In this paper we propose a numerical algorithm for determining the equilibrium configurations assumed by an inflated membrane nearly inextensible in tension. We assume that the membrane reaches its final equilibrium state at the end of two consecutive stages. During the first kinematical phase the membrane undergoes large displacements in the absence of any internal force; on the contrary, during the successive static phase the membrane experiences small displacements accompanied by not negligible internal forces. The soundness of the algorithm is proved by comparing the numerical results relative to a membrane fully inextensible in tension with the few closed form solutions available in literature.
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