Asymptotic analysis and boundary homogenization in linear elasticity
Mustapha El Jarroudi, Ahmed Addou, Alain Brillard · Mathematical Methods in the Applied Sciences · 2000
We describe the asymptotic behaviour of the solution of a linear elastic problem posed in a domain of ℝ3, with homogeneous Dirichlet boundary conditions imposed on small zones of size less than ϵ distributed on the boundary of this domain, when the parameter ϵ goes to 0. We use epi-convergence arguments in order to establish this asymptotic behaviour. We then specialize this general situation to the case of identical strips of size rϵ ϵ-periodically distributed on the lateral surface of an axisymmetric body. We exhibit a critical size of the strips through the limit of the non-negative quantity −1/(ϵ ln rϵ) and we identify the different limit problems according to the values of this limit. Copyright © 2000 John Wiley & Sons, Ltd.