Items related to Introduction to Linear Shell Theory
Synopsis
Hardbound. This monograph is a thorough introduction to recent advances in the mathematical theory of linearly elastic shells.First, it provides a complete analysis of the existence and uniqueness of solutions to the two-dimensional linear membrane, flexural, and Koiter's shell equations. The proofs rely in a crucial way on inequalities of Korn's type on surfaces, which are proved in details.Second, it shows the method of formal asymptotic expansions, with the thickness as the "small" parameter, provides a very effective strategy for justifying the two fundamental classes of membrane and flexural equations of a linearly elastic shell, thus paving the way for the more advanced justification by means of a convergence analysis also carefully reviewed at the end of this monograph.The treatment is essentially self-contained. In particular, all the needed preliminaries from differential geometry, including a direct proof of the three-dimensional Korn i
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