Jan Awrejcewicz & Vadim Anatolevich Krys’ko 
Thermo-Dynamics of Plates and Shells 

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.

Зміст

Three–Dimensional 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.