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Due to the flexibility of the envelope of large stratosphere airships, the aerodynamic solution of such airship is closely related to its shape and the extal aerodynamic forces which lead to the structural deformation. It is essentially one of the Fluid-Structure Interaction (FSI) problems. This article aims at the numerical investigation of nonlinear airship aeroelasticity in consideration of aerodynamics and structure coupling, using an iteration method. The three-dimensional flow around the airship was numerically studied by means of the SIMPLE method based on the finite volume method. Nonlinear finite element analysis was employed for geometrically nonlinear deformation of the airship shape. Comparison of aerodynamic parameters and the pressure distribution between rigid and aeroelastic models was conducted when an airship is in a trimmed flight state in specified flight conditions. The effect of aeroelasticity on the airship aerodynamics was detailed.