NodePoint2DSlope1

A 2D point/slope vector node for planar Bernoulli-Euler ANCF (absolute nodal coordinate formulation) beam elements; the node has 4 displacement degrees of freedom (2 for displacement of point node and 2 for the slope vector ‘slopex’); all coordinates lead to second order differential equations; the slope vector defines the directional derivative w.r.t the local axial (x) coordinate, denoted as \(()^\prime\); in straight configuration aligned at the global x-axis, the slope vector reads \({\mathbf{r}}^\prime=[r_x^\prime\;\;r_y^\prime]^T=[1\;\;0]^T\).

Additional information for NodePoint2DSlope1:

  • This Node has/provides the following types = Position2D, Orientation2D, Point2DSlope1, Position, Orientation
  • Short name for Python = Point2DS1
  • Short name for Python visualization object = VPoint2DS1

The item NodePoint2DSlope1 with type = ‘Point2DSlope1’ has the following parameters:

  • name [type = String, default = ‘’]:
    node’s unique name
  • referenceCoordinates [type = Vector4D, size = 4, default = [0.,0.,1.,0.]]:
    reference coordinates (x-pos,y-pos; x-slopex, y-slopex) of node; global position of node without displacement
  • initialCoordinates [type = Vector4D, size = 4, default = [0.,0.,0.,0.]]:
    initial displacement coordinates: ux, uy and x/y ‘displacements’ of slopex
  • initialVelocities [type = Vector4D, size = 4, default = [0.,0.,0.,0.]]:
    initial velocity coordinates
  • visualization [type = VNodePoint2DSlope1]:
    parameters for visualization of item

The item VNodePoint2DSlope1 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 NodePoint2DSlope1

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

  • Position: \(\LU{0}{{\mathbf{p}}}\cConfig = [p_0,\, p_1,\,0]\cConfig\tp\)
    global 3D position vector of node (=displacement+reference position)
  • Displacement: \(\LU{0}{{\mathbf{u}}}\cConfig = [q_0,\, q_1,\,0]\cConfig\tp\)
    global 3D displacement vector of node
  • Velocity: \(\LU{0}{{\mathbf{v}}}\cConfig = [\dot q_0,\,\dot q_1,\,0]\cConfig\tp\)
    global 3D velocity vector of node
  • Acceleration: \(\LU{0}{{\mathbf{a}}}\cConfig = [\ddot q_0,\,\ddot q_1,\,0]\cConfig\tp\)
    global 3D acceleration vector of node
  • Coordinates:
    coordinates vector of node (2 displacement coordinates + 2 slope vector coordinates)
  • Coordinates\_t:
    velocity coordinates vector of node (derivative of the 2 displacement coordinates + 2 slope vector coordinates)
  • Coordinates\_tt:
    acceleration coordinates vector of node (derivative of the 2 displacement coordinates + 2 slope vector coordinates)

Relevant Examples and TestModels with weblink:

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