zbMATH — the first resource for mathematics

Modélisation de la jonction entre une plaque et une poutre en élasticité linéarisée. (Modelling of the junction between a plate and a rod in linear elasticity). (French. English summary) Zbl 0767.73034
Summary: We give a mathematical justification for the modelisation of the junction between a plate of thickness \(2\varepsilon\) and a rod whose cross section varies as \(4\varepsilon^ 2\) when they are made of linearly elastic materials. We are interested in the case where the rod is partly inserted in the plate and clamped at its free extremity, and we make an asymptotic analysis. Passing to the limit, we show that the transverse displacement of the rod is partly rigid. Moreover, at the junction the torsion of the plate induced by the rod is a constant depending on the total moment of the applied forces.

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
74B05 Classical linear elasticity
Full Text: DOI EuDML
[1] M. AUFRANC [ 1990a], Sur quelques problèmes de jonctions dans les multi-structures élastiques, Thèse de l’Université Pierre et Marie Curie, Paris. Zbl0858.73009 · Zbl 0858.73009
[2] M. AUFRANC [ 1990b], Junctions between three-dimensional and two-dimensional non-linearly elastic structures (submitted to Asymptotic Analysis). Zbl0754.73034 · Zbl 0754.73034
[3] P. G. CIARLET [ 1980], A justification of the Von Kármán equations, Arch. Rational Mech. Anal., 73, 349-389. Zbl0443.73034 MR569597 · Zbl 0443.73034 · doi:10.1007/BF00247674
[4] P. G. CIARLET [ 1990], Plates and junctions in elastic multi-structures : An asymptotic analysis, Masson, Paris. Zbl0706.73046 MR1071376 · Zbl 0706.73046
[5] P. G. CIARLET, P. DESTUYNDER [ 1979a], A justification of the two-dimensional plate model, J. Mecanique, 18, 315-344. Zbl0415.73072 MR533827 · Zbl 0415.73072
[6] P. G. CIARLET, P. DESTUYNDER [ 1979b], A justification of a non linear model in plate theory, Comp. Methods Appl. Mech. Engrg., 17/18, 227-258. Zbl0405.73050 · Zbl 0405.73050 · doi:10.1016/0045-7825(79)90089-6
[7] P. G. CIARLET, H. LE DRET, R. NZENGWA [ 1989], Junctions between three-dimensional and two-dimensional linearly elastic structures, J. Math. Pures Appl., 68, 261-295. Zbl0661.73013 MR1025905 · Zbl 0661.73013
[8] A. CIMETIÈRE, G. GEYMONAT, H LE DRET, A. RAOULT, Z. TUTEK [ 1988], Asymptotic theory and analysis for displacement and stress distribution in nonlinear elastic straight slender rods, J. Elasticity, 19, 111-161. Zbl0653.73010 MR937626 · Zbl 0653.73010 · doi:10.1007/BF00040890
[9] P. DESTUYNDER [ 1980], Sur une justification des modèles de plaques et de coques par les méthodes asymptotiques, Doctoral Dissertation, Université Pierre et Marie Curie, Paris.
[10] P. DESTUYNDER [ 1981], Comparaison entre les modèles tridimensionnels et bidimensionnels de plaques en élasticité, RAIRO Modél. Math. Anal. Numér., 15, 331-369. Zbl0479.73042 MR642497 · Zbl 0479.73042 · eudml:193386
[11] P. DESTUYNDER [ 1986], Une théorie asymptotique des plaques minces en élasticité linéaire, Masson, Paris. Zbl0627.73064 MR830660 · Zbl 0627.73064
[12] H. LE DRET [ 1989a], Folded plates revisited, Comput. Mech., 5, 345-365. Zbl0741.73025 · Zbl 0741.73025 · doi:10.1007/BF01047051
[13] H. LE DRET [ 1989b], Modelling of the junction between two rods, J. Math. Pures Appl., 68, 365-397. Zbl0743.73020 MR1025910 · Zbl 0743.73020
[14] H. LE DRET [ 1990a], Modelling of a folded plate, Comput. Mech., 5, 401-416. Zbl0741.73026 · Zbl 0741.73026 · doi:10.1007/BF01113445
[15] H. LE DRET [ 1990b], Vibrations of a folded plate, Math. Model. & Numer. Anal., à paraître. Zbl0712.73044 · Zbl 0712.73044 · eudml:193604
[16] A. RIGOLOT [ 1972], Sur une théorie asymptotique des poutres, J. Mécanique, 11, 673-703. Zbl0257.73013 MR368552 · Zbl 0257.73013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.