  We present a computational framework for analysing thin shell structures
using the finite element method. The framework is based on a mesh-dependent
shell model which we derive from the general laws of three-dimensional
elasticity. We apply the framework for the so called Girkmann benchmark problem
involving a spherical shell stiffened with a foot ring. In particular, we
compare the accuracy of different reduced strain four-node elements in this
context. We conclude that the performance of the bilinear shell finite elements
depends on the mesh quality but reasonable accuracy of the quantities of
interest of the Girkmann problem can be attained in contrast to earlier results
obtained with general shell elements for the problem.
