Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

• 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.

"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 ... . The outlook 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)