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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.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
74B05 Classical linear elasticity
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