Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics E-Book

Shen R. Wu

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 436

Veröffentlichungsjahr: 2012

Beschreibung

A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: * Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory * Element Technology discusses four-node, three-node, eight-node, and two-node element theories * Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage * Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.

Leseprobe

Contents

Cover

Title Page

Copyright

Dedication

Preface

Part I: Fundamentals

Chapter 1: Introduction

1.1 ERA OF SIMULATION AND COMPUTER AIDED ENGINEERING

1.2 PRELIMINARIES

Chapter 2: Framework Of Explicit Finite Element Method For Nonlinear Transient Dynamics

2.1 TRANSIENT STRUCTURAL DYNAMICS

2.2 VARIATIONAL PRINCIPLES FOR TRANSIENT DYNAMICS

2.3 FINITE ELEMENT EQUATIONS AND THE EXPLICIT PROCEDURES

2.4 MAIN FEATURES OF THE EXPLICIT FINITE ELEMENT METHOD

2.5 ASSESSMENT OF EXPLICIT FINITE ELEMENT METHOD

Part II: Element Technology

Chapter 3: Four-node shell element (reissner–mindlin plate theory)

3.1 FUNDAMENTALS OF PLATES AND SHELLS

3.2 LINEAR THEORY OF R-M PLATE

3.3 INTERPOLATION FOR FOUR-NODE R-M PLATE ELEMENT

3.4 REDUCED INTEGRATION AND SELECTIVE REDUCED INTEGRATION

3.5 PERTURBATION HOURGLASS CONTROL—BELYTSCHKO–TSAY ELEMENT

3.6 PHYSICAL HOURGLASS CONTROL—BELYTSCHKO–LEVIATHAN (QPH) ELEMENT

3.7 SHEAR PROJECTION METHOD—BATHE–DVORKIN ELEMENT

3.8 ASSESSMENT OF FOUR-NODE R-M PLATE ELEMENT

Chapter 4: Three-Node Shell Element (Reissner–Mindlin Plate Theory)

4.1 FUNDAMENTALS OF A THREE-NODE C 0 ELEMENT

4.2 DECOMPOSITION METHOD FOR C0 TRIANGULAR ELEMENT WITH ONE-POINT INTEGRATION

4.3 DISCRETE KIRCHHOFF TRIANGULAR ELEMENT

4.4 ASSESSMENT OF THREE-NODE R-M PLATE ELEMENT

Chapter 5: Eight-Node Solid Element

5.1 TRILINEAR INTERPOLATION FOR THE EIGHT-NODE HEXAHEDRON ELEMENT

5.2 LOCKING ISSUES OF THE EIGHT-NODE SOLID ELEMENT

5.3 ONE-POINT REDUCED INTEGRATION AND THE PERTURBED HOURGLASS CONTROL

5.4 ASSUMED STRAIN METHOD AND SELECTIVE/REDUCED INTEGRATION

5.5 ASSUMED DEVIATORIC STRAIN

5.6 AN ENHANCED ASSUMED STRAIN METHOD

5.7 TAYLOR EXPANSION OF ASSUMED STRAIN ABOUT THE ELEMENT CENTER

5.8 EVALUATION OF EIGHT-NODE SOLID ELEMENT

Chapter 6: Two-Node Element

6.1 TRUSS AND ROD ELEMENT

6.2 TIMOSHENKO BEAM ELEMENT

6.3 SPRING ELEMENT

6.4 SPOT WELD ELEMENT

Part III: Material Models

Chapter 7: Material Model Of Plasticity

7.1 FUNDAMENTALS OF PLASTICITY

7.2 CONSTITUTIVE EQUATIONS

7.3 SOFTWARE IMPLEMENTATION

7.4 EVALUATION OF SHELL ELEMENTS WITH PLASTIC DEFORMATION

Chapter 8: Continuum Mechanics Model Of Ductile Damage

8.1 CONCEPT OF DAMAGE MECHANICS

8.2 GURSON'S MODEL

8.3 CHOW'S ISOTROPIC MODEL OF CONTINUUM DAMAGE MECHANICS

8.4 CHOW'S ANISOTROPIC MODEL OF CONTINUUM DAMAGE MECHANICS

Chapter 9: Models Of Nonlinear Materials

9.1 VISCOELASTICITY

9.2 POLYMER AND ENGINEERING PLASTICS

9.3 RUBBER

9.4 FOAM

9.5 HONEYCOMB

9.6 LAMINATED GLAZING

Part IV: Contact And Constraint Conditions

Chapter 10: Three-Dimensional Surface Contact

10.1 EXAMPLES OF CONTACT PROBLEMS

10.2 DESCRIPTION OF CONTACT CONDITIONS

10.3 VARIATIONAL PRINCIPLE FOR THE DYNAMIC CONTACT PROBLEM

10.4 PENALTY METHOD AND THE REGULARIZATION OF VARIATIONAL INEQUALITY

Chapter 11: Numerical Procedures For Three-Dimensional Surface Contact

11.1 A CONTACT ALGORITHM WITH SLAVE NODE SEARCHING MASTER SEGMENT

11.2 A CONTACT ALGORITHM WITH MASTER SEGMENT SEARCHING SLAVE NODE

11.3 METHOD OF CONTACT TERRITORY AND DEFENSE NODE

11.4 PINBALL CONTACT ALGORITHM

11.5 EDGE (LINE SEGMENT) CONTACT

11.6 EVALUATION OF CONTACT ALGORITHM WITH PENALTY METHOD

Chapter 12: Kinematic Constraint Conditions

12.1 RIGID WALL

12.2 RIGID BODY

12.3 EXPLICIT FINITE ELEMENT PROCEDURE WITH CONSTRAINT CONDITIONS

12.4 APPLICATION EXAMPLES WITH CONSTRAINT CONDITIONS

References

Index

Cover image: © iStockphoto/oonal

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Library of Congress Cataloging-in-Publication Data

Wu, Shen R., 1945– Introduction to the explicit finite element method for nonlinear transient dynamics / Shen R. Wu, Lei Gu. p. cm. Includes index. ISBN 978-0-470-57237-5 (hardback) 1. Finite element method. 2. Numerical analysis. I. Gu, Lei, 1959–II. Title. QA297.W83 2012 518′.25–dc23 2012007291

ISBN: 9780470572375

To our families and friends for their love and support.

PREFACE

This book pertains to the use of the explicit finite element method in simulations of nonlinear transient dynamics problem. The explicit finite element method has developed into a useful tool in solving the large deformation transient dynamics problem. With a better solution to the difficult problems that are commonly encountered when using the implicit finite element method, we are able to widen the application to various contact/impact engineering problems.

Many theories and computational methods of the explicit finite element method have been widely discussed in various technical journals. However, the authors feel that there is a lack of a more systematic and comprehensive reference book on this particular subject. On the basis of years of experience in the application and research of the explicit finite element method, the authors feel that there is a need for such a reference book. We hope that this book can bring some useful insights and a better understanding to researchers and engineers in their study in this area.

The book is organized in four parts containing 12 chapters. Part I describes the fundamentals of the explicit finite element method for nonlinear transient dynamics. Part II describes the finite element technologies. Part III discusses material models. Part IV devotes to contact algorithms and constraint conditions.

Chapter 1 gives an introduction to the explicit finite element method and a summary of elasticity in preparation for our discussions in later parts of the book. Chapter 2 covers the basic variational principle for transient dynamics of large deformation and the formulation of explicit finite element equations. The convergence and accuracy assessment for applications of linear elastodynamics are also introduced. Chapter 3 describes the four-node shell elements based on Reissner–Mindlin plate theory. Various methods, such as reduced integration and projection method, to avoid or control shear locking are discussed. The convergence theory for Bathe–Dvorkin element is briefly introduced. Chapter 4 describes the three-node shell element (based on Reissner–Mindlin plate theory). Techniques, such as decomposition and discrete Kirchhoff theory, to control shear locking are discussed. Chapter 5 covers the eight-node solid element with several methods to control shear locking. Two numerical examples of elastodynamics problems are used to evaluate the elements discussed in Chapters 3–5. Chapter 6 introduces several two-node elements, which can be used for modeling a special feature of structural connection, including spring elements, spot weld, etc. Chapter 7 provides a review of the plasticity theory and the discussion of its material models for software implementation in the explicit finite element. Chapter 8 gives a brief discussion of material failure models based on continuum damage mechanics. It covers Gurson's micromechanics model and Chow's phenomenological models. Chapter 9 describes models of other nonlinear materials, including viscoelasticity, polymer, rubber, foam, honeycomb, and laminated glazing. Chapter 10 discusses contact problems. Several example problems with analytical solutions are introduced. The variational inequality for large deformation of transient dynamics is derived. The penalty method is introduced to regularize the variational inequality. Chapter 11 introduces the numerical procedures for three-dimensional contact based on the penalty method discussed in Chapter 10. Chapter 12 introduces several kinematic constraint conditions used to model certain features of nonlinear transient dynamics, including rigid wall and rigid body.

Unlike the implicit finite element method, the explicit finite element method is still in its developing stages. The above introduction only serves as a foundation for further discussion and exploration. We are primarily concerned about the large deformation of transient dynamics. The explicit finite element method faces similar challenges as the implicit finite element method in regard to certain basic theories and computational methods. The authors hope that this book will generate more interest among fellow researchers to collaborate and study these topics to bring about further improvement in engineering applications.

We wish to express our sincere appreciation to our colleagues and friends who have shown their enthusiastic encouragement in this book project. We would like to express our sincere gratitude to Professor J.T. Oden of University of Texas at Austin and Professor T. Belytschko of Northwestern University for their valuable inputs. We want to extend our deep appreciation to the team at Wiley. We specially thank Dr. Priya Prasad for his continuous encouragement and support in the publication of this book. Finally, we would like to thank our families for their love and support, for without them our work in this book would not have been possible.

SHEN R. WU and LEI GU

PART I

FUNDAMENTALS