Prescribed Rotations

Loading in cylindrical frame : prescribed rotations - radial displacements (around a moving axis)

Displacements and rotations imposed with respect to an axis are extensions of imposed displacements (translations) and are used to rotate/move a set of nodes around an axis, which can be in motion too. As for displacements, this is done with LoadingSet. The motion of the axis is also defined in the LoadingSet.

Translation of the axis

If the axis is defined by points p1 and p2, its motion can be defined by commands similar to the following ones:

loadingset.define(p1, Field1D(TX,RE), dx1, fctX1)
loadingset.define(p1, Field1D(TY,RE), dy1, fctY1)
loadingset.define(p1, Field1D(TZ,RE), dz1, fctZ1)
loadingset.define(p2, Field1D(TX,RE), dx2, fctX2)
loadingset.define(p2, Field1D(TY,RE), dy2, fctY2)
loadingset.define(p2, Field1D(TZ,RE), dz2, fctZ2)

`p1`	reference Point at the origin of the axis
`dx1`, `dy1`, `dz1`	amplitudes of the x,y,z displacements of point p1
`fctX1`, `fctY1`, `fctZ1`	x,y,z displacement Functions y=f(t) of p1
`p2`	reference Point at the end of the axis
`dx2`, `dy2`, `dz2`	amplitudes of the x,y,z displacements of point p2
`fctX2`, `fctY2`, `fctZ2`	x,y,z displacement Functions y=f(t) of p2

Case #1: Radial displacement imposed with respect to the axis

loadingset.defineRad(gObject, Field1D(TX,RE), p1, p2, ampl, fct)

`gObject`	Geometric entity
`field`	name of the variable which is concerned by the motion
`ampl`	amplitude
`fct`	Functions y=f(t) (time dependence)
`p1`	reference Point at the origin of the axis
`p2`	reference Point at the end of the axis

Case #2: Rotation imposed around the axis

loadingset.defineRot(gObject, field, p1, p2, option, ampl, fct)

`gObject`	Geometric entity
`field`	name of the variable which is concerned by the motion (only `Field3D(TXTYTZ,RE)` is allowed)
`ampl`	amplitude
`fct`	Functions y=f(t) (can depend on time and position)
`p1`	reference Point at the origin of the axis
`p2`	reference Point at the end of the axis
`option`	= `False` : the boundary condition is a given angle, in degrees = `True` : the boundary condition is a given angular speed, in degrees/second

Case #3: 2 successive Rotations imposed around 2 axes

loadingset.defineRot2(gObject, field, axe1, ampl1, fct1, 
                                      axe2, ampl2, fct2, option)

`gObject`	Geometric entity
`field`	name of the variable which is concerned by the motion (only `Field3D(TXTYTZ,RE)` is allowed)
`axe1`	first axis of rotation (`Axe` object).
`ampl1`	amplitude of the first rotation
`fct1`	Functions y=f(t) of the first rotation (can only depend on time)
`axe2`	second axis of rotation (`Axe` object). The motion of this axis drives the global translation of the object
`ampl2`	amplitude of the second rotation
`fct2`	Functions y=f(t) of the second rotation (can only depend on time)
`option`	= `False` : the boundary condition is a given angle, in degrees = `True` : the boundary condition is a given angular speed, in degrees/second

The geometry is transformed in the following way:

the rotation around the FIRST axis is applied to the object,
then, the object is translated according to the SECOND axis motion,
finally, the geometry is rotated around the SECOND axis.

In other words, it means that the second axis of defineRot2 behaves as the single axis of defineRot.

Metafor

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