Junction of thin plates

The elasticity problem of a thin plate with an edge is considered using asy mptotic methods. The small parameter epsilon describes the relative thickne ss of the plate. In the case when the elasticity coefficients are everywher e 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 'rigid'). We also consider a junction mode of a narrow filet (the order of its width is O(epsilon)) Of a 'soft' elastic material, the elasticity coefficients being O(epsilon) With respect to those of the p lates. In this case (called 'elastic junction'), the asymptotic modelling c ontains an energy bilinear form associated with the filer which involves th e variation of the angle and the sliding along the junction. (C) 2000 Editi ons scientifiques et medicales Elsevier SAS.