Vadim Anatolevich Krys'ko - Böcker

There are many monographs in the existing literature devoted to the static and dynamic behavior of plates and shells. Plates and shells are enco- tered often in engineering applications being integralparts of a wide range of constructions, such as machines, vehicles, airplanes, rockets, ships, bridges, buildings, and containers, to name a few. In addition to the usual requi- ments posedby engineersrelatedtolightweightness,su?cientrigidityor?- ibility, and robust stability properties, there is an additional class ofapriori dynamicalpropertiesrequiredbymodernengineeringapplicationswheren- homogeneity and non-uniformity of structural components is often the norm incertainapplications. Inaddition,strictoperationalrequirementsinmodern engineering applications towards higher speeds, lighter construction, robust andreliableperformance,dictatessmallermarginsoferrorordeviationsfrom prescribed performances in adverse or uncertain forcing environments. This, in turn, requires the development of new analytical and computational tools capable of addressing challenging and not very well developed topics, such as, nonlinearities a?ecting the system performance, the e?ects of unmodeled dynamics on the stability of operation, and the role of uncertainties in the systemparametersonthestructuralresponse.Asaresult,thereisanongoing e?ort to address such issues, leading to the development of new analytical and computational tools, some of which are discussed in this monograph. The monograph follows an approach based on an integrated treatment of analysis and computation. Such a hybrid approach, coupled with computer algebra, can lead to results that cannot be obtained by other standard th- ries in the ?eld. We show, that in a wide class of problems only a carefully prepared numerical experiment followed by purely mathematical conside- tionscan?nallyleadtothesoughtresults. Thenumerousanalyticalconstr- tions are illustrated by examples of application and computational results.

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.

This monograph is devoted to construction of novel theoretical approaches of m- eling non-homogeneous structural members as well as to development of new and economically ef?cient (simultaneously keeping the required high engineering ac- racy)computationalalgorithmsofnonlineardynamics(statics)ofstronglynonlinear behavior of either purely continuous mechanical objects (beams, plates, shells) or hybrid continuous/lumped interacting mechanical systems. In general, the results presented in this monograph cannot be found in the - isting literature even with the published papers of the authors and their coauthors. We take a challenging and originally developed approach based on the integrated mathematical-numerical treatment of various continuous and lumped/continuous mechanical structural members, putting emphasis on mathematical and physical modeling as well as on the carefully prepared and applied novel numerical - gorithms used to solve the derived nonlinear partial differential equations (PDEs) mainly via Bubnov-Galerkin type approaches. The presented material draws on the ?elds of bifurcation, chaos, control, and s- bility of the objects governed by strongly nonlinear PDEs and ordinary differential equations (ODEs),and may have a positive impact on interdisciplinary ?elds of n- linear mechanics, physics, and applied mathematics. We show, for the ?rst time in a book, the complexity and fascinating nonlinear behavior of continual mechanical objects, which cannot be found in widely reported bifurcational and chaotic dyn- ics of lumped mechanical systems, i. e. , those governed by nonlinear ODEs.

There are many monographs in the existing literature devoted to the static and dynamic behavior of plates and shells. Plates and shells are enco- tered often in engineering applications being integralparts of a wide range of constructions, such as machines, vehicles, airplanes, rockets, ships, bridges, buildings, and containers, to name a few. In addition to the usual requi- ments posedby engineersrelatedtolightweightness,su?cientrigidityor?- ibility, and robust stability properties, there is an additional class ofapriori dynamicalpropertiesrequiredbymodernengineeringapplicationswheren- homogeneity and non-uniformity of structural components is often the norm incertainapplications. Inaddition,strictoperationalrequirementsinmodern engineering applications towards higher speeds, lighter construction, robust andreliableperformance,dictatessmallermarginsoferrorordeviationsfrom prescribed performances in adverse or uncertain forcing environments. This, in turn, requires the development of new analytical and computational tools capable of addressing challenging and not very well developed topics, such as, nonlinearities a?ecting the system performance, the e?ects of unmodeled dynamics on the stability of operation, and the role of uncertainties in the systemparametersonthestructuralresponse.Asaresult,thereisanongoing e?ort to address such issues, leading to the development of new analytical and computational tools, some of which are discussed in this monograph. The monograph follows an approach based on an integrated treatment of analysis and computation. Such a hybrid approach, coupled with computer algebra, can lead to results that cannot be obtained by other standard th- ries in the ?eld. We show, that in a wide class of problems only a carefully prepared numerical experiment followed by purely mathematical conside- tionscan?nallyleadtothesoughtresults. Thenumerousanalyticalconstr- tions are illustrated by examples of application and computational results.

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.