NodePointSlope12

A 3D point/slope vector node for thin ANCF (absolute nodal coordinate formulation) plate elements; the node has 9 ODE2 degrees of freedom (3 for displacement of point node and 2 \(\times\) 3 for the slope vectors ‘slopeX’ and ‘slopeY’); all coordinates lead to second order differential equations; the slopeX vector defines the directional derivative w.r.t the local axial (x) coordinate, etc.; in straight configuration aligned at the global x-axis, the slopeY vector reads \({\mathbf{r}}_y^\prime=[0\;\;1\;\;0]^T\).

Additional information for NodePointSlope12:

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

The item NodePointSlope12 with type = ‘PointSlope12’ 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-slopeX, y-slopeX, z-slopeX; x-slopeY, y-slopeY, z-slopeY) 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 = VNodePointSlope12]:
    parameters for visualization of item

The item VNodePointSlope12 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

DESCRIPTION of NodePointSlope12

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

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