Practical Aspects of Finite Element Modelling of Polymer Processing

Authored by a respected scientist with a growing international reputation this is a self–contained text that can be used by the beginners and the experts alike, to study the basic aspects of finite element modelling. It provides a sound physical understanding of the basis on which mathematical models of polymer processes are built. ∗ Written from a chemical engineering rather then a mathematical perspective it enables the reader to get up to speed in a relatively short time ∗ Provides the ′parts and tools′ required to assemble finite element models, applicable to situations that arise under realistic conditions ∗ Discusses and compares specific finite element schemes that provide the most reliable and robust numerical solution procedures for polymer processing models ∗ Practical examples give a wide ranging view of the application of finite element analysis to industrial problems ∗ Describes non–Newtonian fluid mechanics equations in a self–contained, concise and clear manner ∗ Includes clear and simple readily compiled code to model simple problems that can be extended to solve more complex polymer processing problems This book makes the subject accessible to a wide audience ranging from senior under–graduate to post–graduate engineering students, as well as, researchers and practising engineers involved in polymer industry.

1. The Basic Equations of Non–Newtonian Fluid Mechanics. 1.1 Governing Equations of Non–Newtonian Fluid Mechanics 1.2 Classification of Inelastic Time–Independent Fluids 1.3 Inelatic Time–Dependent Fluids 1.4 Viscoelastic Fluids 2. Weighted Residual Finite Element Methods – An Outline. 2.1 Finite Element Approximation 2.2 Numerical Solutions of Differential Equations by the Weighted Residual Method 3. Finite Element Modelling of Polymeric Flow Processes. 3.1 Solution of the Equations of Continuity and Motion 3.2 Modelling of Viscoelastic Flow 3.3 Solution of the Energy Equation 3.4 Imposition of Boundary Conditions in Polymeric Processing Models 3.5 Free Surface and Moving Boundary Problems 4. Working Equations of the Finite Element Schemes. 4.1 Modelling of Steady State Stokes Flow of a Generalized Newtonian Fluid 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 Modelling of Thermal Energy Balance 4.5 Modelling of Transient Stokes Flow of Generalized Newtonian and Non–Newtonian Fluids 5. Rational Approximations and Illustrative Examples. 5.1 Models based on Simplified Domain Geometry 5.2 Models based on Simplified Governing Equations 5.3 Models representing Selected Segments of a Large Domain 5.4 Models based on Decoupled Flow Equations – Simulation of the Flow inside a Cone–and–Plate Rheometer 5.5 Models based on Thin Layer Approximation 5.6 Stiffness Analysis of Solid Polymeric Materials 6. Finite Element Software – Main Components. 6.1 General Consideration to Finite Element Mesh Generation 6.2 Main Components of Finite Element Processor Programs 6.3 Numerical Solution of the Global Systems of Algebraic Equations 6.4 Solutions Algorithms based on the Gaussian Elimination Method 6.5 Computation Errors 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 Axisymmetric 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 Calculua Relations 8.3 Tensor Algebra 8.4 Some Tensor Calculus Relations Author Index. Subject Index.