One-dimensional problems in the stability of thin shells

Summary Algebraic conditions, sufficient for the infinitestimal stability of elastic shells in the class of one-dimensional perturbations from homogeneous ground states, are considered. A necessary and sufficient condition for superstability is also deduced.The shells are modelled according to the director theory. Unlike three-dimensional elastic continua, the strain energy depends on the displacement components and not only on their gradients. This plays a central role in the analysis of these problems.