The present monograph is devoted to nonlinear dynamics of thin plates and shells with termosensitive excitation. Since the investigated mathematical models are of di?erent sizes (two- and three-dimensional di?erential equation) and di?erent types (di?erential equations of hyperbolic and parabolic types with respect to spatial co- dinates), there is no hope to solve them analytically. On the other hand, the proposed mathematical models and the proposed methods of their solutions allow to achieve more accurate approximation to the real processes exhibited by dynamics of shell (plate) - type structures with thermosensitive excitation. Furthermore, in this mo- graph an emphasis is put into a rigorous mathematical treatment of the obtained di?erential equations, since it helps e?ciently in further developing of various su- able numerical algorithms to solve the stated problems. It is well known that designing and constructing high technology electronic - vices, industrial facilities, ?ying objects, embedded into a temperature ?eld is of particular importance. Engineers working in various industrial branches, and part- ularly in civil, electronic and electrotechnic engineering are focused on a study of stress-strain states of plates and shells with various (sometimes hybrid types) da- ing along their contour, with both mechanical and temperature excitations, with a simultaneous account of heat sources in?uence and various temperature con- tions. Very often heat processes decide on stability and durability of the mentioned objects. Since numerous empirical measurement of heat processes are rather - pensive, therefore the advanced precise and economical numerical approaches are highly required.

Devoted to nonlinear dynamics of thin plates and shells with thermo-sensitive excitation Includes supplementary material: sn.pub/extras

Autorentext

Igor V. Andrianov was born in the Ukraine (former Soviet Union (fSU)) in 1948. He obtained his Master of Applied Mechanics degree from Dnepropetrovsk State University (DSU, Ukraine) in 1971, his PhD in Structural Mechanics from the DSU in 1975, and his DSc in Mechanics of Solids from the Moscow State Institute of Electronics and Mathematics in 1990. From 1974 to 1977, he was a Research Scientist at the DSU, from 1977 to 1990, an Associate Professor, and from 1990 to 1997, a Full Professor of Mathematics at Dnepropetrovsk Civil Engineering Institute. From 2006 to 2013 he was a Research Scientist at RWTH Aachen University (Germany). Andrianov is the author or co-author of 14 books and more than 300 papers in peer-reviewed journals. He has presented papers at more than 150 international congresses, conferences, and seminars, and also supervised 21 PhD students. Selected as a Soros Professor (1996). His research interests include Mechanics of Solids, Mechanics of Composite Materials, Nonlinear Dynamics, and Asymptotic Methods. Jan Awrejcewicz, Head of the Department of Automation, Biomechanics and Mechatronics, Head of Ph.D. School on 'Mechanics' (since 1996) and of graduate/postgraduate programs on Mechatronics (since 2006). Recipient of multi-doctor honoris causa and the Humboldt Award. Author/co-author of over 730 journal papers and refereed international conference papers and 48 monographs. Editor of 22 books and 26 journal special issues. Principal investigator in 39 research grants by Polish Ministry of Education and Science (21), Committee for Scientific Research (17), National Science Centre (2). Member of Editorial Boards of 74 Journals (15 with IF). Organizer and Head of the series of 14 International Conferences Dynamical Systems-Theory and Application (Lodz, 1992-2017) and of 3 International Conferences "Mechatronics: Ideas for Industrial Applications" (Warsaw 2012; Lodz, 2014; Gdansk, 2015), Chair of the "International Conference of the Polish Society of Biomechanics" (Lodz, 2014). Research interest: His papers and research cover various disciplines of mathematics, mechanics, biomechanics, automatics, physics and computer oriented sciences, with main focus on nonlinear processes. Vladyslav V. Danishevskyy obtained his Masters (1996), Ph.D. (1999), and Doctor of Sciences (2008) degrees in Structural Mechanics from Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine. He is a Full Professor at this Academy. He has authored 3 monographs and over 50 journal papers refereed by SCOPUS. Among his awards are 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), institutional academic co-operation grant of the Alexander von Humboldt Foundation (2007), research grant of the German Research Foundation (2014), Marie-Curie Research Fellowship by the European Union's Horizon 2020 research and innovation programme (2015). He has conducted long-term research abroad in RWTH Aachen University, Germany (2001-2002), in the University of Rouen, France (2003-2004), and in Keele University, UK (2015- 2017). His research interests cover mechanics of heterogeneous media and structures, asymptotic methods, nonlinear dynamics.

Klappentext

This monograph is devoted to the investigation of nonlinear dynamics of plates and shells embedded in a temperature field. Numerical approaches and rigorous mathematical proofs of solution existence in certain classes of differential equations with various dimensions are applied. Both closed shell-type constructions and sectorial shells are studied.

The considered problems are approximated by 2D and 3D constructions taking into account various types of nonlinearities (geometrical and/or physical with coupled deformation and temperature fields), and are subjected to an action of stationary and non-stationary thermal loads.

Variational and finite difference numerical approaches are used to study numerous problems important for civil and mechanical engineering.

Furthermore, a novel and exact computational method to solve large systems of linear algebraic equations especially suitable for computational speed and memory storage of a computer is proposed.

This book is expected to be useful for researchers, engineers and students dealing with thermal and dynamical problems of stability and strength of shell-type constructions.

Inhalt
ThreeDimensional Problems of Theory of Plates in Temperature Field.- Stability of Rectangular Shells within Temperature Field.- Dynamical Behaviour and Stability of Closed Cylindrical Shells.- Dynamical Behaviour and Stability of Rectangular Shells with Thermal Load.- Dynamical Behaviour and Stability of Flexurable Sectorial Shells.- Coupled Problems of Thin Shallow Shells in a Temperature Field.- Novel Solution Method for a System of Linear Algebraic Equations.- Mathematical Approaches to Coupled Termomechanical Problems.