Anisotropic finite element estimates and local locking for shells: parabolic case

We consider a thin shell with thickness 2 epsilon with developable middle s urface. A boundary is free along a generator. The loading is normal and non -zero along this generator. The energy concentrates inside a thin layer wit h thickness O(eta), eta = epsilon (1/4). The structure of the layer is desc ribed by a penalty problem so that a locking phenomenon may appear. We give estimates of the error for the approximation with anisotropic finite eleme nts of step O(H) and O(etaH) along and accross the layer respectively. For the same error, the corresponding triangulation includes a number of elemen ts smaller, in the ratio eta, to that of an isotropic mesh. The form and in tensity of the terms of the local locking are made evident. (C) 2001 Academ ie des sciences/Editions scientifiques et medicales Elsevier SAS.