Jan Awrejcewicz, Vadim A. Krysko

Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells (eBook, PDF)

Applications of the Bubnov-Galerkin and Finite Difference Numerical Methods

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 429
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642556777
• Artikelnr.: 53086532

Autorenporträt

From the beginning of his academic career Jan Awrejcewicz has been associated with the Mechanical Faculty of the Lodz University of Technology, where he obtained a master's degree in engineering, a PhD in technical sciences and a postdoctoral degree (habilitatioin). In 1994, he received the title of Professor from the President of Poland. In 1998 he founded the Department of Automation, Biomechanics and Mechatronics, that he is still managing. Since 2013 he has been a member of the Polish Central Commission for Degrees and Titles, and since 2019 also of the Council for Scientific Excellence. He is also an Editor-in-Chief of 3 international journals and member of the Editorial Boards of 90 international journals (23 with IF) as well as editor of 25 books and 28 journal special issues. He also reviewed 45 monographs and textbooks and over 600 journal papers for about of 140 journals. His scientific achievements cover issues related to asymptotic methods for continuous and discrete mechanical systems, taking into account thermoelasticity and tribology, and computer implementations using symbolic calculus, nonlinear dynamics of mechanical systems with friction and impacts, as well as engineering biomechanics. He authored/co-authored over 780 journal papers and refereed international conference papers and 50 monographs. For his scientific merits he recived numerous prestigious awards and distinctions, among them titles of the Honoratry Doctor of Cz¿stochowa University of Technology (2013), University of Technology and Humanities in Bielsko-Biäa (2013), Kielce University of Technology (2019), National Technical University "Kharkiv Polytechnic Institute" (2019), and Gdäsk University of Technology (2019). Vadim Krysko was born in Kiev, Ukraine, on September 21, 1937. He received a master's degree in Civil Engineering from the Saratov State Technical University in 1962. A Ph.D. degree in Mechanics of Solids he obtained from the Saratov State Technical University, USSR in 1967, and D.Sci. degree in Mechanics of Solids he obtained from Moscow Civil Engineering University in 1978. In 1982 he became a full professor, the academic rank of professor obtained from the Department of Higher Mathematics, Saratov State Technical University. He is author/co-author of 329 publications in scientific journals and conference proceedings, 8 monographs in English, 8 monographs in Polish, and 16 monographs in Russian. Topics of his research cover such branches of mechanics as thermoelasticity and thermoplasticity, the theory of optimization of mechanical systems, the theory of propagation of elastic waves upon impact, the theory of coupled problems of thermoelasticity and the interaction of flexible elastic shells with a transonic gas flow, numerical methods for solving nonlinear problems of shells theory. Vadim Krysko was a promoter of 58 PhD (postgraduate student) theses. He is currently the Head of the Department of Mathematicsand Modeling, Saratov State Technical University, Russia. In 2012 he was honored by a title of Doctor Honoris Causa of the Lodz University of Technology, Poland. Vadim Krysko opened and developed novel scientific directions for research in the construction, justification and numerical implementation of new classes of equations of mathematical physics of hyperbolic-parabolic types and proposed effective methods for their numerical solution.

Inhaltsangabe

1 Introduction.- 2 Coupled Thermoelasticity and Transonic Gas Flow.- 2.1 Coupled Linear Thermoelasticity of Shallow Shells.- 2.2 Cylindrical Panel Within Transonic Gas Flow.- 3 Estimation of the Errors of the Bubnov-Galerkin Method.- 3.1 An Abstract Coupled Problem.- 3.2 Coupled Thermoelastic Problem Within the Kirchhoff-Love Model.- 3.3 Case of a Simply Supported Plate Within the Kirchhoff Model.- 3.4 Coupled Problem of Thermoelasticity Within a Timoshenko-Type Model.- 4 Numerical Investigations of the Errors of the Bubnov-Galerkin Method.- 4.1 Vibration of a Transversely Loaded Plate.- 4.2 Vibration of a Plate with an Imperfection in the Form of a Deflection.- 4.3 Vibration of a Plate with a Given Variable Deflection Change.- 5 Coupled Nonlinear Thermoelastic Problems.- 5.1 Fundamental Relations and Assumptions.- 5.2 Differential Equations.- 5.3 Boundary and Initial Conditions.- 5.4 On the Existence and Uniqueness of a Solution.- 6 Theory with Physical Nonlinearities and Coupling.- 6.1 Fundamental Assumptions and Relations.- 6.2 Variational Equations of Physically Nonlinear Coupled Problems.- 6.3 Equations in Terms of Displacements.- 7 Nonlinear Problems of Hybrid-Form Equations.- 7.1 Method of Solution for Nonlinear Coupled Problems.- 7.2 Relaxation Method.- 7.3 Numerical Investigations and Reliability of the Results Obtained.- 7.4 Vibration of Isolated Shell Subjected to Impulse.- 7.5 Dynamic Stability of Shells Under Thermal Shock.- 7.6 Influence of Coupling and Rotational Inertia on Stability.- 7.7 Numerical Tests.- 7.8 Influence of Damping e and Excitation Amplitude A.- 7.9 Spatial-Temporal Symmetric Chaos.- 7.10 Dissipative Nonsymmetric Oscillations.- 7.11 Solitary Waves.- 8 Dynamics of Thin Elasto-Plastic Shells.- 8.1 Fundamental Relations.- 8.2 Method of Solution.- 8.3 Oscillations and Stability of Elasto-Plastic Shells.- 9 Unsolved Problems in Nonlinear Dynamics of Shells.- References.

Rezensionen

"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)