Vibration of Mindlin Plates: Programming the p-Version Ritz Method

Over the last several years, the four authors have jointly conducted research into the analysis of vibrating Mindlin plates as a collaborative project between Nanyang Technological University, The National University of Singapore, and The University of Queensland. The research was prompted by the fact that there is a dearth of vibration results for Mindlin plates when compared to classical thin plate solutions. To generate the vibration results, the authors have successfully employed the Ritz method for general plate shapes and boundary conditions. The Ritz method, once thought to be awkward for general plate analysis, can be automated through suitable trial functions (for displacements) that satisfy the geometric plate boundary conditions a priori. This work has been well-received by academics and researchers, as indicated by the continual requests for the authors' papers and the Ritz software codes. This monograph is written with the view to share this so-called p-Ritz method for the vibration analysis of Mindlin plates and its software codes with the research community. To the authors' knowledge, the monograph contains the first published Ritz plate software codes of its kind.

Kim Meow Liew is the Head and Chair Professor of Civil Engineering at City University of Hong Kong, Hong Kong. His research activities encompass computational mechanics, optimization, numerical methods, nanomechanics and nanomaterials, multi-scale modeling, simulation and bioengineering. He is the Editor-in-Chief of International Review of Civil Engineering (Praiseworthy Prize) and Journal of Modeling in Mechanics & Materials (De Gruyter) and Associate Editor of Journal of Vibration and Control (Sage) and Journal of Nanoscience Letters (Simplex Academic Publishers). He serves on the editorial boards for more than two dozen journals. He has contributed over 750 articles to peer-reviewed journals, and is a Fellow of the HKIE (Hong Kong), ASME (USA), IMechE (UK) and IES (Singapore). He is listed by the Institute for Scientific Information (ISI) as a Highly Cited Researcher in engineering.