Mathematical elasticity, Volume II, Theory of plates:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1997
|
| Schriftenreihe: | Studies in mathematics and its applications
27 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 K̀rm̀n 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 Includes bibliographical references and indexes |
| Beschreibung: | 1 Online-Ressource (/ ill) |
| ISBN: | 9780444825704 0444825703 |
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| 245 | 1 | 0 | |a Mathematical elasticity, Volume II, Theory of plates |c Philippe G. Ciarlet |
| 246 | 1 | 3 | |a Theory of plates |
| 264 | 1 | |a Amsterdam |b North-Holland |c 1997 | |
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| 490 | 1 | |a Studies in mathematics and its applications |v v. 27 | |
| 500 | |a 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 K̀rm̀n 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 | ||
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 7 | |a Elasticiteit |2 gtt | |
| 650 | 7 | |a Elastic plates and shells |2 fast | |
| 650 | 7 | |a Elasticity |2 fast | |
| 650 | 4 | |a Elasticity | |
| 650 | 4 | |a Elastic plates and shells | |
| 830 | 0 | |a Studies in mathematics and its applications |v 27 |w (DE-604)BV023068024 |9 27 | |
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Datensatz im Suchindex
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| author | Ciarlet, Philippe G. 1938- |
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| dewey-full | 531/.381 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531/.381 |
| dewey-search | 531/.381 |
| dewey-sort | 3531 3381 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV042317357 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444825704 0444825703 |
| language | English |
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| publisher | North-Holland |
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| series | Studies in mathematics and its applications |
| series2 | Studies in mathematics and its applications |
| spelling | Ciarlet, Philippe G. 1938- Verfasser (DE-588)143368362 aut Mathematical elasticity, Volume II, Theory of plates Philippe G. Ciarlet Theory of plates Amsterdam North-Holland 1997 1 Online-Ressource (/ ill) txt rdacontent c rdamedia cr rdacarrier Studies in mathematics and its applications v. 27 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 K̀rm̀n 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 Includes bibliographical references and indexes Elasticiteit gtt Elastic plates and shells fast Elasticity fast Elasticity Elastic plates and shells Studies in mathematics and its applications 27 (DE-604)BV023068024 27 http://www.sciencedirect.com/science/book/9780444825704 Verlag Volltext |
| spellingShingle | Ciarlet, Philippe G. 1938- Mathematical elasticity, Volume II, Theory of plates Studies in mathematics and its applications Elasticiteit gtt Elastic plates and shells fast Elasticity fast Elasticity Elastic plates and shells |
| title | Mathematical elasticity, Volume II, Theory of plates |
| title_alt | Theory of plates |
| title_auth | Mathematical elasticity, Volume II, Theory of plates |
| title_exact_search | Mathematical elasticity, Volume II, Theory of plates |
| title_full | Mathematical elasticity, Volume II, Theory of plates Philippe G. Ciarlet |
| title_fullStr | Mathematical elasticity, Volume II, Theory of plates Philippe G. Ciarlet |
| title_full_unstemmed | Mathematical elasticity, Volume II, Theory of plates Philippe G. Ciarlet |
| title_short | Mathematical elasticity, Volume II, Theory of plates |
| title_sort | mathematical elasticity volume ii theory of plates |
| topic | Elasticiteit gtt Elastic plates and shells fast Elasticity fast Elasticity Elastic plates and shells |
| topic_facet | Elasticiteit Elastic plates and shells Elasticity |
| url | http://www.sciencedirect.com/science/book/9780444825704 |
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