Direct dynamic coupling using dual time stepping for moving meshes

Direct dynamic coupling methodology for moving meshes depends on the structural model. In the case of a linear or weakly non-linear model, the de­formation of the structure may be described using a modal basis. The grid deformation and velocity are then given by a linear combination of modal grid deformations and velocities at any time. The grid motion is interpolated. In the strongly non-linear case, structural deformations and velocities have to be computed at each time step of the coupled system from a finite element model. The grid’s motion has to be fully computed at each time step as well.

Assuming now that we use a linear structural model, the dynamic behavior of the structure is properly given by a linear combination of modal deforma­tions. We may write at any time t the vector 1І of the displacement at node M as:

Ft (M, t) = ^ qi (t) hi (M)

i

where qi (t) stands for the instantaneous generalized coordinates. Writing the mechanical principle in the modal basis gives :

Mq(t) + Dq(t) + Kq(t) = Fa (q, <q, t)

where M, D, K and Fa respectively stand for the mass, damping and stiffness matrices and the instantaneous aerodynamic forces.