Dear Ali,
The SubDyn module of FAST is based on a linear beam finite-element approach and the BeamDyn module of FAST is based on a nonlinear beam finite-element approach. I wouldn’t call the ElastoDyn module a finite-element approach, although the tower and blades are similar to a finite-element approach in that shape functions (in this case mode shapes) are used to form generalized mass, stiffness, and damping matrices (and geometric nonlinear terms as well). However–as described in the forum topic I linked above: Coupled blade modes in FAST --ElastoDyn employs a combined modal and multibody dynamics formulation.
Best regards,