A free boundary approach to solve the equilibrium equations of a membrane

This chapter deals with a mathematical problem related to the equilibrium analysis of a membrane with rigid and cable boundary. The membrane and its boundary are respectively identified with a regular surface and a set of regular curves. The equilibrium is directly expressed by means of an elliptic problem, in terms of the shape of the membrane and its stress tensor; therefore, a free boundary numerical resolution procedure is presented and applied in a particular case