Why do you want to turn off bending stiffness?
Please reply and insert an image of the geometry, mesh, loads and supports and an image of the Force Convergence Plot under the Solution Information folder.
Is there a plane of symmetry for the geometry, loads and supports that would cut the model size in half?
Under Mesh Controls, set the Element Order to Linear.
Under Analysis Settings, turn on Auto Time Stepping, with Initial and Minimum Substeps to 100, Maximum to 200.
Turn on Large Deflection.
Turn on Stabilization.
Add a Command Object to the Model: NEQIT,100
I assume the load creates some tension in the membrane. Try using the INISTATE command to apply some initial stress (or strain) to the elements before the solver starts. This requires a Command Object, so try the steps above before you resort to this.