PolarMomentOfInertia

Compute the polar moment of inertia of a sideset w.r.t. a point and a direction

Overview

This postprocessor computes the polar moment of inertia $var element = document.getElementById("moose-equation-629f68c2-1114-49c4-98c0-2d97beb720a6");katex.render("J", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ (or $var element = document.getElementById("moose-equation-0b3bdd4b-dc2d-4f93-80ee-6cecceb97548");katex.render("I_z", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ ) of a surface with respect to a reference point (origin) and an axis of rotation (direction). Its result is needed by the Torque boundary condition.

Example Input File Syntax

Input Parameters

boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector<BoundaryName>
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
directionAxis direction
C++ Type:libMesh::VectorValue<double>
Options:
Description:Axis direction
originAxis origin
C++ Type:libMesh::Point
Options:
Description:Axis origin

Required Parameters

execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, TRANSFER
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files

(modules/tensor_mechanics/test/tests/action/material_output_order.i)
(modules/tensor_mechanics/test/tests/torque/torque_small.i)
(modules/tensor_mechanics/test/tests/torque/ad_torque_small.i)

(modules/tensor_mechanics/test/tests/action/material_output_order.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  origin = '0 0 2'
  direction = '0 0 1'
  polar_moment_of_inertia = pmi
  factor = t
[]

[Mesh]
  [ring]
    type = AnnularMeshGenerator
    nr = 1
    nt = 30
    rmin = 0.95
    rmax = 1
  []
  [extrude]
    type = MeshExtruderGenerator
    input = ring
    extrusion_vector = '0 0 2'
    bottom_sideset = 'bottom'
    top_sideset = 'top'
    num_layers = 5
  []
[]

[AuxVariables]
  [alpha_var]
  []
  [shear_stress_var]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [alpha]
    type = RotationAngle
    variable = alpha_var
  []
  [shear_stress]
    type = ParsedAux
    variable = shear_stress_var
    args = 'stress_yz stress_xz'
    function = 'sqrt(stress_yz^2 + stress_xz^2)'
  []
[]

[BCs]
  # fix bottom
  [fix_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0
  []
  [fix_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
  []
  [fix_z]
    type = DirichletBC
    boundary = bottom
    variable = disp_z
    value = 0
  []

  # twist top
  [twist_x]
    type = Torque
    boundary = top
    variable = disp_x
  []
  [twist_y]
    type = Torque
    boundary = top
    variable = disp_y
  []
  [twist_z]
    type = Torque
    boundary = top
    variable = disp_z
  []
[]

[Modules/TensorMechanics/Master]
  [all]
    add_variables = true
    strain = SMALL
    generate_output = 'vonmises_stress stress_yz stress_xz'
  []
[]

[Postprocessors]
  [pmi]
    type = PolarMomentOfInertia
    boundary = top
    # execute_on = 'INITIAL NONLINEAR'
    execute_on = 'INITIAL'
  []
  [alpha]
    type = SideAverageValue
    variable = alpha_var
    boundary = top
  []
  [shear_stress]
    type = ElementAverageValue
    variable = shear_stress_var
  []
[]

[Materials]
  [stress]
    type = ComputeLinearElasticStress
  []
  [elastic]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 0.3
    shear_modulus = 100
  []
[]

[Executioner]
  # type = Steady
  type = Transient
  num_steps = 1
  solve_type = PJFNK
  petsc_options_iname = '-pctype'
  petsc_options_value = 'lu'
  nl_max_its = 150
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = true
[]

(modules/tensor_mechanics/test/tests/torque/torque_small.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  origin = '0 0 2'
  direction = '0 0 1'
  polar_moment_of_inertia = pmi
  factor = t
[]

[Mesh]
  [ring]
    type = AnnularMeshGenerator
    nr = 1
    nt = 30
    rmin = 0.95
    rmax = 1
  []
  [extrude]
    type = MeshExtruderGenerator
    input = ring
    extrusion_vector = '0 0 2'
    bottom_sideset = 'bottom'
    top_sideset = 'top'
    num_layers = 5
  []
[]

[AuxVariables]
  [alpha_var]
  []
  [shear_stress_var]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [alpha]
    type = RotationAngle
    variable = alpha_var
  []
  [shear_stress]
    type = ParsedAux
    variable = shear_stress_var
    args = 'stress_yz stress_xz'
    function = 'sqrt(stress_yz^2 + stress_xz^2)'
  []
[]

[BCs]
  # fix bottom
  [fix_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0
  []
  [fix_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
  []
  [fix_z]
    type = DirichletBC
    boundary = bottom
    variable = disp_z
    value = 0
  []

  # twist top
  [twist_x]
    type = Torque
    boundary = top
    variable = disp_x
  []
  [twist_y]
    type = Torque
    boundary = top
    variable = disp_y
  []
  [twist_z]
    type = Torque
    boundary = top
    variable = disp_z
  []
[]

[Modules/TensorMechanics/Master]
  [all]
    add_variables = true
    strain = SMALL
    generate_output = 'vonmises_stress stress_yz stress_xz'
  []
[]

[Postprocessors]
  [pmi]
    type = PolarMomentOfInertia
    boundary = top
    # execute_on = 'INITIAL NONLINEAR'
    execute_on = 'INITIAL'
  []
  [alpha]
    type = SideAverageValue
    variable = alpha_var
    boundary = top
  []
  [shear_stress]
    type = ElementAverageValue
    variable = shear_stress_var
  []
[]

[Materials]
  [stress]
    type = ComputeLinearElasticStress
  []
  [elastic]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 0.3
    shear_modulus = 100
  []
  []

[Executioner]
  # type = Steady
  type = Transient
  num_steps = 1
  solve_type = PJFNK
  petsc_options_iname = '-pctype'
  petsc_options_value = 'lu'
  nl_max_its = 150
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = true
[]

(modules/tensor_mechanics/test/tests/torque/ad_torque_small.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  origin = '0 0 2'
  direction = '0 0 1'
  polar_moment_of_inertia = pmi
  factor = t
[]

[Mesh]
  [ring]
    type = AnnularMeshGenerator
    nr = 1
    nt = 30
    rmin = 0.95
    rmax = 1
  []
  [extrude]
    type = MeshExtruderGenerator
    input = ring
    extrusion_vector = '0 0 2'
    bottom_sideset = 'bottom'
    top_sideset = 'top'
    num_layers = 5
  []
[]

[AuxVariables]
  [alpha_var]
  []
  [shear_stress_var]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [alpha]
    type = RotationAngle
    variable = alpha_var
  []
  [shear_stress]
    type = ParsedAux
    variable = shear_stress_var
    args = 'stress_yz stress_xz'
    function = 'sqrt(stress_yz^2 + stress_xz^2)'
  []
[]

[BCs]
  # fix bottom
  [fix_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0
  []
  [fix_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
  []
  [fix_z]
    type = DirichletBC
    boundary = bottom
    variable = disp_z
    value = 0
  []

  # twist top
  [twist_x]
    type = ADTorque
    boundary = top
    variable = disp_x
  []
  [twist_y]
    type = ADTorque
    boundary = top
    variable = disp_y
  []
  [twist_z]
    type = ADTorque
    boundary = top
    variable = disp_z
  []
[]

[Modules/TensorMechanics/Master]
  [all]
    add_variables = true
    strain = SMALL
    use_automatic_differentiation = true
    generate_output = 'vonmises_stress stress_yz stress_xz'
  []
[]

[Postprocessors]
  [pmi]
    type = PolarMomentOfInertia
    boundary = top
    # execute_on = 'INITIAL NONLINEAR'
    execute_on = 'INITIAL'
  []
  [alpha]
    type = SideAverageValue
    variable = alpha_var
    boundary = top
  []
  [shear_stress]
    type = ElementAverageValue
    variable = shear_stress_var
  []
[]

[Materials]
  [stress]
    type = ADComputeLinearElasticStress
  []
  [elastic]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 0.3
    shear_modulus = 100
  []
[]

[Executioner]
  # type = Steady
  type = Transient
  num_steps = 1
  solve_type = NEWTON
  petsc_options_iname = '-pctype'
  petsc_options_value = 'lu'
  nl_max_its = 150
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = true
[]

Overview
Example Input File Syntax
Input Parameters
Input Files

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