with the help of Jason Jonkman I already found that the mass matrix to be solved is computed in the subroutine ElastoDyn.f90/FillAugMat(). Thank you!
Additionally I was told that the stiffness- and damping matrices are only computed during a linearization analysis.
I would appreciate if you also can tell where to find the routines that compute these mentioned matrices. Thank you very much in advance!
The ElastoDyn routine ElastoDyn.f90/ED_JacobianPContState() computes dX/dx using a central-difference perturbation method, which is the derivative of the state equations with respect to the states i.e. the linear state matrix “A”, which contains 0, I, -[ M^-1 ]*K and -[ M^-1 ]*C as sub block matrices. With knowledge of the mass matrix (M), this matrix can be used to derive the stiffness (K) and damping (C) matrices.
I hope that helps.