Meshless Methods in Solid Mechanics

by Chen, Youping; Lee, James D.; Eskandarian, Azim

• ISBN13: 9780387307367
• ISBN10: 0387307362
• Format: Hardcover
• Copyright: 2006-06-01
• Publisher: Springer Verlag

Summary

"The main objective of this book is to provide a textbook for graduate courses on the computational analysis of continuum and solid mechanics based on meshless (also known as mesh free) methods. It can also be used as a reference book for engineers and scientists who are exploring the physical world through computer simulations. Emphasis of this book is given to the understanding of the physical and mathematical characteristics of the procedures of computational solid mechanics. It naturally brings the essence, advantages and challenging problems of meshless methods into the picture."--BOOK JACKET.

Author Biography

Professor James D. Lee earned his Ph.D from Princeton University in 1971 and has been teaching and/or doing research in universities (Purdue U., West Virginia U., U. of Akron, U. of Minnesota and GWU), industry (The General Tire and Rubber Company), and US government laboratories (NIST and NASA). His research has included liquid crystals, fracture mechanics, composite materials, numerical analyses, control, robotics, metal forming process, finite element methods, meshless methods, atomistic and micro-continuum physics. He has directed eight doctoral dissertations and several master theses, and has published more than 100 technical papers including 50 referred journal articles. He is a registered Professional Engineer in Washington, DC and a member of ASME, American Academy of Mechanics, New York Academy of Science, and Sigma Xi. Dr. Youping Chen is a senior research scientist at the School of Engineering and Applied Science of GWU. She is currently contributing to two major research centers within GWU: The Center for Intelligent Systems Research in smart materials and the FHWA/NHTSA National Crash Analysis Center in computational mechanics. She has over 13 years of experience in engineering mechanics and structural dynamics. Her research experience includes modeling and simulating high-speed railway system, thermoplastic analysis of high-speed impact, meshless methods, atomistic physics and continuum mechanics. She has been conducting advanced research at NCAC on meshless and optimization methods for structures under impact loading. Dr. Chen is currently extending the atomistic physics and continuum mechanics theory in modeling of electromechanical and smart materials. She received a M.S. degree in Engineering Mechanics from Huazhong University of Science and Technology, China in 1991 and D.Sc. degree in Mechanical Engineering from The George Washington University in 2002. Professor Azim Eskandarian was the co-founder (in 1992) and the Director of the FHWA/NHTSA National Crash Analysis Center from 1998-2003, where he conducted extensive research in impact dynamics for crashworthiness of structures/materials. He has conducted research in optimization of structures under impact. This research required exploring meshless methods as a better alternative to non-linear explicit dynamic finite element methods due to reshaping of the structures, contact algorithms, and various complexities of impact phenomena. This research is continuing and has lead to the development of draft manuscript for the proposed book addressing the advantages and critical issues of meshless methods in Solid mechanics. Prof. Eskandarian has twenty-one years of experience in engineering R&D, six years in industry and fifteen years in academia. Dr. Eskandarian is the founding Director of the Center for Intelligent Systems Research which focuses in smart materials/systems and intelligent methods in transportation and automotive applications. He has been Principal Investigator and Co-principal Investigator of over $18.6 million of sponsored research anddirected research groups of more than fifty, including faculty, staff, and students. He has published over 100 technical journal and conference papers. He is a member of ASME, ASCE, SAE, Sigma Xi, Tau Beta Pi, Pi Tau Sigma, and serves on several professional committees. Prof. Eskandarian earned his doctoral and Masters and bachleros degrees in Mechanical engineering in 1991, 1983, and 1982 from George Washington University (Washington, DC), Virginia Polytechnique Institute and State University (Blacksburg , VA) and GWU, respectively.

Table of Contents

Acknowledgments	vi
Preface	vii
1 Introduction	1	(5)
Foundation of Physical Theories	1	(1)
Atomistic Modeling and Computation	2	(2)
PDE-Based Continuum Modeling and Computation	4	(2)
2 Fundamental of Continuum Mechanics	6	(25)
Kinematics	6	(5)
Basic Laws of Motion	11	(5)
Constitutive Theory	16	(4)
Thermoviscoelastic Solid and Its Special Cases	20	(4)
Problems	24	(7)
3 Fundamentals of Finite Element Method	31	(24)
Integral Formulation of Continuum Problems	31	(2)
Weighted Residual Methods	33	(4)
Variational Principle	37	(5)
Introduction to Finite Element Method	42	(1)
Shape Functions in Finite Element Method	42	(5)
Finite Element Formulation	47	(1)
Numerical Integration in Finite Element Method	48	(4)
Problems	52	(3)
4 An Overview on Meshless Methods and Their Applications	55	(13)
Approximation Function	55	(5)
Numerical Implementation	60	(3)
Applications	63	(4)
Problems	67	(1)
5 Procedures of Meshless Methods	68	(15)
Construction of the Approximation	68	(2)
Choice of Weight Function	70	(2)
Formulation of Meshless Analysis	72	(2)
Evaluation of the Integral	74	(2)
Treatment of Discontinuity	76	(1)
Treatment of Mirror Symmetry	77	(1)
H- and P-Refinements	78	(3)
Problems	81	(2)
6 Meshless Analysis of Elastic Problems	83	(30)
Background Theory for Applications of Elastostatics	83	(5)
Meshless Analysis of Elastostatic Problems	88	(7)
General Dynamic Problems	95	(6)
Meshless Analysis of Elastodynamic Problems	101	(4)
Meshless Analysis of Multiphase Materials	105	(5)
Problems	110	(3)
7 Meshless Analysis of Nonlocal Continua	113	(12)
Introduction to Nonlocal Theory	113	(1)
The Framework of Nonlocal Theory	114	(2)
Material Instability and Intrinsic Length	116	(1)
Nonlocal Constitutive Relations	116	(1)
Formulation of Nonlocal Meshless Method	117	(2)
Numerical Examples by Nonlocal Meshless Method	119	(3)
Discussions	122	(2)
Problems	124	(1)
8 Meshless Analysis of Plasticity	125	(28)
Constitutive Relations	125	(4)
Return Mapping Algorithm	129	(2)
J2 Flow Theory	131	(3)
Meshless Analysis of High-Speed Impact/Contact Problem	134	(9)
Incremental Plasticity and Slow Crack Growth Problem	143	(8)
Remarks	151	(1)
Problems	151	(2)
Appendix A Vectors and Tensors	153	(9)
Appendix B Representations of Isotropic Scalar, Vector, and Tensor Functions (Wang, 1970, 1971)	162	(3)
Appendix C Classification of Partial Differential Equations	165	(7)
Appendix D User's Manual: Meshless Computer Program for Electrostatics and Electrodynamics	172	(7)
Appendix E User's Manual: Meshless Computer Program for Analysis of Crack Growth in Elastoplastic Continuum	179	(7)
Bibliography	186	(10)
Index	196