NodePointSlope1
A 3D point/slope vector node for spatial Bernoulli-Euler ANCF (absolute nodal coordinate formulation) beam elements, with 3 position and 3 slope coordinates, all ODE2; the slope vector is the derivative of the position with respect to the axial coordinate, \([1,\;0,\;0]\tp\) for a straight beam along the global \(x\)-axis.
Interface
Provides:
Position,PointSlope1Node markers that can be attached: MarkerNodePosition
Objects that take this node: ObjectMassPoint, ObjectANCFCable
Parameters
The parameters of the item; in a dictionary, its type is ‘PointSlope1’:
name |
type |
size |
default |
description |
|---|---|---|---|---|
name |
String |
‘’ |
node’s unique name |
|
referenceCoordinates |
Vector6D |
6 |
[0.,0.,0.,1.,0.,0.] |
reference coordinates (x-pos,y-pos,z-pos; x-slopex, y-slopex, z-slopex) of node; global position of node without displacement |
initialCoordinates |
Vector6D |
6 |
[0.,0.,0.,0.,0.,0.] |
initial displacement coordinates: ux, uy, uz and x/y/z ‘displacements’ of slopex |
initialVelocities |
Vector6D |
6 |
[0.,0.,0.,0.,0.,0.] |
initial velocity coordinates |
visualization |
VNodePointSlope1 |
parameters for visualization of item |
Visualization parameters
The parameters of VNodePointSlope1, given as visualization:
name |
type |
size |
default |
description |
|---|---|---|---|---|
show |
Bool |
True |
set true, if item is shown in visualization and false if it is not shown |
|
drawSize |
float |
-1. |
drawing size (diameter, dimensions of underlying cube, etc.) for item; size == -1.f means that default size is used |
|
color |
Float4 |
4 |
[-1.,-1.,-1.,-1.] |
Default RGBA color for nodes; 4th value is alpha-transparency; R=-1.f means, that default color is used |
Drawing
Drawn as all nodes; with nodes.showNodalSlopes, also its slope vector.
Settings beyond those of all nodes: nodes.showNodalSlopes.
Output variables
Available as OutputVariableType in sensors, Get...Output() and other functions:
output variable |
symbol |
description |
|---|---|---|
Position |
\(\LU{0}{\pv}\cConfig = [p_0,\, p_1,\, p_2]\cConfig\tp\) |
global 3D position vector of node (=displacement+reference position) |
Displacement |
\(\LU{0}{\uv}\cConfig = [q_0,\, q_1,\, q_2]\cConfig\tp\) |
global 3D displacement vector of node |
Velocity |
\(\LU{0}{\vv}\cConfig = [\dot q_0,\,\dot q_1,\,\dot q_2]\cConfig\tp\) |
global 3D velocity vector of node |
Acceleration |
\(\LU{0}{\av}\cConfig = [\ddot q_0,\,\ddot q_1,\,\ddot q_2]\cConfig\tp\) |
global 3D acceleration vector of node |
CoordinatesTotal |
displacement plus reference coordinates of node |
|
Coordinates |
coordinates vector of node (3 displacement coordinates + 3 slope vector coordinates) |
|
Coordinates_t |
velocity coordinates vector of node (derivative of the 3 displacement coordinates + 3 slope vector coordinates) |
|
Coordinates_tt |
acceleration coordinates vector of node (derivative of the 3 displacement coordinates + 3 slope vector coordinates) |
Detailed description
Coordinates
index |
symbol |
kind |
meaning |
frame |
|---|---|---|---|---|
0, 1, 2 |
\(q_0,\,q_1,\,q_2\) |
displacement of the node position \(\rv\) |
global |
|
3, 4, 5 |
\(q_3,\,q_4,\,q_5\) |
change of the slope vector \(\rv^\prime\) |
global |
Configuration
The slope vector
The slope vector is the derivative of the position of the beam axis with respect to the axial coordinate \(x\) of the element in its reference configuration, \(\rv^\prime = \partial \rv / \partial x\). In a straight beam along the global \(x\)-axis it is \([1,\;0,\;0]\tp\), the default of the reference coordinates. Its direction is the tangent of the beam axis and its length one plus the axial strain, \(\varepsilon = \|\rv^\prime\| - 1\). A single slope vector carries no rotation about the beam axis: the element that uses the node has no torsion.
Frame and interpretation
All six coordinates are global (absolute nodal coordinates). The node is used by the spatial ANCF
cable element ObjectANCFCable.
Action on the equations of motion
The six coordinates lead to six ODE2 equations, which the element provides; a force at the node enters the first three.
Mini example
#a cantilever of one 3D ANCF cable element: position and slope (r_x) at each node
L = 1; EI = 100; F = -0.1
n0 = mbs.AddNode(NodePointSlope1(referenceCoordinates=[0,0,0, 1,0,0])) #position, slope = axis
n1 = mbs.AddNode(NodePointSlope1(referenceCoordinates=[L,0,0, 1,0,0]))
mbs.AddObject(ObjectANCFCable(nodeNumbers=[n0,n1], length=L, massPerLength=1,
bendingStiffness=EI, axialStiffness=1e5))
mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nGround, coordinate=0))
for i in [0,1,2,4,5]: #clamped: the position and the transverse components of the slope
mCoord = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=n0, coordinate=i))
mbs.AddObject(ObjectConnectorCoordinate(markerNumbers=[mGround, mCoord]))
mTip = mbs.AddMarker(MarkerNodePosition(nodeNumber=n1))
mbs.AddLoad(LoadForceVector(markerNumber=mTip, loadVector=[0,0,F]))
mbs.Assemble()
mbs.SolveStatic()
#the cubic element is exact for a tip load: F*L^3/(3*EI) = -1/3000
exu.sys['testResult'] = mbs.GetNodeOutput(n1, exu.OutputVariableType.Displacement)[2]*1000 #-1/3
Relevant Examples (Ex) and TestModels (TM) with weblink to github: accessFunctionsTest.py (TM), energiesFlexibleBodiesTest.py (TM)