ObjectANCFThinPlate.rst

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

#to be done

#check result
exudynTestGlobals.testResult = 0
#ux=-0.5013058140308901

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