/LOAD/CENTRI

Block Format Keyword Apply a centrifugal force on a set of nodes according a body rotational velocity around the defined direction.

Format

Field	Contents	SI Unit Example
`load_ID`	Load identifier (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier (Integer, maximum 10 digits)
`load_title`	Load title (Character, maximum 100 characters)
`fct_ID`_T	Time function identifier, giving the rotational velocity $ω$ versus time. (Integer)
`Dir`	Direction of rotation (input XX, YY or ZZ) (Text)
`frame_ID`	Frame identifier = 0 Rotation is expressed in global reference system ≠ 0 Rotation is expressed with respect to the frame. (Integer)
`sens_ID`	Sensor identifier. (Integer)
`grnod_ID`	Node group to which the load is applied. (Integer)
`Ivar`	Flag to disregard variation of velocity with respect to time, for the calculation of the force. = 1 (Default) Variation of velocity is not taken into account. = 2 Variation of velocity is taken into account. (Integer)
`Ascale`_x	Abscissa scale factor. Default = 1.0 (Real)	$[s]$
`Fscale`_y	Ordinate scale factor. Default = 1.0 (Real)	$[\frac{rad}{s}]$

A force is computed corresponding to a body rotational velocity around the direction Dir of the global reference system if frame_ID = 0, or the reference system defined by the frame if frame_ID ≠ 0.
This option is not a kinematic condition (velocity of the nodes is not specified).
If frame_ID = 0, the force applied to the node of mass $m$ , at location $M$ is computed as:(1)
$F = m (\frac{d ω}{d t} \land O M + ω \land ω \land O M)$

If Ivar = 1:

$\frac{d ω}{d t} \land O M$ is not taken into account.(2)
$F = m (ω \land ω \land O M)$
If frame_ID ≠ 0, the force applied to a node is computed as: (3)
$F = f_{r} + f_{e} + f_{c}$

Driving force:(4)
$f_{e} = m (γ (A) + (\frac{d Ω_{(R' / R)}}{d t}) \land A M + Ω_{(R' / R)} \land (Ω_{(R' / R)} \land A M))$

Coriolis force:(5)
$f_{c} = m (2 Ω_{(R' / R)} \land v {(M)}_{/ R'})$

Relative force:(6)
$f_{r} = m (\frac{d ω}{d t} \land A M + ω \land ω \land A M)$

If Ivar = 1:

$\frac{d ω}{d t} \land A M$ is not taken into account in relative force.

(7)
$f_{r} = m (ω \land ω \land A M)$

Where,

R

Global reference system

R'

Reference system defined by the frame

A

Origin of the frame

M

A point of the defined group of node

$Ω_{(R' / R)}$

Rotational velocity of the frame with respect to the global reference system

$ω$

Rotational velocity defined by the time function