Some solutions to the asymptotic bending problem of non-inhibited shells.

We study the asymptotic limit bending problem of thin linearly elastic shells as the thickness goes to zero. Such asymptotic bending problem makes sense whenever bendings are admissible. We present two alternate expressions of the change of curvature tensor giving new formulations for the asymptotic bending problem. In some case of cylinders and hyperbolic surfaces, we are able present solutions, eventually analytic. Such solutions can constitute tests for the membrane locking