- temperaturetemperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:temperature
- thermal_conductivityDerivativeParsedMaterial for cost of materials.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:DerivativeParsedMaterial for cost of materials.
ThermalCompliance
Computes cost sensitivity needed for multimaterial SIMP method.
Overview
This material creates a thermal compliance, K, material based on temperature gradients and thermal conductivities using the equation:
E=21∇TK˙∇˙TThe resulting material can be used for analysis purposes and for setting up topology optimization Solid Isotropic Material Penalization-type of problems.
Example Input File Syntax
[Materials]
[thermal_compliance]
type = ThermalCompliance
temperature = temp
thermal_conductivity = thermal_cond
[]
[]Input Parameters
- blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
- boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
- computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
- constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
- declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
- 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
Controllable:No
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
- output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
- outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
Outputs Parameters
- prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
- use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Material Property Retrieval Parameters
Input Files
- (modules/combined/test/tests/optimization/compliance_sensitivity/three_materials_thermal.i)
- (modules/combined/examples/optimization/thermomechanical/thermal_sub.i)
- (modules/combined/test/tests/optimization/compliance_sensitivity/thermal_test.i)
- (modules/heat_transfer/test/tests/thermal_materials/2d.i)
- (modules/combined/test/tests/optimization/thermal_sensitivity/2d_root.i)
(modules/combined/test/tests/optimization/compliance_sensitivity/three_materials_thermal.i)
vol_frac = 0.4
cost_frac = 0.4
power = 4
# Stiffness (not optimized in this test)
E0 = 1.0e-6
E1 = 0.2
E2 = 0.6
E3 = 1.0
# Densities
rho0 = 1.0e-6
rho1 = 0.4
rho2 = 0.7
rho3 = 1.0
# Costs
C0 = 1.0e-6
C1 = 0.5
C2 = 0.8
C3 = 1.0
# Thermal conductivity
TC0 = 1.0e-6
TC1 = 0.2
TC2 = 0.6
TC3 = 1.0
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
[MeshGenerator]
type = GeneratedMeshGenerator
dim = 2
nx = 40
ny = 40
xmin = 0
xmax = 40
ymin = 0
ymax = 40
[]
[node]
type = ExtraNodesetGenerator
input = MeshGenerator
new_boundary = hold
nodes = 0
[]
[push_left]
type = ExtraNodesetGenerator
input = node
new_boundary = push_left
coord = '20 0 0'
[]
[push_center]
type = ExtraNodesetGenerator
input = push_left
new_boundary = push_center
coord = '40 0 0'
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[temp]
initial_condition = 100.0
[]
[]
[AuxVariables]
[Dc]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[Cc]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[Tc]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[Cost]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[mat_den]
family = MONOMIAL
order = CONSTANT
initial_condition = ${vol_frac}
[]
[thermal_compliance]
order = CONSTANT
family = MONOMIAL
[]
[]
# [ICs]
# [mat_den]
# type = RandomIC
# seed = 4
# variable = mat_den
# max = '${fparse vol_frac+0.25}'
# min = '${fparse vol_frac-0.25}'
# []
# []
[AuxKernels]
[Cost]
type = MaterialRealAux
variable = Cost
property = Cost_mat
[]
[thermal_compliance]
type = MaterialRealAux
property = thermal_compliance
variable = thermal_compliance
execute_on = timestep_end
[]
[]
[Kernels]
[heat_conduction]
type = HeatConduction
variable = temp
diffusion_coefficient = thermal_cond
[]
[heat_source]
type = HeatSource
value = 1e-2 # W/m^3
variable = temp
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = SMALL
add_variables = true
incremental = false
[]
[]
[BCs]
[no_y]
type = DirichletBC
variable = disp_y
boundary = hold
value = 0.0
[]
[no_x_symm]
type = DirichletBC
variable = disp_x
boundary = right
value = 0.0
[]
[top]
type = DirichletBC
variable = temp
boundary = top
value = 0
[]
[bottom]
type = DirichletBC
variable = temp
boundary = bottom
value = 0
[]
[right]
type = DirichletBC
variable = temp
boundary = right
value = 0
[]
[left]
type = DirichletBC
variable = temp
boundary = left
value = 0
[]
[]
[NodalKernels]
[push_left]
type = NodalGravity
variable = disp_y
boundary = push_left
gravity_value = -1e-6 # -3
mass = 1
[]
[push_center]
type = NodalGravity
variable = disp_y
boundary = push_center
gravity_value = -1e-6 # -3
mass = 1
[]
[]
[Materials]
[thermal_cond]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; "
"A2:=(${TC1}-${TC2})/(${rho1}^${power}-${rho2}^${power}); "
"B2:=${TC1}-A2*${rho1}^${power}; TC2:=A2*mat_den^${power}+B2; "
"A3:=(${TC2}-${TC3})/(${rho2}^${power}-${rho3}^${power}); "
"B3:=${TC2}-A3*${rho2}^${power}; TC3:=A3*mat_den^${power}+B3; "
"if(mat_den<${rho1},TC1,if(mat_den<${rho2},TC2,TC3))"
coupled_variables = 'mat_den'
property_name = thermal_cond
[]
[thermal_compliance]
type = ThermalCompliance
temperature = temp
thermal_conductivity = thermal_cond
[]
[elasticity_tensor]
type = ComputeVariableIsotropicElasticityTensor
youngs_modulus = E_phys
poissons_ratio = poissons_ratio
args = 'mat_den'
[]
[E_phys]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
"A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
"B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
"A3:=(${E2}-${E3})/(${rho2}^${power}-${rho3}^${power}); "
"B3:=${E2}-A3*${rho2}^${power}; E3:=A3*mat_den^${power}+B3; "
"if(mat_den<${rho1},E1,if(mat_den<${rho2},E2,E3))"
coupled_variables = 'mat_den'
property_name = E_phys
[]
[Cost_mat]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
"B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; "
"A2:=(${C1}-${C2})/(${rho1}^(1/${power})-${rho2}^(1/${power})); "
"B2:=${C1}-A2*${rho1}^(1/${power}); C2:=A2*mat_den^(1/${power})+B2; "
"A3:=(${C2}-${C3})/(${rho2}^(1/${power})-${rho3}^(1/${power})); "
"B3:=${C2}-A3*${rho2}^(1/${power}); C3:=A3*mat_den^(1/${power})+B3; "
"if(mat_den<${rho1},C1,if(mat_den<${rho2},C2,C3))"
coupled_variables = 'mat_den'
property_name = Cost_mat
[]
[CostDensity]
type = ParsedMaterial
property_name = CostDensity
coupled_variables = 'mat_den Cost'
expression = 'mat_den*Cost'
[]
[poissons_ratio]
type = GenericConstantMaterial
prop_names = poissons_ratio
prop_values = 0.3
[]
[stress]
type = ComputeLinearElasticStress
[]
[dc]
type = ComplianceSensitivity
design_density = mat_den
youngs_modulus = E_phys
[]
[cc]
type = CostSensitivity
design_density = mat_den
cost = Cost_mat
[]
[tc]
type = ThermalSensitivity
design_density = mat_den
thermal_conductivity = thermal_cond
temperature = temp
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[UserObjects]
[rad_avg]
type = RadialAverage
radius = 4
weights = linear
prop_name = sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_cost]
type = RadialAverage
radius = 4
weights = linear
prop_name = cost_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_thermal]
type = RadialAverage
radius = 4
weights = linear
prop_name = thermal_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[update]
type = DensityUpdateTwoConstraints
density_sensitivity = Dc
cost_density_sensitivity = Cc
cost = Cost
cost_fraction = ${cost_frac}
design_density = mat_den
volume_fraction = ${vol_frac}
bisection_lower_bound = 0
bisection_upper_bound = 1.0e12 # 100
use_thermal_compliance = true
thermal_sensitivity = Tc
# Only account for thermal optimizxation
weight_mechanical_thermal = '0 1'
relative_tolerance = 1.0e-8
bisection_move = 0.05
adaptive_move = false
execute_on = TIMESTEP_BEGIN
[]
# Provides Dc
[calc_sense]
type = SensitivityFilter
density_sensitivity = Dc
design_density = mat_den
filter_UO = rad_avg
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Cc
[calc_sense_cost]
type = SensitivityFilter
density_sensitivity = Cc
design_density = mat_den
filter_UO = rad_avg_cost
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Tc
[calc_sense_thermal]
type = SensitivityFilter
density_sensitivity = Tc
design_density = mat_den
filter_UO = rad_avg_thermal
execute_on = TIMESTEP_END
force_postaux = true
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
nl_abs_tol = 1e-10
dt = 1.0
num_steps = 12
[]
[Outputs]
[out]
type = CSV
execute_on = 'TIMESTEP_END'
[]
print_linear_residuals = false
[]
[Postprocessors]
[right_flux]
type = SideDiffusiveFluxAverage
variable = temp
boundary = right
diffusivity = 10
[]
[mesh_volume]
type = VolumePostprocessor
execute_on = 'initial timestep_end'
[]
[total_vol]
type = ElementIntegralVariablePostprocessor
variable = mat_den
execute_on = 'INITIAL TIMESTEP_END'
[]
[vol_frac]
type = ParsedPostprocessor
expression = 'total_vol / mesh_volume'
pp_names = 'total_vol mesh_volume'
[]
[sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = sensitivity
[]
[cost_sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = cost_sensitivity
[]
[cost]
type = ElementIntegralMaterialProperty
mat_prop = CostDensity
[]
[cost_frac]
type = ParsedPostprocessor
expression = 'cost / mesh_volume'
pp_names = 'cost mesh_volume'
[]
[objective]
type = ElementIntegralMaterialProperty
mat_prop = strain_energy_density
execute_on = 'INITIAL TIMESTEP_END'
[]
[objective_thermal]
type = ElementIntegralMaterialProperty
mat_prop = thermal_compliance
execute_on = 'INITIAL TIMESTEP_END'
[]
[](modules/combined/test/tests/optimization/compliance_sensitivity/three_materials_thermal.i)
vol_frac = 0.4
cost_frac = 0.4
power = 4
# Stiffness (not optimized in this test)
E0 = 1.0e-6
E1 = 0.2
E2 = 0.6
E3 = 1.0
# Densities
rho0 = 1.0e-6
rho1 = 0.4
rho2 = 0.7
rho3 = 1.0
# Costs
C0 = 1.0e-6
C1 = 0.5
C2 = 0.8
C3 = 1.0
# Thermal conductivity
TC0 = 1.0e-6
TC1 = 0.2
TC2 = 0.6
TC3 = 1.0
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
[MeshGenerator]
type = GeneratedMeshGenerator
dim = 2
nx = 40
ny = 40
xmin = 0
xmax = 40
ymin = 0
ymax = 40
[]
[node]
type = ExtraNodesetGenerator
input = MeshGenerator
new_boundary = hold
nodes = 0
[]
[push_left]
type = ExtraNodesetGenerator
input = node
new_boundary = push_left
coord = '20 0 0'
[]
[push_center]
type = ExtraNodesetGenerator
input = push_left
new_boundary = push_center
coord = '40 0 0'
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[temp]
initial_condition = 100.0
[]
[]
[AuxVariables]
[Dc]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[Cc]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[Tc]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[Cost]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[mat_den]
family = MONOMIAL
order = CONSTANT
initial_condition = ${vol_frac}
[]
[thermal_compliance]
order = CONSTANT
family = MONOMIAL
[]
[]
# [ICs]
# [mat_den]
# type = RandomIC
# seed = 4
# variable = mat_den
# max = '${fparse vol_frac+0.25}'
# min = '${fparse vol_frac-0.25}'
# []
# []
[AuxKernels]
[Cost]
type = MaterialRealAux
variable = Cost
property = Cost_mat
[]
[thermal_compliance]
type = MaterialRealAux
property = thermal_compliance
variable = thermal_compliance
execute_on = timestep_end
[]
[]
[Kernels]
[heat_conduction]
type = HeatConduction
variable = temp
diffusion_coefficient = thermal_cond
[]
[heat_source]
type = HeatSource
value = 1e-2 # W/m^3
variable = temp
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = SMALL
add_variables = true
incremental = false
[]
[]
[BCs]
[no_y]
type = DirichletBC
variable = disp_y
boundary = hold
value = 0.0
[]
[no_x_symm]
type = DirichletBC
variable = disp_x
boundary = right
value = 0.0
[]
[top]
type = DirichletBC
variable = temp
boundary = top
value = 0
[]
[bottom]
type = DirichletBC
variable = temp
boundary = bottom
value = 0
[]
[right]
type = DirichletBC
variable = temp
boundary = right
value = 0
[]
[left]
type = DirichletBC
variable = temp
boundary = left
value = 0
[]
[]
[NodalKernels]
[push_left]
type = NodalGravity
variable = disp_y
boundary = push_left
gravity_value = -1e-6 # -3
mass = 1
[]
[push_center]
type = NodalGravity
variable = disp_y
boundary = push_center
gravity_value = -1e-6 # -3
mass = 1
[]
[]
[Materials]
[thermal_cond]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; "
"A2:=(${TC1}-${TC2})/(${rho1}^${power}-${rho2}^${power}); "
"B2:=${TC1}-A2*${rho1}^${power}; TC2:=A2*mat_den^${power}+B2; "
"A3:=(${TC2}-${TC3})/(${rho2}^${power}-${rho3}^${power}); "
"B3:=${TC2}-A3*${rho2}^${power}; TC3:=A3*mat_den^${power}+B3; "
"if(mat_den<${rho1},TC1,if(mat_den<${rho2},TC2,TC3))"
coupled_variables = 'mat_den'
property_name = thermal_cond
[]
[thermal_compliance]
type = ThermalCompliance
temperature = temp
thermal_conductivity = thermal_cond
[]
[elasticity_tensor]
type = ComputeVariableIsotropicElasticityTensor
youngs_modulus = E_phys
poissons_ratio = poissons_ratio
args = 'mat_den'
[]
[E_phys]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
"A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
"B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
"A3:=(${E2}-${E3})/(${rho2}^${power}-${rho3}^${power}); "
"B3:=${E2}-A3*${rho2}^${power}; E3:=A3*mat_den^${power}+B3; "
"if(mat_den<${rho1},E1,if(mat_den<${rho2},E2,E3))"
coupled_variables = 'mat_den'
property_name = E_phys
[]
[Cost_mat]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
"B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; "
"A2:=(${C1}-${C2})/(${rho1}^(1/${power})-${rho2}^(1/${power})); "
"B2:=${C1}-A2*${rho1}^(1/${power}); C2:=A2*mat_den^(1/${power})+B2; "
"A3:=(${C2}-${C3})/(${rho2}^(1/${power})-${rho3}^(1/${power})); "
"B3:=${C2}-A3*${rho2}^(1/${power}); C3:=A3*mat_den^(1/${power})+B3; "
"if(mat_den<${rho1},C1,if(mat_den<${rho2},C2,C3))"
coupled_variables = 'mat_den'
property_name = Cost_mat
[]
[CostDensity]
type = ParsedMaterial
property_name = CostDensity
coupled_variables = 'mat_den Cost'
expression = 'mat_den*Cost'
[]
[poissons_ratio]
type = GenericConstantMaterial
prop_names = poissons_ratio
prop_values = 0.3
[]
[stress]
type = ComputeLinearElasticStress
[]
[dc]
type = ComplianceSensitivity
design_density = mat_den
youngs_modulus = E_phys
[]
[cc]
type = CostSensitivity
design_density = mat_den
cost = Cost_mat
[]
[tc]
type = ThermalSensitivity
design_density = mat_den
thermal_conductivity = thermal_cond
temperature = temp
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[UserObjects]
[rad_avg]
type = RadialAverage
radius = 4
weights = linear
prop_name = sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_cost]
type = RadialAverage
radius = 4
weights = linear
prop_name = cost_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_thermal]
type = RadialAverage
radius = 4
weights = linear
prop_name = thermal_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[update]
type = DensityUpdateTwoConstraints
density_sensitivity = Dc
cost_density_sensitivity = Cc
cost = Cost
cost_fraction = ${cost_frac}
design_density = mat_den
volume_fraction = ${vol_frac}
bisection_lower_bound = 0
bisection_upper_bound = 1.0e12 # 100
use_thermal_compliance = true
thermal_sensitivity = Tc
# Only account for thermal optimizxation
weight_mechanical_thermal = '0 1'
relative_tolerance = 1.0e-8
bisection_move = 0.05
adaptive_move = false
execute_on = TIMESTEP_BEGIN
[]
# Provides Dc
[calc_sense]
type = SensitivityFilter
density_sensitivity = Dc
design_density = mat_den
filter_UO = rad_avg
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Cc
[calc_sense_cost]
type = SensitivityFilter
density_sensitivity = Cc
design_density = mat_den
filter_UO = rad_avg_cost
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Tc
[calc_sense_thermal]
type = SensitivityFilter
density_sensitivity = Tc
design_density = mat_den
filter_UO = rad_avg_thermal
execute_on = TIMESTEP_END
force_postaux = true
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
nl_abs_tol = 1e-10
dt = 1.0
num_steps = 12
[]
[Outputs]
[out]
type = CSV
execute_on = 'TIMESTEP_END'
[]
print_linear_residuals = false
[]
[Postprocessors]
[right_flux]
type = SideDiffusiveFluxAverage
variable = temp
boundary = right
diffusivity = 10
[]
[mesh_volume]
type = VolumePostprocessor
execute_on = 'initial timestep_end'
[]
[total_vol]
type = ElementIntegralVariablePostprocessor
variable = mat_den
execute_on = 'INITIAL TIMESTEP_END'
[]
[vol_frac]
type = ParsedPostprocessor
expression = 'total_vol / mesh_volume'
pp_names = 'total_vol mesh_volume'
[]
[sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = sensitivity
[]
[cost_sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = cost_sensitivity
[]
[cost]
type = ElementIntegralMaterialProperty
mat_prop = CostDensity
[]
[cost_frac]
type = ParsedPostprocessor
expression = 'cost / mesh_volume'
pp_names = 'cost mesh_volume'
[]
[objective]
type = ElementIntegralMaterialProperty
mat_prop = strain_energy_density
execute_on = 'INITIAL TIMESTEP_END'
[]
[objective_thermal]
type = ElementIntegralMaterialProperty
mat_prop = thermal_compliance
execute_on = 'INITIAL TIMESTEP_END'
[]
[](modules/combined/examples/optimization/thermomechanical/thermal_sub.i)
vol_frac = 0.4
power = 2.0
E0 = 1.0e-6
E1 = 1.0
rho0 = 0.0
rho1 = 1.0
C0 = 1.0e-6
C1 = 1.0
TC0 = 1.0e-16
TC1 = 1.0
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
[MeshGenerator]
type = GeneratedMeshGenerator
dim = 2
nx = 40
ny = 40
xmin = 0
xmax = 40
ymin = 0
ymax = 40
[]
[node]
type = ExtraNodesetGenerator
input = MeshGenerator
new_boundary = hold
nodes = 0
[]
[push_left]
type = ExtraNodesetGenerator
input = node
new_boundary = push_left
coord = '16 0 0'
[]
[push_center]
type = ExtraNodesetGenerator
input = push_left
new_boundary = push_center
coord = '24 0 0'
[]
[extra]
type = SideSetsFromBoundingBoxGenerator
input = push_center
bottom_left = '-0.01 17.999 0'
top_right = '5 22.001 0'
boundary_new = n1
boundaries_old = left
[]
[dirichlet_bc]
type = SideSetsFromNodeSetsGenerator
input = extra
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[temp]
initial_condition = 100.0
[]
[]
[AuxVariables]
[Dc]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[Cc]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[Tc]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[Cost]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[mat_den]
family = MONOMIAL
order = FIRST
initial_condition = ${vol_frac}
[]
[]
[AuxKernels]
[Cost]
type = MaterialRealAux
variable = Cost
property = Cost_mat
[]
[]
[Kernels]
[heat_conduction]
type = HeatConduction
variable = temp
diffusion_coefficient = thermal_cond
[]
[heat_source]
type = HeatSource
value = 1e-2 # W/m^3
variable = temp
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = SMALL
add_variables = true
incremental = false
[]
[]
[BCs]
[no_y]
type = DirichletBC
variable = disp_y
boundary = hold
value = 0.0
[]
[no_x_symm]
type = DirichletBC
variable = disp_x
boundary = right
value = 0.0
[]
[left_n1]
type = DirichletBC
variable = temp
boundary = n1
value = 0.0
[]
[top]
type = NeumannBC
variable = temp
boundary = top
value = 0
[]
[bottom]
type = NeumannBC
variable = temp
boundary = bottom
value = 0
[]
[right]
type = NeumannBC
variable = temp
boundary = right
value = 0
[]
[left]
type = NeumannBC
variable = temp
boundary = left
value = 0
[]
[]
[NodalKernels]
[push_left]
type = NodalGravity
variable = disp_y
boundary = push_left
gravity_value = 0.0 # -1e-8
mass = 1
[]
[push_center]
type = NodalGravity
variable = disp_y
boundary = push_center
gravity_value = 0.0 # -1e-8
mass = 1
[]
[]
[Materials]
[thermal_cond]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; TC1"
coupled_variables = 'mat_den'
property_name = thermal_cond
outputs = 'exodus'
[]
[thermal_compliance]
type = ThermalCompliance
temperature = temp
thermal_conductivity = thermal_cond
outputs = 'exodus'
[]
[elasticity_tensor]
type = ComputeVariableIsotropicElasticityTensor
youngs_modulus = E_phys
poissons_ratio = poissons_ratio
args = 'mat_den'
[]
[E_phys]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; E1"
coupled_variables = 'mat_den'
property_name = E_phys
[]
[Cost_mat]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
"B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; C1"
coupled_variables = 'mat_den'
property_name = Cost_mat
[]
[CostDensity]
type = ParsedMaterial
property_name = CostDensity
coupled_variables = 'mat_den Cost'
expression = 'mat_den*Cost'
[]
[poissons_ratio]
type = GenericConstantMaterial
prop_names = poissons_ratio
prop_values = 0.3
[]
[stress]
type = ComputeLinearElasticStress
[]
[dc]
type = ComplianceSensitivity
design_density = mat_den
youngs_modulus = E_phys
[]
[cc]
type = CostSensitivity
design_density = mat_den
cost = Cost_mat
outputs = 'exodus'
[]
[tc]
type = ThermalSensitivity
design_density = mat_den
thermal_conductivity = thermal_cond
temperature = temp
outputs = 'exodus'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[UserObjects]
[rad_avg]
type = RadialAverage
radius = 0.1
weights = linear
prop_name = sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_cost]
type = RadialAverage
radius = 0.1
weights = linear
prop_name = cost_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_thermal]
type = RadialAverage
radius = 0.1
weights = linear
prop_name = thermal_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
# Provides Dc
[calc_sense]
type = SensitivityFilter
density_sensitivity = Dc
design_density = mat_den
filter_UO = rad_avg
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Cc
[calc_sense_cost]
type = SensitivityFilter
density_sensitivity = Cc
design_density = mat_den
filter_UO = rad_avg_cost
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Tc
[calc_sense_thermal]
type = SensitivityFilter
density_sensitivity = Tc
design_density = mat_den
filter_UO = rad_avg_thermal
execute_on = TIMESTEP_END
force_postaux = true
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
nl_abs_tol = 1e-12
dt = 1.0
num_steps = 500
[]
[Outputs]
exodus = true
[out]
type = CSV
execute_on = 'TIMESTEP_END'
[]
print_linear_residuals = false
[]
[Postprocessors]
[right_flux]
type = SideDiffusiveFluxAverage
variable = temp
boundary = right
diffusivity = 10
[]
[mesh_volume]
type = VolumePostprocessor
execute_on = 'initial timestep_end'
[]
[total_vol]
type = ElementIntegralVariablePostprocessor
variable = mat_den
execute_on = 'INITIAL TIMESTEP_END'
[]
[vol_frac]
type = ParsedPostprocessor
expression = 'total_vol / mesh_volume'
pp_names = 'total_vol mesh_volume'
[]
[sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = sensitivity
[]
[cost_sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = cost_sensitivity
[]
[cost]
type = ElementIntegralMaterialProperty
mat_prop = CostDensity
[]
[cost_frac]
type = ParsedPostprocessor
expression = 'cost / mesh_volume'
pp_names = 'cost mesh_volume'
[]
[objective]
type = ElementIntegralMaterialProperty
mat_prop = strain_energy_density
execute_on = 'INITIAL TIMESTEP_END'
[]
[objective_thermal]
type = ElementIntegralMaterialProperty
mat_prop = thermal_compliance
execute_on = 'INITIAL TIMESTEP_END'
[]
[](modules/combined/test/tests/optimization/compliance_sensitivity/thermal_test.i)
vol_frac = 0.4
cost_frac = 10.0
power = 2.0
E0 = 1.0e-6
E1 = 1.0
rho0 = 0.0
rho1 = 1.0
C0 = 1.0e-6
C1 = 1.0
TC0 = 1.0e-16
TC1 = 1.0
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
[MeshGenerator]
type = GeneratedMeshGenerator
dim = 2
nx = 10
ny = 10
xmin = 0
xmax = 40
ymin = 0
ymax = 40
[]
[node]
type = ExtraNodesetGenerator
input = MeshGenerator
new_boundary = hold
nodes = 0
[]
[push_left]
type = ExtraNodesetGenerator
input = node
new_boundary = push_left
coord = '16 0 0'
[]
[push_center]
type = ExtraNodesetGenerator
input = push_left
new_boundary = push_center
coord = '24 0 0'
[]
[extra]
type = SideSetsFromBoundingBoxGenerator
input = push_center
bottom_left = '-0.01 17.999 0'
top_right = '5 22.001 0'
boundary_new = n1
included_boundaries = left
[]
[dirichlet_bc]
type = SideSetsFromNodeSetsGenerator
input = extra
[]
[]
[Variables]
[disp_x]
[]
[disp_y]
[]
[temp]
initial_condition = 100.0
[]
[]
[AuxVariables]
[Dc]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[Cc]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[Tc]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[Cost]
family = MONOMIAL
order = FIRST
initial_condition = -1.0
[]
[mat_den]
family = MONOMIAL
order = FIRST
initial_condition = ${vol_frac}
[]
[]
[AuxKernels]
[Cost]
type = MaterialRealAux
variable = Cost
property = Cost_mat
[]
[]
[Kernels]
[heat_conduction]
type = HeatConduction
variable = temp
diffusion_coefficient = thermal_cond
[]
[heat_source]
type = HeatSource
value = 1e-2 # W/m^3
variable = temp
[]
[]
[Physics/SolidMechanics/QuasiStatic]
[all]
strain = SMALL
add_variables = true
incremental = false
[]
[]
[BCs]
[no_y]
type = DirichletBC
variable = disp_y
boundary = hold
value = 0.0
[]
[no_x_symm]
type = DirichletBC
variable = disp_x
boundary = right
value = 0.0
[]
[left_n1]
type = DirichletBC
variable = temp
boundary = n1
value = 0.0
[]
[top]
type = NeumannBC
variable = temp
boundary = top
value = 0
[]
[bottom]
type = NeumannBC
variable = temp
boundary = bottom
value = 0
[]
[right]
type = NeumannBC
variable = temp
boundary = right
value = 0
[]
[left]
type = NeumannBC
variable = temp
boundary = left
value = 0
[]
[]
[NodalKernels]
[push_left]
type = NodalGravity
variable = disp_y
boundary = push_left
gravity_value = 0.0 # -1e-8
mass = 1
[]
[push_center]
type = NodalGravity
variable = disp_y
boundary = push_center
gravity_value = 0.0 # -1e-8
mass = 1
[]
[]
[Materials]
[thermal_cond]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; TC1"
coupled_variables = 'mat_den'
property_name = thermal_cond
outputs = 'exodus'
[]
[thermal_compliance]
type = ThermalCompliance
temperature = temp
thermal_conductivity = thermal_cond
outputs = 'exodus'
[]
[elasticity_tensor]
type = ComputeVariableIsotropicElasticityTensor
youngs_modulus = E_phys
poissons_ratio = poissons_ratio
args = 'mat_den'
[]
[E_phys]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; E1"
coupled_variables = 'mat_den'
property_name = E_phys
[]
[Cost_mat]
type = DerivativeParsedMaterial
# ordered multimaterial simp
expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
"B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; C1"
coupled_variables = 'mat_den'
property_name = Cost_mat
[]
[CostDensity]
type = ParsedMaterial
property_name = CostDensity
coupled_variables = 'mat_den Cost'
expression = 'mat_den*Cost'
[]
[poissons_ratio]
type = GenericConstantMaterial
prop_names = poissons_ratio
prop_values = 0.3
[]
[stress]
type = ComputeLinearElasticStress
[]
[dc]
type = ComplianceSensitivity
design_density = mat_den
youngs_modulus = E_phys
[]
[cc]
type = CostSensitivity
design_density = mat_den
cost = Cost_mat
outputs = 'exodus'
[]
[tc]
type = ThermalSensitivity
design_density = mat_den
thermal_conductivity = thermal_cond
temperature = temp
outputs = 'exodus'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[UserObjects]
[rad_avg]
type = RadialAverage
radius = 0.1
weights = linear
prop_name = sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_cost]
type = RadialAverage
radius = 0.1
weights = linear
prop_name = cost_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[rad_avg_thermal]
type = RadialAverage
radius = 0.1
weights = linear
prop_name = thermal_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[update]
type = DensityUpdateTwoConstraints
density_sensitivity = Dc
cost_density_sensitivity = Cc
cost = Cost
cost_fraction = ${cost_frac}
design_density = mat_den
volume_fraction = ${vol_frac}
bisection_lower_bound = 0
bisection_upper_bound = 1.0e12 # 100
use_thermal_compliance = true
thermal_sensitivity = Tc
weight_mechanical_thermal = '0 1'
relative_tolerance = 1.0e-12
bisection_move = 0.015
adaptive_move = false
execute_on = TIMESTEP_BEGIN
[]
# Provides Dc
[calc_sense]
type = SensitivityFilter
density_sensitivity = Dc
design_density = mat_den
filter_UO = rad_avg
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Cc
[calc_sense_cost]
type = SensitivityFilter
density_sensitivity = Cc
design_density = mat_den
filter_UO = rad_avg_cost
execute_on = TIMESTEP_END
force_postaux = true
[]
# Provides Tc
[calc_sense_thermal]
type = SensitivityFilter
density_sensitivity = Tc
design_density = mat_den
filter_UO = rad_avg_thermal
execute_on = TIMESTEP_END
force_postaux = true
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
nl_abs_tol = 1e-12
dt = 1.0
num_steps = 5
[]
[Outputs]
exodus = true
[out]
type = CSV
execute_on = 'TIMESTEP_END'
[]
print_linear_residuals = false
[]
[Postprocessors]
[right_flux]
type = SideDiffusiveFluxAverage
variable = temp
boundary = right
diffusivity = 10
[]
[mesh_volume]
type = VolumePostprocessor
execute_on = 'initial timestep_end'
[]
[total_vol]
type = ElementIntegralVariablePostprocessor
variable = mat_den
execute_on = 'INITIAL TIMESTEP_END'
[]
[vol_frac]
type = ParsedPostprocessor
expression = 'total_vol / mesh_volume'
pp_names = 'total_vol mesh_volume'
[]
[sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = sensitivity
[]
[cost_sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = cost_sensitivity
[]
[cost]
type = ElementIntegralMaterialProperty
mat_prop = CostDensity
[]
[cost_frac]
type = ParsedPostprocessor
expression = 'cost / mesh_volume'
pp_names = 'cost mesh_volume'
[]
[objective]
type = ElementIntegralMaterialProperty
mat_prop = strain_energy_density
execute_on = 'INITIAL TIMESTEP_END'
[]
[objective_thermal]
type = ElementIntegralMaterialProperty
mat_prop = thermal_compliance
execute_on = 'INITIAL TIMESTEP_END'
[]
[](modules/heat_transfer/test/tests/thermal_materials/2d.i)
power = 2.0
rho0 = 0.0
rho1 = 1.0
TC0 = 1.0e-16
TC1 = 1.0
[Mesh]
[planet]
type = ConcentricCircleMeshGenerator
has_outer_square = false
radii = 1
num_sectors = 10
rings = 2
preserve_volumes = false
[]
[moon]
type = ConcentricCircleMeshGenerator
has_outer_square = false
radii = 0.5
num_sectors = 8
rings = 2
preserve_volumes = false
[]
[combine]
type = CombinerGenerator
inputs = 'planet moon'
positions = '0 0 0 -1.5 -0.5 0'
[]
[]
[GlobalParams]
illumination_flux = '1 1 0'
[]
[AuxVariables]
[mat_den]
family = MONOMIAL
order = CONSTANT
initial_condition = 0.1
[]
[]
[Variables]
[u]
[]
[v]
[]
[]
[Kernels]
[diff_u]
type = Diffusion
variable = u
[]
[dt_u]
type = TimeDerivative
variable = u
[]
[diff_v]
type = Diffusion
variable = v
[]
[dt_v]
type = TimeDerivative
variable = v
[]
[]
[Materials]
[thermal_compliance]
type = ThermalCompliance
temperature = u
thermal_conductivity = thermal_cond
outputs = 'exodus'
[]
[thermal_cond]
type = DerivativeParsedMaterial
expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
"B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; TC1"
coupled_variables = 'mat_den'
property_name = thermal_cond
outputs = 'exodus'
[]
[thermal_compliance_sensitivity]
type = ThermalSensitivity
design_density = mat_den
thermal_conductivity = thermal_cond
temperature = u
outputs = 'exodus'
[]
[]
[BCs]
[flux_u]
type = DirectionalFluxBC
variable = u
boundary = outer
[]
[flux_v]
type = DirectionalFluxBC
variable = v
boundary = outer
self_shadow_uo = shadow
[]
[]
[Postprocessors]
[ave_v_all]
type = SideAverageValue
variable = v
boundary = outer
[]
[ave_v_exposed]
type = ExposedSideAverageValue
variable = v
boundary = outer
self_shadow_uo = shadow
[]
[]
[UserObjects]
[shadow]
type = SelfShadowSideUserObject
boundary = outer
execute_on = INITIAL
[]
[]
[Executioner]
type = Transient
dt = 0.1
num_steps = 1
[]
[Outputs]
exodus = true
[](modules/combined/test/tests/optimization/thermal_sensitivity/2d_root.i)
vol_frac = 0.5
E0 = 1
Emin = 1e-4
power = 1
[Mesh]
[MeshGenerator]
type = GeneratedMeshGenerator
dim = 2
nx = 20
ny = 20
xmin = 0
xmax = 40
ymin = 0
ymax = 40
[]
[]
[Variables]
[T]
initial_condition = 100
[]
[]
[AuxVariables]
[Dc]
family = MONOMIAL
order = CONSTANT
initial_condition = -1.0
[]
[mat_den]
family = MONOMIAL
order = CONSTANT
initial_condition = ${vol_frac}
[]
[]
[Kernels]
[heat]
type = HeatConduction
diffusion_coefficient = k
variable = T
[]
[heat_source]
type = HeatSource
function = 1e-2
variable = T
[]
[]
[DiracKernels]
[src]
type = ConstantPointSource
variable = T
point = '0 5 0'
value = 10
[]
[]
[BCs]
[no_x]
type = DirichletBC
variable = T
boundary = 'right top bottom'
value = 0.0
[]
[]
[Materials]
[k]
type = DerivativeParsedMaterial
# Emin + (density^penal) * (E0 - Emin)
expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
coupled_variables = 'mat_den'
property_name = k
[]
[dc]
type = ThermalSensitivity
temperature = T
design_density = mat_den
thermal_conductivity = k
[]
#only needed for objective function output in postprocessor
[thermal_compliance]
type = ThermalCompliance
temperature = T
thermal_conductivity = k
[]
[]
[UserObjects]
[rad_avg]
type = RadialAverage
radius = 3
weights = linear
prop_name = thermal_sensitivity
execute_on = TIMESTEP_END
force_preaux = true
[]
[update]
type = DensityUpdate
density_sensitivity = Dc
design_density = mat_den
volume_fraction = ${vol_frac}
execute_on = TIMESTEP_BEGIN
[]
[calc_sense]
type = SensitivityFilter
density_sensitivity = Dc
design_density = mat_den
filter_UO = rad_avg
execute_on = TIMESTEP_END
force_postaux = true
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
petsc_options_value = 'lu superlu_dist'
nl_abs_tol = 1e-8
dt = 1.0
dtmin = 1.0
num_steps = 20
[]
[Outputs]
[out]
type = CSV
execute_on = 'FINAL'
[]
print_linear_residuals = false
[]
[Postprocessors]
[mesh_volume]
type = VolumePostprocessor
execute_on = 'initial timestep_end'
[]
[total_vol]
type = ElementIntegralVariablePostprocessor
variable = mat_den
execute_on = 'INITIAL TIMESTEP_END'
[]
[vol_frac]
type = ParsedPostprocessor
expression = 'total_vol / mesh_volume'
pp_names = 'total_vol mesh_volume'
[]
[sensitivity]
type = ElementIntegralMaterialProperty
mat_prop = thermal_sensitivity
[]
[objective_thermal]
type = ElementIntegralMaterialProperty
mat_prop = thermal_compliance
execute_on = 'INITIAL TIMESTEP_END'
[]
[]