1.11.7 Rigid bodies with temperature DOFs, heat capacitance, and nodal-based thermal loads

Products: ABAQUS/Standard  ABAQUS/Explicit  

I. Rigid bodies with temperature DOFs

Elements tested

CAX3T    CAX4HT    CAX4RT    CAX4T    CAX6MT    CAX8HT   

CPE3T    CPE4RT    CPE4T    CPE6MT    CPE8T   

CPS3T    CPS4RT    CPS4T    CPS6MT    CPS8T   

C3D4T    C3D6T    C3D8HT    C3D8RT    C3D8T    C3D10MT   

Problem description

Most of the verification tests in this section are based on the recommendations of the National Agency for Finite Element Methods and Standards (U.K.). The *RIGID BODY, ISOTHERMAL=NO and *RIGID BODY, ISOTHERMAL=YES options are tested in these problems.

The test problems are:

  1. One-dimensional heat transfer with radiation.

  2. One-dimensional transient heat transfer.

  3. Two-dimensional heat transfer with convection.

  4. Patch test for heat transfer elements.

  5. Temperature-dependent film condition.

  6. One-element lumped model.

Detailed descriptions of problems (a)–(e) can be found in

The models presented here are the same as the models described in these sections, but the elements are now assigned to rigid bodies using the *RIGID BODY, ISOTHERMAL=NO option.

The one-element lumped model tests the *RIGID BODY, ISOTHERMAL=YES option. The simulation consists of two steps. In the first step the rigid body is cooled by convection from an initial temperature of =100 to the ambient temperature =20. In the second step the body is heated by a prescribed flux, q. All the thermal properties are equal to unity. In addition to its own thermal capacitance, a second capacitance is lumped into the model using a HEATCAP element.

Results and discussion

The target solutions are reproduced accurately for all the problems tested. For the one-element model the analytical solution is

Step 1:

Step 2:

In the above equation h is the heat transfer coefficient, is the heat capacitance, is the area associated with the convective flux, is the time at the end of previous step, and denotes the area on which the prescribed flux is applied. The temperatures at the nodes are the same because the rigid body is isothermal; therefore, the temperature varies only in time.

In ABAQUS/Explicit the internal heat energy ALLIHE and the external heat energy through the external fluxes ALLHF are available. The analytical solutions for the energies are

Step 1:

Step 2:

The energies are in good agreement with the analytical solutions, and the heat energy balance is respected.

Input files

ABAQUS/Standard input files

One-dimensional heat transfer with radiation:


One-dimensional transient heat transfer:


rbisono_1dhtcdc_std_cax4t.inp

CAX4T elements, coarse mesh.

rbisono_1dhtcdf_std_cax8ht.inp

CAX8HT elements, fine mesh.

rbisono_1dhtcdc_std_cpe4t.inp

CPE4T elements, coarse mesh.

rbisono_1dhtcdf_std_cpe8t.inp

CPE8T elements, fine mesh.

Two-dimensional heat transfer with convection:


rbisono_2dhtcvc_std_cps4t.inp

CPS4T elements, coarse mesh.

rbisono_2dhtcvf_std_cps8t.inp

CPS8T elements, fine mesh.

rbisono_2dhtcvc_std_c3d8t.inp

C3D8T elements, coarse mesh.

Patch test for heat transfer:


Temperature-dependent film condition:


rbisono_tempdepfm_std_cps4t.inp

CPS4T elements and the user subroutine *FILM.

One-element lumped model:


ABAQUS/Explicit input files

One-dimensional heat transfer with radiation:


One-dimensional transient heat transfer:


rbisono_1dhtcdc_xpl_cax3t.inp

CAX3T elements, coarse mesh.

rbisono_1dhtcdc_xpl_cax4rt.inp

CAX4RT elements, coarse mesh.

rbisono_1dhtcdc_xpl_cax6mt.inp

CAX6MT elements, coarse mesh.

rbisono_1dhtcdc_xpl_cpe3t.inp

CPE3T elements, coarse mesh.

rbisono_1dhtcdc_xpl_cpe4rt.inp

CPE4RT elements, coarse mesh.

rbisono_1dhtcdc_xpl_cpe6mt.inp

CPE6MT elements, coarse mesh.

rbisono_1dhtcdc_xpl_cps3t.inp

CPS3T elements, coarse mesh.

rbisono_1dhtcdc_xpl_cps4rt.inp

CPS4RT elements, coarse mesh.

rbisono_1dhtcdc_xpl_cps6mt.inp

CPS6MT elements, coarse mesh.

rbisono_1dhtcdf_xpl_cax3t.inp

CAX3T elements, fine mesh.

rbisono_1dhtcdf_xpl_cax4rt.inp

CAX4RT elements, fine mesh.

rbisono_1dhtcdf_xpl_cpe3t.inp

CPE3T elements, fine mesh.

rbisono_1dhtcdf_xpl_cpe4rt.inp

CPE4RT elements, fine mesh.

rbisono_1dhtcdf_xpl_cps3t.inp

CPS3T elements, fine mesh.

rbisono_1dhtcdf_xpl_cps4rt.inp

CPS4RT elements, fine mesh.

Two-dimensional heat transfer with convection:


rbisono_2dhtcvc_xpl_cpe3t.inp

CPE3T elements, coarse mesh.

rbisono_2dhtcvc_xpl_cpe4rt.inp

CPE4RT elements, coarse mesh.

rbisono_2dhtcvc_xpl_cpe6mt.inp

CPE6MT elements, coarse mesh.

rbisono_2dhtcvc_xpl_cps3t.inp

CPS3T elements, coarse mesh.

rbisono_2dhtcvc_xpl_cps4rt.inp

CPS4RT elements, coarse mesh.

rbisono_2dhtcvc_xpl_cps6mt.inp

CPS6MT elements, coarse mesh.

rbisono_2dhtcvc_xpl_c3d6t.inp

C3D6T elements, coarse mesh.

rbisono_2dhtcvc_xpl_c3d8rt.inp

C3D8RT elements, coarse mesh.

rbisono_2dhtcvf_xpl_cpe3t.inp

CPE3T elements, fine mesh.

rbisono_2dhtcvf_xpl_cpe4rt.inp

CPE4RT elements, fine mesh.

rbisono_2dhtcvf_xpl_cps3t.inp

CPS3T elements, fine mesh.

rbisono_2dhtcvf_xpl_cps4rt.inp

CPS4RT elements, fine mesh.

rbisono_2dhtcvf_xpl_c3d6t.inp

C3D6T elements, fine mesh.

rbisono_2dhtcvf_xpl_c3d8rt.inp

C3D8RT elements, fine mesh.

Temperature-dependent film condition:


II. Heat capacitance

Elements tested

DCAX4    DC2D4    DC2D8    DC3D6    DC3D8    DC3D8   

CAX4T    CPS4T    CPS8RT    C3D8T   

DCAX4E    DC2D4E    DC2D8E    DC3D8E   

CAX4RT    CAX6MT    CPE4RT    CPE6MT    CPEG4T    CPEG8T    CPS6MT    C3D8RT    C3D10MT   

Problem description

The test is based on the one-element lumped model described in the previous section.

Results and discussion

The results match the analytical solution.

Elements tested

DC1D2    DC1D3    DCAX3    DCAX4    DCAX6    DCAX8    DC2D3    DC2D4   

DC2D6    DC2D8    DC3D8   

CAX8HT    CPE4T    CPEG4T    CPEG8T    C3D8HT    T2D2T   

DCAX6E    DC1D2E    DC2D3E    DC3D8E   

CAX3T    CAX4RT    CPE4RT    CPE6MT    CPS4RT    C3D6T    C3D8RT   

Problem description

The tests are based on the problem presented in T2: One-dimensional heat transfer with radiation, Section 4.3.2 of the ABAQUS Benchmarks Manual. In the tests presented here, the *RADIATE option is replaced by equivalent nodal loads using the *CRADIATE option.

Results and discussion

The results are in good agreement with the target temperature of 653.85°C. For the second-order elements tested in ABAQUS/Standard, the radiative loads at the nodes are weighted appropriately to apply consistent nodal loads. For the coupled temperature-displacement and coupled thermal-electrical elements, dummy mechanical and electrical properties are used, respectively, since only the heat transfer analysis is of interest.

Input files

ABAQUS/Explicit input files

Elements tested

DCAX4    DC2D4    DC2D8    DC3D6    DC3D8    CAX3T    CPS4RT    C3D6T   

CAX4T    CPS4T    CPS8RT    C3D8T   

DCAX4E    DC2D4E    DC2D8E    DC3D8E   

CAX3T    CAX6MT    CPE6MT    CPEG4T    CPEG8T    CPS4RT    CPS6MT    C3D6T    C3D10MT   

Problem description

The tests are based on the one-element lumped model described earlier. The nodal thermal loads *CFILM and *CFLUX are used for cooling and heating the body, respectively. As with the *CRADIATE tests described earlier, in ABAQUS/Standard the nodal loads are weighted appropriately for the second-order elements; dummy mechanical and electrical properties are used for the coupled temperature-displacement and coupled thermal-electrical analyses, respectively.

Results and discussion

The temperature values are in good agreement with the analytical solution.

Input files

ABAQUS/Explicit input files

V. Thermal contact between rigid bodies

Elements tested

CPE4T    CPS4T   

CPE4RT    CPS4RT    CPE6MT   

Problem description

The tests are based on the problems presented in Thermal surface interaction, Section 1.7.1, and Coupled temperature-displacement analysis: one-dimensional gap conductance and radiation, Section 1.6.3 of the ABAQUS Benchmarks Manual. In the first set of tests only the temperature variation in the rigid bodies involved in contact is considered, since the deformations are not of interest. In ABAQUS/Explicit two types of thermal contact are considered: thermal contact between a rigid body and an analytical rigid surface and thermal contact between two rigid bodies.

The second test is done in ABAQUS/Standard to test the friction dependency on field variables. The test is described in Coupled temperature-displacement analysis: one-dimensional gap conductance and radiation, Section 1.6.3 of the ABAQUS Benchmarks Manual; however, here we release the constraints in the tangential direction of contact.

Results and discussion

The temperature values match the results obtained with deformable elements for the first set of tests. In the second set of tests the results obtained using the field variable-dependent friction agree exactly with the results obtained without field variable dependence.

Input files

ABAQUS/Standard input files

rb_rb_thcontactc_std_cpe4t.inp

CPE4T elements as rigid bodies; *GAP CONDUCTANCE test.

rb_rb_thcontactr_std_cps4t.inp

CPS4T elements as rigid bodies; *GAP RADIATION test.

field_contactp_std_cps4t.inp

CPS4T elements, with field variable-dependent friction; pressure-dependent *GAP CONDUCTANCE.

nofield_contactp_std_cps4t.inp

CPS4T elements, without field variable-dependent friction; pressure-dependent *GAP CONDUCTANCE.

ABAQUS/Explicit input files

rb_ar_thcontactc_xpl_cps4rt.inp

CPS4RT elements and an analytical rigid surface; *GAP CONDUCTANCE test.

rb_rb_thcontactc_xpl_cpe4rt.inp

CPE4RT elements as rigid bodies; *GAP CONDUCTANCE test.

rb_rb_thcontactc_xpl_cpe6mt.inp

CPE6MT elements as rigid bodies; *GAP CONDUCTANCE test.

rb_ar_thcontactr_xpl_cpe4rt.inp

CPE4RT elements and an analytical rigid surface; *GAP RADIATION test.

rb_ar_thcontactr_xpl_cpe6mt.inp

CPE6MT elements and an analytical rigid surface; *GAP RADIATION test.

rb_rb_thcontactr_xpl_cps4rt.inp

CPS4RT elements as rigid elements; *GAP RADIATION test.