| Description |
1 online resource : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Studies in mathematics and its applications ; v. 27 |
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Studies in mathematics and its applications ; v. 27.
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| Summary |
The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the nonlinear case, again after ad hoc 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 `K`rmn 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. |
| Bibliography |
Includes bibliographical references and indexes. |
| Note |
Print version record. |
| Contents |
v. 1. Three-dimensional elasticity -- v. 2. Theory of plates -- v. 3. Theory of shells. |
| Subject |
Elasticity.
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Elastic plates and shells.
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Elasticity |
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Élasticité.
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Plaques et coques élastiques.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Mechanics -- Solids.
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Elastic plates and shells
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Elasticity
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Elasticiteit.
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| Added Title |
Theory of plates |
| Other Form: |
Ciarlet, Philippe G. Mathematical elasticity. Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988-2000 0444702598 (DLC) 87023741 (OCoLC)16684938 |
| ISBN |
9780444825704 |
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0444825703 |
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9780080535913 (electronic book) |
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0080535917 (electronic book) |
| Standard No. |
AU@ 000048130441 |
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CHNEW 001006712 |
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DEBBG BV036962368 |
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DEBBG BV039830236 |
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DEBBG BV042317357 |
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DEBSZ 482356456 |
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NZ1 12433662 |
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NZ1 15192907 |
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