Practical Aspects of Finite Element Modelling of Polymer Processing

by Vahid Nassehi

Providing a detailed reference that explains methodology and practice, Practical Aspects of Finite Element Modeling of Polymer Processing facilitates the transition from the theoretical treatment of the subject through to practical procedure via:

• a descriptive approach that does not require knowledge of advanced mathematical topics
• a detailed methodology for finite element modeling of various polymer processing flows
• working equations of various polymeric flow models in co-ordinate systems, which can be directly translated into computer code
• modelling methods illustrated by worked examples

Practical Aspects of Finite Element Modeling of Polymer Processing develops finite element solution schemes for the governing equations of polymer processing flows and provides coverage of:

• Equations of non-Newtonian fluids mechanics
• Weighted residual finite element methods
• Polymeric flow process modeling
• Working equations of finite element schemes
• Finite element software
• Computer simulations

Contents:

1. The Basic Equations of Non-Newtonian Fluid Mechanics
   • Governing Equations of Non-Newtonian Fluid Mechanics
   • Classification of Inelastic Time-Independent Fluids
   • Inelatic Time-Dependent Fluids
   • Viscoelastic Fluids

2. Weighted Residual Finite Element Methods - An Outline
   • Finite Element Approximation
   • Numerical Solutions of Differential Equations by the Weighted Residual Method

3. Finite Element Modelling of Polymeric Flow Processes
   • Solution of the Equations of Continuity and Motion
   • Modelling of Viscoelastic Flow
   • Solution of the Energy Equation
   • Imposition of Boundary Conditions in Polymeric Processing Models
   • Free Surface and Moving Boundary Problems

4. Working Equations of the Finite Element Schemes
   • Modelling of Steady State Stokes Flow of a Generalized Newtonian Fluid
   • Variations of Viscosity
   • Modelling of Steady State Viscometric Flow - Working Equations of the Continuous Penalty Scheme in Cartesian Coordinate Systems
   • Modelling of Thermal Energy Balance
   • Modelling of Transient Stokes Flow of Generalized Newtonian and Non-Newtonian Fluids

5. Rational Approximations and Illustrative Examples
   • Models based on Simplified Domain Geometry
   • Models based on Simplified Governing Equations
   • Models representing Selected Segments of a Large Domain
   • Models based on Decoupled Flow Equations - Simulation of the Flow inside a Cone-and-Plate Rheometer
   • Models based on Thin Layer Approximation
   • Stiffness Analysis of Solid Polymeric Materials

6. Finite Element Software - Main Components
   • General Consideration to Finite Element Mesh Generation
   • Main Components of Finite Element Processor Programs
   • Numerical Solution of the Global Systems of Algebraic Equations
   • Solutions Algorithms based on the Gaussian Elimination Method
   • Computation Errors

7. Computer Simulations - Finite Element Program
   • Program Structure and Algorithm
   • Program Specifications
   • Input Data File
   • Extension of PPVN.f to Axisymmetric Problems
   • Circulatory Flow in a Rectangular Domain
   • Source Code of PPVN.f

Appendices - Summary of Vector and Tensor Analysis

1. Vector Algebra
2. Some Vector Calculua Relations
3. Tensor Algebra
4. Some Tensor Calculus Relations

Index

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