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.
A free boundary approach to solve the equilibrium equations of a membrane
VIGLIALORO, GIUSEPPE;
2015
Abstract
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.
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