Qualitative Theory in Structural Mechanics: Qualitative Properties and Existence of Solutions

This book focuses on the qualitative theory in structural mechanics, an area that remains underdeveloped. The qualitative theory mainly deals with the static deformation and vibrational modes of linear elastic structures, and cover subjects such as qualitative properties and the existence of solutions.

Qualitative properties belong to one type of structure, are at the system level and of clear regularity, and often result from analytical derivation and logical reasoning. As for the existence of solutions, it addresses a fundamental issue in structural mechanics, and has far-reaching implications for engineering applications.

A better understanding of qualitative properties can assist in both numerical computation and experimental studies. It also promotes the development of better dynamic designs for structures. At the same time, a sound grasp of the existence of solutions and related subjects can aid in quantitative analysis, and help researchers establish the theoretical background essential to their work. 

This book is among the few that is dedicated exclusively to the qualitative theory in structural mechanics and systematically introduces the important and challenging area to a wide audience, including graduate students in engineering.

Dajun Wang received his B.Sc. degree in Applied Mechanics from Peking University, Beijing in 1956. He then began teaching at Peking University and became a professor at the Department of Mechanics and Engineering Science. In a career spanning over 60 years, Professor Wang has conducted in-depth research in a number of areas, including qualitative theories in structural mechanics, existence of solutions, engineering applications, nonlinear dynamic systems involving fluid–structure interactions, mechanical behaviors of ancient Chinese relics, etc. He has published two monographs and more than 160 papers in peer-reviewed journals and conference proceedings. In addition, he has been invited to deliver more than 150 technical lectures at many universities and research institutions around the world. His colleagues, both domestic and international, have spoken highly of his unified proof for the existence of solutions in structural theories and his theory on the validity of structural models. The results of related work have been referred to as “the two China theorems.”

Qishen Wang received his B.Sc. degree in Applied Mechanics from Peking University in 1970, and is currently a Professor at the School of Physics and Electrical Engineering, Anqing Normal University. His research areas include qualitative theories in structural mechanics, inverse problems in vibration, and applied mathematics. Professor Wang has published one monograph and over 100 papers in peer-reviewed journals and conference proceedings. He received a special grant from the State Council of China for his exceptional scientific achievements.

Beichang (Bert) graduated from Peking University with a B.Sc. degree in Applied Mechanics in 1985 and received his M.Sc. degree in Solid Mechanics in 1988. He subsequently studied Computational Mechanics at Carnegie Mellon University and received his Ph.D. in 2004. He has worked in the industry for nearly one and a half decades, first as a senior engineer and project manager at the Global Research Center of General Electric, and later as a technical leader in the company’s Energy Infrastructure Division. Currently, he is an independent consultant. His research interests include areas such as qualitative theories in structural mechanics, inverse problems in vibration, numerical optimization, computer-aided design and engineering (CAD and CAE), and design automation. He has authored 25 journal/conference papers and internal R&D reports, written one monograph, and translated a technical book. While working for General Electric, he made significant contributions in areas such as design productivity, engineering cost reduction, and product quality improvement.