Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions

Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics)
with mixed boundary conditions.

The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method.

The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed.

Key features:

• Includes analytical solving of mixed boundary value problems

• Introduces modern asymptotic and summation procedures

• Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates

• Covers statics, dynamics and stability of plates with mixed boundary conditions

• Explains links between the Adomian and homotopy perturbation approaches

Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.

Igor V. Andrianov obtained his Master (1971) and PhD (1975) degrees from the Dnepropetrovsk State University (Ukraine). He obtained the Doctor of Sciences degree in Mechanics of Solids from the Moscow State Institute of Electronics and Mathematics (Russia) in 1990. During 1974-1977, he was a Research Scientist at the Dnipropetrovs’k State University, during 1977-1990, an Associated Professor, and during 1990-1997, a Full Professor of Mathematics in the Dnepropetrovsk Civil Engineering Institute. Currently he is a Research Scientist in the RWTH Aachen University in Germany. Prof. Andrianov is the author or co-author of 12 books and over 250 papers in refereed journals and conference proceedings. He has presented papers at numerous International Conferences, and he has supervised 25 PhD Theses. His research interests are in Mechanics of Solids, Nonlinear Dynamics, and Asymptotic Methods.

Jan Awrejcewicz graduated from Lodz University of Technology in 1977 (Mechanics) and from the University of Lodz in 1978 (Philosophy). He obtained his PhD (Habilitation) in 1981 (1990), and become a Full Professor in 1997. He has authored and/or co-authored 17 monographs in English; 2 textbooks; 12 edited conference proceedings; 275 journal papers; 340 conference papers; 18 chapters in books. He has served as an editor of 9 books, and as a Guest-Editor of 15 journal special issues. His research includes Nonlinear Mechanics, Mechatronics and Control, and Biomechanics. He is a recipient of the Humboldt Research Award.

Vladyslav V. Danishevs'kyy obtained his Masters (1996), Ph.D. (1999) degrees, and Doctor of Sciences degree in Structural Mechanics (2008) from the Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine. He is a Professor at this State Academy. He has authored 2 monographs and over 70 refereed papers. Among his awards are the Soros Post-Graduate Student’s Award (1997), Prize of the National Academy of Sciences of Ukraine for the best academic achievement among young scientists (2000), Alexander von Humboldt Foundation Research Fellowship (2001), NATO Research Fellowship (2003), NATO Reintegration Grant (2005), and institutional academic co-operation grant of the Alexander von Humboldt Foundation (2007). He conducted research at the Institute of General Mechanics in the RWTH Aachen University, Germany (2001–2002) and at the Group of Physics of Materials in the University of Rouen, France (2003–2004). His research interests are in asymptotic methods, nonlinear dynamics, and heterogeneous materials and structures.

Andrey O. Ivankov, PhD is the author of more than author of more than 30 research publications. His main areas of research include ODE, PDE, Mixed BVPs and Padé approximants.