Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/44079
Título: | Characterization of the Bernoulli-Navier model for a rectangular section beam as the limit of the Kirchhoff-Love model for a plate |
Autor(es): | Ribeiro, Carolina Paula Baptista Viaño, J. M. Figueiredo, Jorge Manuel Rodríguez-Arós, Á. |
Palavras-chave: | Asymptotic analysis Beams Rods Plates Linear elasticity Bernoulli-Navier Kirchhoff- Love |
Data: | Out-2016 |
Editora: | Springer |
Revista: | Zeitschrift für Angewandte Mathematik und Physik |
Resumo(s): | In this paper we compare the Kirchhoff-Love model for a linearly elastic rectangular plate Ωtε = (0, L) × (−t, t) × (−ε, ε) of thickness 2ε with the Bernoulli-Navier model for the same solid considered as a linearly elastic beam of length L and cross-section ω tε 1 = (−t, t) × (−ε, ε). We assume that the solid is clamped on both ends {0, L} × [−t, t] × [−ε, ε]. We show that the scaled version of the displacements field ζ t in the middle plane, solution of the Kirchhoff-Love model, converges strongly to the unique solution of a one-dimensional problem when the plate width parameter t tends to zero. Moreover, after re-scaling this limit, we show that, as a matter of fact, it is the solution of the Bernoulli-Navier model for the beam. This means that, under appropriate assumptions on the order of magnitude of the data, the Bernoulli-Navier displacement field is the natural approximation of the Kirchhoff-Love displacement field when the cross-section of the plate is rectangular and its width is sufficiently small and homothetic to thickness. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/44079 |
DOI: | 10.1007/s00033-016-0710-7 |
ISSN: | 0044-2275 |
e-ISSN: | 1420-9039 |
Arbitragem científica: | yes |
Acesso: | Acesso restrito UMinho |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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BN_KL_Repositorium.pdf Acesso restrito! | 378,83 kB | Adobe PDF | Ver/Abrir |