Asymptotic behaviour of thin linearly elastic layers of oscillating thickness
Mustapha El Jarroudi · IMA Journal of Applied Mathematics · 2009
We consider a 3D linearly elastic material whose thickness is a positive Lipschitz continuous function rε(x1, x2) ≤ ε. We study the asymptotic behaviour, when ε tends to 0, of the associated sequence of rescaled energy functionals using Γ-convergence methods. According to the bounds of the function rε, we obtain two possible asymptotic behaviours: a membrane and a flexure one.