NodePointSlope23

A 3D point/slope vector node for spatial, shear and cross-section deformable ANCF (absolute nodal coordinate formulation) beam elements; the node has 9 ODE2 degrees of freedom (3 for displacement of point node and 2 \(\times\) 3 for the slope vectors ‘slopeY’ and ‘slopeZ’); all coordinates lead to second order differential equations; the slopeY vector defines the directional derivative w.r.t the local axial (y) coordinate, etc.; the slopeY vector reads \({\mathbf{r}}_y^\prime=[0\;\;1\;\;0]^T\) and slopeZ gets \({\mathbf{r}}_z^\prime=[0\;\;0\;\;1]^T\).

Additional information for NodePointSlope23:

• This Node has/provides the following types = Position, Orientation

The item NodePointSlope23 with type = ‘PointSlope23’ has the following parameters:

• name [type = String, default = ‘’]:

  node’s unique name
• referenceCoordinates [type = Vector9D, size = 9, default = [0.,0.,0.,1.,0.,0.,1.,0.,0.]]:

  reference coordinates (x-pos,y-pos,z-pos; x-slopey, y-slopey, z-slopey; x-slopez, y-slopez, z-slopez) of node; global position of node without displacement
• initialCoordinates [type = Vector9D, size = 9, default = [0.,0.,0.,0.,0.,0.,0.,0.,0.]]:

  initial displacement coordinates relative to reference coordinates
• initialVelocities [type = Vector9D, size = 9, default = [0.,0.,0.,0.,0.,0.,0.,0.,0.]]:

  initial velocity coordinates
• visualization [type = VNodePointSlope23]:

  parameters for visualization of item

The item VNodePointSlope23 has the following parameters:

• show [type = Bool, default = True]:

  set true, if item is shown in visualization and false if it is not shown
• drawSize [type = float, default = -1.]:

  drawing size (diameter, dimensions of underlying cube, etc.) for item; size == -1.f means that default size is used
• color [type = Float4, size = 4, default = [-1.,-1.,-1.,-1.]]:

  Default RGBA color for nodes; 4th value is alpha-transparency; R=-1.f means, that default color is used

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DESCRIPTION of NodePointSlope23

The following output variables are available as OutputVariableType in sensors, Get…Output() and other functions:

• Position: \(\LU{0}{{\mathbf{p}}}\cConfig = \LU{0}{[p_0,\, p_1,\, p_2]}\cConfig\tp\)

  global 3D position vector of node (=displacement+reference position)
• Displacement: \(\LU{0}{{\mathbf{u}}}\cConfig = \LU{0}{[q_0,\, q_1,\, q_2]}\cConfig\tp\)

  global 3D displacement vector of node
• Velocity: \(\LU{0}{{\mathbf{a}}}\cConfig = \LU{0}{[\dot q_0,\,\dot q_1,\,\dot q_2]}\cConfig\tp\)

  global 3D velocity vector of node
• Acceleration: \(\LU{0}{{\mathbf{a}}}\cConfig = \LU{0}{[\ddot q_0,\,\ddot q_1,\,\ddot q_2]}\cConfig\tp\)

  global 3D acceleration vector of node
• Coordinates:

  coordinate vector of node (relative to reference configuration)
• Coordinates\_t:

  velocity coordinates vector of node
• Coordinates\_tt:

  acceleration coordinates vector of node
• RotationMatrix: \([A_{00},\,A_{01},\,A_{02},\,A_{10},\,\ldots,\,A_{21},\,A_{22}]\cConfig\tp\)

  vector with 9 components of the rotation matrix \(\LU{0b}{\Rot}\cConfig\) in row-major format, in any configuration; the rotation matrix transforms local (\(b\)) to global (0) coordinates
• Rotation: \([\varphi_0,\,\varphi_1,\,\varphi_2]\tp\cConfig\)

  vector with 3 components of the Euler / Tait-Bryan angles in xyz-sequence
• AngularVelocity: \(\LU{0}{\tomega}\cConfig = \LU{0}{[\omega_0,\,\omega_1,\,\omega_2]}\cConfig\tp\)

  global 3D angular velocity vector of node
• AngularVelocityLocal: \(\LU{b}{\tomega}\cConfig = \LU{b}{[\omega_0,\,\omega_1,\,\omega_2]}\cConfig\tp\)

  local (body-fixed) 3D angular velocity vector of node

Relevant Examples and TestModels with weblink:

ANCFBeamEigTest.py (TestModels/), ANCFBeamTest.py (TestModels/), geometricallyExactBeamTest.py (TestModels/), rightAngleFrame.py (TestModels/)

The web version may not be complete. For details, consider also the Exudyn PDF documentation : theDoc.pdf