Justification de la condition aux limites d’encastrement d’une plaque par une méthode asymptotique. (Justification of the boundary conditions of a clamped plate by an asymptotic analysis). (French) Zbl 0679.73008
Summary: We consider a problem in three-dimensional linearized elasticity, posed over a domain consisting of a plate of thickness \(2\epsilon\), inserted into a three-dimensional supporting elastic structure. Assuming that the Lamé constants of the material constituting the plate vary as \(\epsilon^{-3}\) and that those of the supporting structure vary as \(\epsilon^{-2-s}\), \(s>0\), we establish the \(H^ 1\)-convergence of the (appropriately scaled) components of the displacement vector field, as \(\epsilon\) approaches zero, towards the solution of the well-known boundary value problem of a clamped plate. In this fashion, we show that the classical boundary conditions of a clamped plate can be obtained by a rigorous “limit analysis” that also takes into account the elastic character of the supporting structure.
MSC:
74S30 | Other numerical methods in solid mechanics (MSC2010) |
49J27 | Existence theories for problems in abstract spaces |
49J40 | Variational inequalities |
74K20 | Plates |