Stiffness in the Normal Direction
When membrane elements are used separately, not supported by other structural elements, a prestress is necessary in order to avoid a singularity. The unstressed membrane has no stiffness in the normal direction. It is the geometrically nonlinear effects (stress stiffening) which supply the out-of-plane stiffness. A prestress can be given either through initial stress and strain or through a tensile boundary load. Prestress is not necessary in cases where inertia effects are included in a dynamic analysis. A small prestress can, however, still be useful to stabilize the analysis in the initial state. In order to obtain the prestress effect, you must select Include geometric nonlinearity in the settings for the study step.
If you want to explicitly prescribe the stress field for a prestressed analysis rather than solving for it, you should not use the two study step procedure. In such a case, prescribe the stress field using an Initial Stress and Strain, External Stress, or External Strain node. Then add a separate Eigenfrequency or Frequency Domain study and select Include Geometric Nonlinearity in the settings for the study step.