axisymmetric coordinate systems
coordinate systems
coordinate systems
4.2 Variations of Viscosity
4.3 Modelling of Steady-State Viscometric Flow - Working
Equations of the Continuous Penalty Scheme in Cartesian
Coordinate Systems
4.4.1 Working equations of the streamline upwind (SU) scheme for
4.4 Modelling of Thermal Energy Balance
the steady-state energy equation in Cartesian, polar and
axisymmetric coordinate sys,tems
schemes
4.4.2 Least-squares and streamline upwind Petrov-Galerkin (SUPG)
4.5 Modelling of Transient Stokes Flow of Generalized Newtonian
References
and Non-Newtonian Fluids
5 RATIONAL APPROXIMATIONS AND
ILLUSTRATIVE EXAMPLES
5.1 Models Based on Simplified Domain Geometry
5.1.1 Modelling of the dispersion stage in partially filled batch
internal mixers
Flow simulation in a single blade partially jilled mixer
Flow simulation in a partially jlled twin blade mixer
146x CONTENTS
Models Based on Simplified Governing Equations
5.2.1 Simulation of the Couette flow of silicon rubber - generalized
5.2.2 Simulation of the Couette flow of silicon rubber - viscoelastic
Newtonian model
model
Models Representing Selected Segments of a Large
Domain
5.3.1 Prediction of stress overshoot in the contracting sections of a
5.3.2 Simulation of wall slip in a rubber mixer
Models Based on Decoupled Flow quations - Simulation of
the Flow Inside a Cone-and-Plate Rheometer
5.4.1 Governing equations
5.4.2 Finite element discretization of the governing equations
Models Based on Thin Layer Approximation
5.5.1 Finite element modelling of flow distribution in an
5.5.2 Generalization of the Hele-Shaw approach to flow in thin
symmetric flow domain
extrusion die
curved layers
Asymptotic expansion scheme
Stiffness Analysis of Solid Polymeric Materials
5.6.1 Stiffness analysis of polymer composites filled with spherical
particles
References
6 FINITE ELEMENT SOFTWARE - MAIN
COMPONENTS
General Considerations Related to Finite Element Mesh
Generation
6.1.1 Mesh types
Block-structured grids
Overset grids
Hybrid grids
6.1.2 Common methods of mesh generation
Main Components of Finite Element Processor Programs
Numerical Solution of the Global Systems of Algebraic
Equations
6.3.1 Direct solution methods
Pivoting
Guussiun elimination with partial pivoting
Number of operations in the Guussiun elimination method
Solution algorithms based on the Gaussian elimination
method
6.4.1 LU decomposition technique
6.4.2 Frontal solution technique
205CONTENTS xi
6.5 Computational Errors
6.5.1 Round-off error
6.5.2 Iterative improvement of the solution of systems of linear
equations
References
7 COMPUTER SIMULATIONS - FINITE ELEMENT
PROGRAM
7.1 Program Structure and Algorithm
7.2 Program Specifications
7.3 Input Data File
7.4 Extension of PPVN.f to Axisyrnmetric Problems
7.5 Circulatory Flow in a Rectangular Domain
7.6 Source Code of PPVN.f
References
8 APPENDIX - SUMMARY OF VECTOR AND
TENSOR ANALYSIS
8.1 Vector Algebra
8.2 Some Vector Calculus Relations
8.2.1 Divergence (Gauss’) theorem
8.2.2 Stokes theorem
8.2.3 Reynolds transport theorem
8.2.4 Covariant and contravariant vectors
8.2.5 Second order tensors
8.3 Tensor Algebra
8.4 Some Tensor Calculus Relatiolns
8.3.1 Invariants of a second-order tensor ( T )
8.4.1 Covariant, contravariant and mixed tensors
8.4.2 The length of a line and metric tensor
Author Index
Subject Index
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