1st Edition

# Magnetic Materials and 3D Finite Element Modeling

By

## João Pedro A. Bastos

,

ISBN 9781466592513
Published October 16, 2013 by CRC Press
402 Pages 263 B/W Illustrations

USD \$215.00

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## Book Description

Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering.

The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes.

• Furnishes algorithms in computational language

• Summarizes concepts related to the FE method

• Uses classical algebra to present the method, making it easily accessible to engineers

Written in an easy-to-understand tutorial format, the text begins with a short presentation of Maxwell’s equations, discusses the generation mechanism of iron losses, and introduces their static and dynamic components. It then demonstrates simplified models for the hysteresis phenomena under alternating magnetic fields. The book also focuses on the Preisach and Jiles–Atherton models, discusses vector hysterisis modeling, introduces the FE technique, and presents nodal and edge elements applied to 3D FE formulation connected to the hysteretic phenomena.

The book discusses the concept of source-field for magnetostatic cases, magnetodynamic fields, eddy currents, and anisotropy. It also explores the need for more sophisticated coding, and presents techniques for solving linear systems generated by the FE cases while considering advantages and drawbacks.

Statics and Quasi-Statics Electromagnetics - Brief Presentation
Introduction
The Maxwell Equations
The Maxwell Equations: Local Form
The Maxwell Equations: Integral Form
The Maxwell Equations in Low Frequency
The Electrostatics
Magnetostatic Fields
Magnetic Materials
Inductance and Mutual Inductance
Magnetodynamic Fields
Fields Defined by Potentials
Final Considerations
References

Ferromagnetic Materials and Iron Losses
Introduction
Basic Concepts
Losses Components
Iron Losses under Alternating, Rotating and DC Biased Inductions
Final Considerations
References

Scalar Hysteresis Modeling
Introduction
The Preisach’s Scalar Model
The Jiles-Atherton Scalar Model
Final Considerations
References

Vector Hysteresis Modeling
Introduction
Vector Model Obtained with the Superposition of Scalar Models
Vector Generalizations of the Jiles-Atherton Scalar Models
Some Remarks Concerning the Vector Behavior of Hysteresis
Final Considerations
References

Brief Presentation of the Finite Element Method
Introduction
The Galerkin Method: Basic Concepts using Real Coordinates
Generalization of the FEM: Using Reference Coordinates
Numerical Integration
Some Finite Elements
Using Edge Elements
References

Using Nodal Elements with Magnetic Vector Potential
Introduction
Main Equations
Applying Galerkin Method
Uniqueness of the Solution; the Coulomb’s Gauge
Implementation
Example and Comparisons
Final Considerations
References

The Source-Field Method for 3D Magnetostatic Fields
Introduction
The Magnetostatic Case – Scalar Potential
The Magnetostatic Case – Vector Potential
Implementation Aspects and Conventions
Computational Implementation
Example and Results
References

The Source-Field Method for 3D Magnetodynamic Fields
Introduction
Formulation Considering Eddy Currents – Time Stepping
Formulation Considering Eddy Currents – Complex Formulation
Field-Circuit Coupling
Computational Implementation
The Differential Permeability Method
Example and Results
References

A Matrix-Free Iterative Solution Procedure for Finite Element Problems
Introduction
The Classical FEM: T-Scheme
The Proposed Technique: N-Scheme
Implementation
Convergence
Implementation of N-Scheme with SOR
Applying Non-Stationary Iterative Solver to the N-Scheme
CG Algorithm Implementation
Examples and Results
Results and Discussion
References

...

## Author(s)

### Biography

João Pedro A. Bastos completed his doctoral thesis (Docteur d’Etat) at Université Pierre et Marie Curie, Paris VI, in 1984. He then returned to Brazil at the Universidade Federal de Santa Catarina (UFSC) and became a full professor in 1992. He founded GRUCAD in 1985—a group that plays an important role in the development of the area of electromagnetic field analysis in Brazil. Dr. Bastos worked as a visiting professor at the University of Akron, Ohio, in 1992 and 2001. He is also the author of four books and has published several papers in periodic journals and conferences.

Nelson Sadowski received his engineering and master of science degrees from Universidade Federal de Santa Catarina (UFSC) in 1982 and 1985, respectively. In 1993, he received his PhD from the Institut National Polytechnique de Toulouse (INPT). He then returned to Brazil and continued his research and teaching activities at GRUCAD-UFSC and became a full professor in 1996. In 2000, he received his HDR (Habilitation) diploma, also from the INPT. Dr. Sadowski has been active on international agreements with universities in France, Germany, and Belgium. He is also the author of several conference and journal papers. He is also very active on industrial consulting.

## Reviews

"… an important contribution to the area of numerical design in electromagnetics and in particular in low frequency design, including electric machines and actuators. It is a thorough, balanced presentation of the theory and its application."
—Dr. Nathan Ida, The University of Akron

"Written by specialists in the modeling of electromagnetism …useful for researchers and teachers with experience in the area or for students, wishing to acquire knowledge in the field."
—F. Bouillaultm, Professor at Paris Sud University

"Anyone who wants to learn how to model magnetic cores, especially transformer core materials, in 3D will find this book extremely useful."
IEEE Electrical Insulation Magazine, January/February 2015