Rotating Frame and Gravity
You can add Rotating Frame and Gravity nodes to create the loads caused by gravity or accelerated frames. This gives load contributions from all nodes in the physics interface which have a density or mass, such as Linear Elastic Material, Rigid Domain, Added Mass, or Point Mass.
Only features which have a geometrical selection contribute to the mass forces. The Mass and Moment of Inertia nodes are global features and will not get any contribution from Rotating Frame and Gravity nodes.
In the following, the mass density ρ should be considered as generalized. It can represent mass per unit volume, mass per unit area, mass per unit length, or even mass, depending on the dimensionality of the object giving the contribution.
Rotating Frame
Centrifugal, Coriolis and Euler forces are fictitious forces that need to be introduced in a rotating frame of reference, since it is not an inertial system. They can be added as loads.
Alternatively, the total acceleration in the rotating frame can be augmented to include the frame acceleration effects:
Gravity
The gravity acts in a fixed spatial direction eg. The intensity is
where g is the acceleration of gravity. The action of gravity can also be presented as a linearly accelerated frame of reference. Thus, it can be accounted for as a contribution into the total acceleration via the frame acceleration term given by:
Centrifugal Force
A centrifugal force acts radially outward from the axis of rotation defined by the axial direction vector eax. The rotation is represented by the angular velocity vector:
where Ω is the angular velocity. In vector form, the acceleration contribution and the loads are:
where rp is the rotation position vector that contains the coordinates with respect to any point on the axis of rotation. The point is given by its radius vector in the global coordinate system rbp.
Spin-softening Effect
The structural displacement can be accounted for when computing the rotation position, so that
This results in a contribution from the extra acceleration terms caused by the deformation into the system’s stiffness matrix. The effect is often called spin-softening.
Coriolis Force
For a Coriolis force to appear, the object studied must have a velocity relative to the rotating frame. The acceleration contribution and the load are:
This gives a damping contribution since it is proportional to the velocity.
Euler Force
The Euler force occurs when the rate of rotation is not constant in time. The force acts in the plane of rotation perpendicular to the centrifugal force. The acceleration contribution and the load are: