Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

This monograph describes some approaches to the nonlinear theory of plates and shells. By nonclassical approaches we mean the desciption of problems with mathematical models of different sizes (two-and three-dimensional dif­ ferential equations) and different types (differential equations of hyperbolic and parabolic type in the spatial coordinates). The nonlinearities investigated are also of various categories: geometrical, physical, elasto-plastic, and peri­ odic. Creating such types of mathematical models and their detailed justifica­ tion allows us to achieve the most accurate description of the real behaviour of shell-type structures. These models allow us to include interaction between the strain and temperature fields and coupling between the displacement field and the external influence of a transonic gas flow. The mathematical treatment of such models helps us greatly in obtaining reliable results by numerical computation. It appears that the most dangerous situation for thin shallow shells is the conjunction of a static load with dynamic interactions. Such combined loads very often cause buckling of shell structures, and in many cases a series of bucklings, which can cause fracture. The failure of a structure usually needs a small amount of time. Therefore the lifetime of a shell structure depends strongly on nonelastic deflections and it is important to mathematically model shell structures as precisely as possible. This monograph is one of several devoted to this subject. Now we shall briefly describe the contents of the book. Note that not all of the results presented here have been published in textbook format.

"A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The outlook of the book is quite inviting, and with 222 vivid illustrations and a lucid language style of the text, the book is able to absorb and engage the reader quite well. The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." (Journal of Sound and Vibration, 266/5, 2003)

"The authors made every effort to keep the text intelligible for both practitioners and graduate students, although they offer a rigorous treatment of both purely mathematical and numerical approaches presented, so that the reader can understand, analyse and follow the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviour." (Zentralblatt MATH 1015, 2003)

"This book presents a 'collection' of mathematical and numerical results pertaining to thermoelastic shell problems. ... this book can certainly be useful to shell experts, especially as regards the techniques demonstrated to model and mathematically analyse thermoelastic effects in shell structures." (Dominique Chapelle, SIAM Review, Vol. 48 (1), 2006)

"In this book the authors describe the non-linear theory of plates and shells. Geometric, physical, elastoplastic and periodic nonlinearities are considered. … The book is very useful for research activity, concerning both theoretical and applied problems, in nonclassical thermomechanics. Among other merits of the book, I would like to note an advanced analysis of a ‘transition’ problem, where different physical regimes may exist in different domains of the same problem … ." (Michele Ciarletta, Mathematical Reviews, 2003 m)

"A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. A comprehensive review of previous research work … must prove very useful to young researchers … . Theoutlook of the book is quite inviting, and with 222 vivid illustrations and a lucid language style … the book is able to absorb and engage the reader quite well. The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity … ." (K. M. Liew, Journal of Sound Vibration, Vol. 266 (5), 2003)

"This monograph is devoted to nonclassical thermoelastic modelling of the nonlinear dynamics of shells. … The authors make every effort to keep the text intelligible for both practiotioners and graduate students … so that the reader can understand, analyse and follow the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviour." (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1015, 2003)