In this paper a method of solution is presented for determining the equilibrium configurations of inflated inextensible membranes of generic shape. To solve this problem, we assume that each membrane reaches its final configuration through two consecutive stages: a first kinematical phase where the membrane undergoes large displacements in the absence of any internal force precedes a static one where small displacements are associated to relevant internal tensile-only forces. A numerical algorithm based on a central finite differences scheme is proposed to solve the governing system of non-linear differential equations. Applications concern cases of inflated axisymmetric membranes inextensible in tension.
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