Hydrostatic fluid loading in non-linear finite element analysis

Deformation dependent pressure loading on solid structures is created by the interaction of fluids with the deformable surface of a structure. Such fairly simple load models are valid for static and quasistatic analyses and they are a very efficient tool to represent the influence of a fluid on the behaviour of structures. Completing previous studies on the deformation dependence of the loading with the assumption of finite gas volumes, the current contribution focuses on the influence of modifications of the size and shape of a finite structure containing an incompressible fluid with a free surface. The linearization of the corresponding virtual work expression necessary for a Newton-type solution leads to additional terms for the volume dependence. Investigating these terms the conservativeness of the problem can be proven by the symmetry of the linearized form. Similarly to gas loading, the discretization of the structure with finite elements leads to standard stiffness matrix forms plus the so-called load stiffness matrices and a rank-one update for each filled structure part, if the loaded surface segments are identical with element surfaces. Some numerical examples show the effectiveness of the approach and the necessity to take the corresponding terms in the variational expression and the following linearization into account