Resumen de Linear elasticity modelling of the behaviour of a pre-stressed material

R. Luce, C. Poutous, Jean Marie Thomas

• In order to study the behavior of the outer envelop of an airship with great payloads, we have to modelize the behaviour of an inflated material structure. Indeed, the envelop is made of a succession of independant longitudinal lobes. Each lobe is made of two rectangular pieces of material stuck on their lengths and widths to the metallic armature of the airship. The inner volume thus obtained is inflated with a perfect gas so as to pre-stress the whole structure. The expected result is to stabilize the geometry of the airship in case of wind, shocks, impacts, turbulences ... and to protect the Helium envelops which are inside. Assuming that the problem is stationnary, that the material is orthotropic, that the outer disturbances are known and that the inner pressure is uniform, we modelize in 3D this fluid-structure interaction problem and we prove the existence and uniqueness of the solution. We explicitely calculate the pre-stress.