Non-linear finite element analysis of an elastic structure loaded by hydrostatic follower forces

Abstract

This study deals with the non-linear finite element computation of thin flexible structures loaded by hydrostatic forces due to the presence of an internal liquid at rest. In aerospace application, the dynamic behaviour of structures containing an inviscid incompressible fluid (i.e. launcher with liquid propellant, tank of satellite, etc.) is generally computed considering an equilibrium state resulting from a linear fluid-structure interaction problem. It is important to note that in this case, the gravity plays an important role in vibrations and the so called elastogravity operator should be taken into account [1,2]. In the present work, we consider the large deformation behavior of a structure loaded by hydrostatic follower forces in order to obtain an accurate static equilibrium state. The solution is computed using a Newton-Raphson algorithm considering the geometrical and material tangent stiffness matrices as well as the contribution of the follower forces [3]. Those linearized operators of the iterative algorithm are used to compute the dependancy between the incremental horizontal level of the free surface, under the fluid volume conservation constraint [4]. Special attention is paid to the finite element discretization of the wetted surface, considering a level-set method [6,7]. Some numerical examples are analyzed to show the efficiency of the proposed approach.