PATHOLOGICAL PHENOMENA IN COMPUTATION OF THIN ELASTIC SHELLS

We give short account of difficulties appearing when computing thin elastic shells. «Thin» is understood in the sense that the ratio e between the thickness and any other characteristic length of the shell is small. For small e the solution ue itself (independently of its numerical approximation ) exhibits peculiarities which depend highly on the shape and the boundary conditions of the shell. These peculiarities are mainly of three kinds, which do not necessarily appear simultaneously: 1) Boundary layers, 2)Global instability known as “sensitivity”, 3) Constrained solutions in subspaces. The numerical approximation should be reliable in these situations. Finite element schemes involving higher order polynomials appear as more efficient than others. Moreover, an explicit analysis of convergence of the numerical approximation in several typical examples shows that, in order to obtain a good approximation, the mesh step must be taken smaller and smaller as e decreases. Anisotropic adaptive meshes should pro...