Methods of Fundamental Solutions in Solid Mechanics

Methods of Fundamental Solutions in Solid Mechanics presents the fundamentals of continuum mechanics, the foundational concepts of the MFS, and methodologies and applications to various engineering problems. Eight chapters give an overview of meshless methods, the mechanics of solids and structures, the basics of fundamental solutions and radical basis functions, meshless analysis for thin beam bending, thin plate bending, two-dimensional elastic, plane piezoelectric problems, and heat transfer in heterogeneous media. The book presents a working knowledge of the MFS that is aimed at solving real-world engineering problems through an understanding of the physical and mathematical characteristics of the MFS and its applications.

Author Biography: Dr. HUI WANG was born in Luoyang City of China in 1976. He received his Bachelor degree in Theoretical and Applied Mechanics from Lanzhou University, China in 1999. Subsequently he joined the College of Science as an assistant lecturer at Zhongyuan University of Technology (ZYUT) and spent two years teaching at ZYUT. He earned his Master degree from Dalian University of Technology in 2004 and Doctoral degree from Tianjin University in 2007, both of which are in Solid Mechanics. Since 2007, he has worked at College of Civil Engineering and Architecture, Henan University of Technology as a lecturer. He was promoted to Associate Professor in 2009 and Professor in 2015. From August 2014 to August 2015, he worked at Australian National University (ANU) as a visiting scholar, and then from February 2016 to February 2017, he joined the ANU as a Research Fellow. His research interests include computational mechanics, meshless methods, hybrid finite element method and mechanics of composites. So far, he has authored three academic books by CRC Press and Tsinghua University Press respectively, 7 book chapters and 62 academic journal papers (47 indexed by SCI and 8 indexed by EI). In 2010, He was awarded the Australia Endeavour Award. Dr. QINGHUA QIN born in Guilin City of China in 1958 received his Bachelor of Engineering degree in mechanical engineering from Chang An University, China in 1982, earning his Master of Science degree in 1984 and Doctoral degree in 1990 from Huazhong University of Science and Technology (HUST) in China. Both degrees are in applied mechanics. He joined the Department of Mechanics as an associate lecturer at HUST in 1984, and was promoted to lecturer in mechanics in 1987 during his PhD candidature period. After spending 10 years lecturing at HUST, he was awarded the DAAD/K.C. Wong research fellowship in 1994, which enabled him to work at the University of Stuttgart in Germany for nine months. In 1995 he left HUST to take up a postdoctoral research fellowship at Tsinghua University, China, where he worked until 1997. He was awarded a Queen Elizabeth II fellowship in 1997 and a Professorial fellowship in 2002 at the University of Sydney and stayed there till December 2003, both by the Australian Research Council, and is currently working as a professor in the Research School of Engineering (RSE) at the Australian National University, Australia. He was appointed a guest professor at HUST in 2000. He was also awarded a Cheung Kong Professorship at Tianjin University in 2001 from the Ministry of Education of China. He has published more than 300 journal papers and 7 books in the field of applied mechanics.

1. Overview of meshless methods 2. Mechanics of solids and structures 3. Basics of fundamental solutions and radial basis functions 4. Meshless analysis for thin beam bending problems 5. Meshless analysis for thin plate bending problems 6. Meshless analysis for two-dimensional elastic problems 7. Meshless analysis for plane piezoelectric problems 8. Meshless analysis for heat transfer in heterogeneous media Appendix A. Derivatives of function in terms of radial variable r B. Transformations C. Derivatives of approximated particular solutions in inhomogeneous plane elasticity