Comparing hinged and supported rectangular plates
Athanasios Stylianou, Guido H. Sweers · Comptes Rendus Mécanique · 2010
We consider the Kirchhoff–Love model for the supported plate, that is, the fourth order differential equation Δ 2 u = f ⩽ 0 in a two-dimensional bounded domain Ω with the condition u | ∂ Ω ⩾ 0 and supplemented with natural boundary conditions. We show that the solution differs from the solution of the hinged plate problem, that is, the bi-Laplace equation with u = Δ u = 0 on the boundary, in the case of a rectangular domain.