modelBeam

Information

Standard beam model for DS Library. This block can be used to model either rigid or flexible beams, by setting the value of the "rigid" flag to either true or false.

The length of the beam should be set here in the beam block. Cross-sectional dimensions and cross section type should be passed in via one of the DeployStructLib.Properties.BeamXProperties records. Material properties should similarly be supplied by an DeployStructLib.Properties.MaterialProperties record.

For rigid beams only: If parameter useQuaternions is true (this is the default), then 4 quaternions are potential states. Additionally, the coordinates of the absolute angular velocity vector of the body are 3 potential states.
If useQuaternions in the "Advanced" menu is false, then 3 angles and the derivatives of these angles are potential states. The orientation of frame_a is computed by rotating the world frame along the axes defined in parameter vector "sequence_angleStates" (default = {1,2,3}, i.e., the Cardan angle sequence) around the angles used as potential states. For example, the default is to rotate the x-axis of the world frame around angles[1], the new y-axis around angles[2] and the new z-axis around angles[3], arriving at frame_a.

The quaternions have the slight disadvantage that there is a non-linear constraint equation between the 4 quaternions. Therefore, at least one non-linear equation has to be solved during simulation. A tool might, however, analytically solve this simple constraint equation. Using the 3 angles as states has the disadvantage that there is a singular configuration in which a division by zero will occur. If it is possible to determine in advance for an application class that this singular configuration is outside of the operating region, the 3 angles might be used as potential states by setting useQuaternions = false.

Parameters

Type	Name	Default	Description
Boolean	rigid	false
Boolean	useLumpedMassMatrix	false	=true, use a lumped mass matrix formulation else use a consistent mass matrix formulation
Boolean	useEAGJ	false	=true, use the EAGJ formulation for the beam, requires EAGJ_BeamProperty input parameter
Boolean	useQuaternions	true
Boolean	useGravity	false	=true, use gravity in the simulation (computational speedup if not used)
SI.Length	L		Beam length
beamXProperty	xprop		Beam cross-section properties
isotropicMaterialProperty	matProp		Beam material properties
EAGJ_BeamProperty	EAGJprop		Beam properties in EAGJ format
SI.Length	centroid	{0, 0}	Cross section centroid relative to frame_a
Boolean	animation	true
SI.Position[3]	r_0_start	{0, 0, 0}
Initialization
SI.Angle[3]	angles_start	{0, 0, 0}	Initial values of angles to rotate frame_a around 'sequence_start' axes into frame_b
Types.RotationSequence	sequence_start	{1, 2, 3}	Sequence of rotations to rotate frame_a into frame_b at initial time

Connectors

Type	Name	Default	Description
Modelica.Mechanics.MultiBody.Interfaces.Frame_a	frame_a
Modelica.Mechanics.MultiBody.Interfaces.Frame_b	frame_b

Components

Type	Name	Default	Description
Utilities.RigidBeam	beamR
Utilities.FlexBeam	beamF
Utilities.FlexBeamEAGJ	beamEAGJ