Theory of Plates Vol. II
| Author/creator | Ciarlet, P. G. Author |
| Other author | Lemm, Jeffrey M. Author |
| Format | Electronic |
| Publication Info | North Holland [Imprint] San Diego : Elsevier Science & Technology Books |
| Description | 497 p. ill |
| Supplemental Content | Full text available from eBook - Mathematics pre-2007 |
| Subjects |
| Series | Studies in Mathematics and its Applications Ser. |
| Summary | Annotation The objective of Volume II is to show how asymptotic methods, with the thickness as thesmallparameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any<i>a priori</i>assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in<i>H</i>1towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.<p>In the nonlinear case, again after<i>ad hoc</i>scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.</p> |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| ISBN | 9780444825704 |
| ISBN | 0444825703 (Trade Cloth) Active Record |
| Standard identifier# | 9780444825704 |
| Stock number | 00991439 |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |