To model a chain I think you should use many CBEAM elements. Keep bending stiffness very low and give correct axial stiffness.
Use sol 106 and PARAM LGDISP 1 (large displacement on).
In this way you are able to evaluate the correct sag of your cable.
You could try (I've never done) to release the bending DOF of beams end (5&6). in this case You must give to element bending stiffness iwo eliminate singularity.
Let me know which system work better for you!
Onda