Axisymmetrical Finite Element For Membrane Large Strains And Displacements
Author(s)
R. Bouzidi, Y. Ravaut & C. Wielgosz
Abstract
This paper presents numerical developments for calculating membrane deflections under lateral pressure. The computation is made by construction of an axisymmetrical finite element in the case of finite strains and large displacements. The numerical procedure is based on the minimization of the total potential energy. The choice of this numerical scheme is justified by the fact that both numerical and some physical instabilities are correctly treated. This numerical approach is applied to the case of membranes with no flexural stiffness like fabrics. For this kind of problems, the use of classical finite element scheme based on equilibrium equations, needs to add to the rigdity matrix the non-linear terms as geometric stiffness and those arising from the follower forces [l]. In the case of pressurized membranes we show that it is more interesting to solve the stationarity of the potential energy by direct numerical minimization. This numerical scheme presents more stability and is easiest to be constructed. Moreover we can take into account all non-linear terms due to the large strains and displacements and to the follower forces
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