FINITE ELEMENTS, ELECTROMAGNETICS AND DESIGN

Transcription

1 FINITE ELEMENTS, ELECTROMAGNETICS AND DESIGN Edited by S. RATNAJEEVAN H. HOOLE Professor of Engineering Harvey Mudd College Claremont, CA, USA and Senior Fellow, 1993/94 Department of Electrical Engineering National University of Singapore Singapore 1995 ELSEVIER Amsterdam - Lausanne - New York - Oxford - Shannon - Tokyo

2 S. Ratnajeevan H. Hoole (Ed.) TABLE OF CONTENTS Dedication Editor's Preface Table of Contents List of Contributors v vii ix xv 1. S. Ratnajeevan H. Hoole, "Electromagnetic Field Computation" The Need for Computer Assisted Analysis and Design The Governing Equations Simplified Equations Differential and Integral Methods The Finite Element Method - A Simple Presentation The Galerkin Scheme T. Nakata, N. Takahashi, and K. Fujiwara, "Solution of 3-D Eddy Current Problems by Finite Elements" Introduction Linear Finite Element Analysis (The А-ф Method) Nonlinear Finite Element Analysis (The А-ф Method) Various Kinds of Methods Various Finite Elements G. Bedrosian and M. V. K. Chari, "Coupling Finite Element Models of Electrical Machinery to External Circuits" Introduction The Finite Element Method Circuit Models of Electrical Machinery Magnetostatic Model of a Transformer Eddy Current Model of an Induction Motor with Locked Rotor Rotating Grid Model of a Generator Conclusion S. J. Salon, С J. Slavik, M. J. DeBortoli and G. Reyne, "Analysis of Magnetic Vibrations in Rotating Electric Machines" Introduction Dynamic Electromechanical Finite Element Analysis of Electric Machines 120

3 X Contents 4.3 Magnetic Force Computation Vibrations of the Stator Core Applications Conclusions A Appendix: Frequency and Spatial Distribution Harmonics of the Magnetic Flux Field of a Cage Induction Motor B Appendix: Relationship of 2f, 4f, 6f and 8f Induction Motor Vibrations to Air Gap Magnetic Flux Harmonics С Appendix: Extension of Stress Tensor Equation to Standard Maxwell Stress Expressions D Appendix: Kerruish's Formulae for the Deflection of Smooth Thick Cylindrical Ring Influenced by 2-Pole-Pair and 4-Pole-Pair Force Waves Bruce E. Mac Neal and J. R. Brauer, "Electrical Circuits and Finite Element Field Models: A General Approach" Introduction The Finite Element Formulation Circuits and Finite Elements Example Problems Conclusions G. Meunier and J.-C. Sabonnadiere, "Modeling Magnetic Materials for Finite Element Simulation" Introduction Setting-up of the B(H) Relationship Finite Element Formulations Model of Permanent Magnets Model of Soft Magnetic Materials Conclusion F. Ossart, G. Meunier and J.-C. Sabonnadiere, "Finite Elements in the Analysis of Recording Devices" Introduction The Magnetic Recording Process Modeling Hysteresis Computation of Magnetic Field Including Hysteresis Conclusion A. Konrad, and I. A. Tsukerman, "Application of Integral and Differential Methods to Electromagnetic Field Problems" Some Mathematical Tools for Field Problems 259

4 S. Ratnajeevan H. Hoole (Ed.) XI 8.2 Example of Integral Methods: Capacitance Example of Integral Methods: Wire Antennas The Finite Element Method Example of FEM: Homogeneous Waveguides Example of FEM: Inhomogeneous Waveguides Example of FEM: Scattering Conclusion A Appendix: Capacitance by Harrington's Method B Appendix: The Wire Antenna C Appendix: FEA of TM and ТЕ Modes in a Waveguide Srisivane Subramaniam and S. Ratnajeevan H. Hoole, "Edge Elements" The Finite Element Method The History of the Edge-Based Finite Element Method Rectangular Tangential Vector Elements Triangular Tangential Elements Compatibility and Unisolvence Normal Edge Elements Higher Order Elements S. Ratnajeevan H. Hoole, "Synthesizing Devices through Finite Element Performance Modeling" Inverse Problems The State of the Art of Inverse Problem Solution in Finite Element Analysis Differentiation of the Finite Element Matrices An Example and Mesh Considerations Force Mapping of Parameters Mathematical Optimization System Identifiction Constrained Optimization S. Ratnajeevan H. Hoole, "Parallel Algorithms and Matrix Solvers in Finite Element Field Analysis" Introduction Coding Considerations Electromagnetic Field Analysis Pre- and Post- Processing Equation Formation Matrix Solution Adaptive Mesh Generation Inverse Problems Multigrid Algorithms Coupled Problems 455

5 XII Contents Systems with Limited Processors S. Kalaichelvan, "Numerical Methods for Characterizing High-Speed Interconnects in Digital Circuits" Introduction Digital System and Signal Integrity Electromagnetic Field Equations Field Formulations Numerical Solution Techniques Conclusions T. Kirubarajan and P. Ratnamahilan P. Hoole, "Electromagnetic Signal Processing: A A Case Study" 499 Introduction 499 Overview 500 Electromagnetic Signal Measurement 503 Application of the Estimator: Electromagnetic Vibration Controller 511 Summary 522 Appendix: The State Estimator Using MATLAB P. Ratnamahilan P. Hoole and B. A. A. P. Balasuriya, "Computation of Pulsed Electromagnetic Fields: With Neural Network Applications" Outline Basic Equations for Transient Electromagnetic Fields Some Common Types of Transient Pulses The Basic Linear Element for Integral Solution of Pulsed Electromagnetic FieldS Finite Element Formulation for the Wave Equation General Formulations for the Time-Domain Finite Element Scheme Analysis of Stability and Accuracy Software Techniques for the One Dimensional Wave Equation Neural Network Filter for Electromagnetic Noise A Appendix: Field Radiated by Line Current B Appendix: Program Transmission С Appendix: The Hopfield Algorithm for Recognizing Noise in EM Pulses Dhammika Kurumbalapitiya and S. Ratnajeevan H. Hoole, "Open Boundary Problems

6 S. Ratnajeevan H. Hoole (Ed.) with Finite Elements" Open Boundary Problems Existing Computational Schemes Implementational Aspects Examples Abd. A. Arkadan, "On the Features of Electromagnetic Finite Element Analysis Software Packages" Introduction Field Solvers Preprocessor Postprocessor 610 Appendix A: Vector Identities 613 Appendix B: The Uniqueness of the Scalar Potential 614 Appendix C: The Uniqueness of the Vector Field 616 Appendix D: Integration of Triangular Coordinates 617 Collected Bibliography 621