By Goerge Z. Voyiadjis, George Z. Voyiadjis, D. Karamanlidis

ISBN-10: 0444417583

ISBN-13: 9780444417589

ISBN-10: 0444883665

ISBN-13: 9780444883667

Plates and shells play a tremendous position in structural, mechanical, aerospace and production functions. the idea of plates and shells have complex long ago 20 years to address extra complex difficulties that have been formerly past achieve. during this ebook, the newest advances during this region of study are documented. those contain issues comparable to thick plate and shell analyses, finite rotations of shell buildings, anisotropic thick plates, dynamic research, and laminated composite panels.

The booklet is split into components. partly I, emphasis is put on the theoretical facets of the research of plates and shells, whereas half II offers with smooth purposes. various eminent researchers within the a number of parts of plate and shell analyses have contributed to this paintings which will pay distinctive cognizance to elements of analysis corresponding to thought, dynamic research, and composite plates and shells.

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Ft) Let Xy Y be two Banach spaces. , v = s/u. The set M is called the domain of operator s/ and is denoted by @(s/). Instead of the operator stf we shall speak also of the mapping st'. 64 linear differential equations, we now find ourselves confronted with basic theoretical problems: a) the problem of the existence of the solution of a boundary value problem, b) the problem of determining this solution. As far as problem b) is concerned, we note immediately that an explicit formula giving the solution of a boundary value problem in nonlinear differential equations can be found only in quite exceptional cases.

Let B be an operator mapping a subset M of the Banach space X into the same Banach space X. , if the element u is mapped by the operator B into itself. By the fixed point principle we mean a theorem which states sufficient conditions under which a fixed point of an operator exists. , [51]) which says: (i) Let B be an operator defined on the Banach space X with values in X. Z c\\u - v\\x. Then there exists precisely one fixed point of the operator B. (8) 65 The Banach contraction principle is not only the oldest and simplest fixed point principle, but it also has the advantage that the method of its proof includes instruc tions as to how to find that fixed point.

Essentially, the present book is devoted to problem a). Methods will be described here which have been developed in the past few decades on the basis of new mathe matical tools, which are dealt with in the coming chapters. Below, we present the socalled linearization method which is based on more profound results concerning the solvability of boundary value problems in linear differential equations and on the so-called fixed point principles. By means of this method we obtain (in a special case) results concerning the existence of a solution, naturally under assumptions which are rather restrictive as compared with the methods discussed in Chapters IV and V.

### Advances in the theory of plates and shells by Goerge Z. Voyiadjis, George Z. Voyiadjis, D. Karamanlidis

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