Prescribed Displacements, Velocities, and Accelerations
The most fundamental constraint is the prescribed displacement, where the individual components of displacement or rotation can be prescribed to zero or non-zero values for points, edges, boundaries, or domains.
For dynamic analysis, you can also directly prescribe the velocity or acceleration. The conditions for prescribing displacements, velocities, or accelerations are mutually exclusive for the same geometrical object since they prescribe the same degree of freedom.
In frequency domain, a prescribed velocity vp or prescribed acceleration ap can be directly interpreted as a prescribed displacement up:
where ω is the angular frequency.
In the case of a time-dependent analysis, the prescribed displacement is obtained as
or
where u0 and v0 are is given by the initial conditions. It is not possible to set explicit initial conditions, but if initial values are taken from a previous study, they will be respected. In order to compute the integrals, up is introduced as a separate degree of freedom which is solved for by adding an extra ODE.
As prescribing the velocity or acceleration in time domain comes with an extra cost, you should always consider using a prescribed displacement instead. As long as the time history of the velocity or acceleration is a known a priori and does not depend on the solution itself, this is possible.
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When the velocity or acceleration has a simple time dependence, you can integrate it analytically one or two times to obtain the displacement, and directly prescribe the displacement instead.
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When you have complicated known velocity or acceleration histories, for example from measurements, you can use the integrate() operator. In this case, you enter the prescribed displacement as integrate(my_data(tau),tau,0,t). Here my_data is the measured data as function of time, and tau is a dummy integration variable
In a stationary analysis, the prescribed velocity and acceleration nodes can have two different behaviors. As a default, they are ignored, but you can also select that the degrees of freedom having a prescribed velocity or acceleration in a dynamic analysis should be constrained to zero in a static analysis.
When a local coordinate system is used for prescribing a prescribed velocity or acceleration, the axis directions must be fixed in space. As an example, you cannot use a Boundary System rotating with the deformation.