ObjectANCFThinPlate

A 3D thin Kirchhoff plate finite element based on the absolute nodal coordinate formulation, using 4 nodes of type NodePointSlope12. The geometry as well as (deformed and distorted) reference configuration is given by the nodes. The localPosition follows unit-coordinates in the range [-1,1] for X, Y and Z coordinates; the thickness of the plate is h; This element is under construction.

Additional information for ObjectANCFThinPlate:

  • This Object has/provides the following types = Body, MultiNoded
  • Requested Node type = Position

The item ObjectANCFThinPlate with type = ‘ANCFThinPlate’ has the following parameters:

  • name [type = String, default = ‘’]:
    objects’s unique name
  • physicsThickness [\(h\), type = UReal, default = 0.]:
    [SI:m] thickness of plate
  • physicsDensity [\(\rho\), type = UReal, default = 0.]:
    [SI:kg/m\(^3\)] density of the plate, possibly averaged over thickness
  • physicsStrainCoefficients [\({\mathbf{D}}_\varepsilon\), type = Matrix3D, default = [[1,0,0], [0,1,0], [0,0,1]]]:
    [SI:N/m] stiffness coefficients related to inplane normal and shear strains, integrated over height of the plate
  • physicsCurvatureCoefficients [\({\mathbf{D}}_\kappa\), type = Matrix3D, default = [[1,0,0], [0,1,0], [0,0,1]]]:
    [SI:Nm] stiffness coefficients related to curvatures, integrated over height of the plate
  • strainIsRelativeToReference [\(f\cRef\), type = Real, default = 1.]:
    if set to 1., a pre-deformed reference configuration is considered as the stressless state; if set to 0., the straight configuration serves as a reference geometry; allows also values between 0. and 1. to perform a transition during static computation
  • nodeNumbers [type = NodeIndex4, default = [invalid [-1], invalid [-1], invalid [-1], invalid [-1]]]:
    4 NodePointSlope12 node numbers
  • useReducedOrderIntegration [type = Index, default = 0]:
    0/false: use highest Gauss integration for virtual work of strains
  • visualization [type = VObjectANCFThinPlate]:
    parameters for visualization of item

The item VObjectANCFThinPlate has the following parameters:

  • show [type = Bool, default = True]:
    set true, if item is shown in visualization and false if it is not shown; note that all quantities are computed at the beam centerline, even if drawn on surface of cylinder of beam; this effects, e.g., Displacement or Velocity, which is drawn constant over cross section
  • color [type = Float4, default = [-1.,-1.,-1.,-1.]]:
    RGBA color of the object; if R==-1, use default color

DESCRIPTION of ObjectANCFThinPlate

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

  • Position: \(\LU{0}{{\mathbf{p}}\cConfig(x,0,0)} = {\mathbf{r}}\cConfig(x) + y\cdot {\mathbf{n}}\cConfig(x)\)
    global position vector of local position \([x,0,0]\)
  • Displacement: \(\LU{0}{{\mathbf{u}}\cConfig(x,0,0)} = \LU{0}{{\mathbf{p}}\cConfig(x,0,0)} - \LU{0}{{\mathbf{p}}\cRef(x,0,0)}\)
    global displacement vector of local position
  • Velocity: \(\LU{0}{{\mathbf{v}}(x,0,0)} = \LU{0}{\dot {\mathbf{r}}(x)}\)
    global velocity vector of local position
  • Director1: \({\mathbf{r}}'(x)\)
    (axial) slope vector of local axis position (at \(y\)=0)
  • StrainLocal: \(\varepsilon\)
    axial strain (scalar) of local axis position (at Y=Z=0)
  • CurvatureLocal: \([K_x, K_y, K_z]\tp\)
    local curvature vector
  • ForceLocal: \(N\)
    (local) section normal force (scalar, including reference strains) (at \(y\)=\(z\)=0); note that strains are highly inaccurate when coupled to bending, thus consider useReducedOrderIntegration=2 and evaluate axial strain at nodes or at midpoint
  • TorqueLocal: \(M\)
    (local) bending moment (scalar) (at \(y\)=\(z\)=0), which are bending moments as there is no torque
  • Acceleration: \(\LU{0}{{\mathbf{a}}(x,0,0)} = \LU{0}{\ddot {\mathbf{r}}(x)}\)
    global acceleration vector of local position

MINI EXAMPLE for ObjectANCFThinPlate

1#to be done
2
3#check result
4exudynTestGlobals.testResult = 0
5#ux=-0.5013058140308901

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