Junction of thin plates

The elasticity problem of a thin plate with an edge is considered using asymptotic methods. The small parameter ε describes the relative thickness of the plate. In the case when the elasticity coefficients are everywhere of the same order of magnitude, the asymptotic behaviour of the plate is such that the angle of the edge remains constant under the deformation (the junction is called `rigidʹ). We also consider a junction mode of a narrow filet (the order of its width is O(ε)) of a `softʹ elastic material, the elasticity coefficients being O(ε) with respect to those of the plates. In this case (called `elastic junctionʹ), the asymptotic modelling contains an energy bilinear form associated with the filet which involves the variation of the angle and the sliding along the junction.