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

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

Rigid bodies with temperature DOFs
Heat capacitance
Node-based radiation conditions
Node-based film conditions and concentrated heat fluxes
Thermal contact between rigid bodies

ProductsAbaqus/StandardAbaqus/Explicit

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

SC8RT
SC6RT

S3RT
S4RT

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.). Rigid body constraints and isothermal rigid body constraints are tested in these problems.

The test problems are:

One-dimensional heat transfer with radiation.
One-dimensional transient heat transfer.
Two-dimensional heat transfer with convection.
Patch test for heat transfer elements.
Temperature-dependent film condition.
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.

The one-element lumped model tests the isothermal rigid body constraints. The simulation consists of two steps. In the first step the rigid body is cooled by convection from an initial temperature of $T_{0}$ =100 to the ambient temperature $T_{a}$ =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:

T (t) = T_{a} + (T_{0} - T_{a}) \exp [\frac{- h A_{1}}{{(ρ c V)}_{t o t a l}} (t - t_{0})]

Step 2:

T (t) = T_{a} + \frac{q A_{2}}{{(ρ c V)}_{t o t a l}} (t - t_{0})

In the above equation h is the heat transfer coefficient, ${(ρ c V)}_{t o t a l}$ is the heat capacitance, $A_{1}$ is the area associated with the convective flux, $t_{0}$ is the time at the end of previous step, and $A_{2}$ 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:

A L L I H E (t) = {(ρ c V)}_{t o t a l} T (t),

A L L H F (t) = - \int_{t_{0}}^{t} h A_{1} (T - T_{a}) d t = {(ρ c V)}_{t o t a l} (T_{0} - T_{a}) [\exp (\frac{- h A_{1}}{{(ρ c V)}_{t o t a l}} (t - t_{0})) - 1]

Step 2:

A L L I H E (t) = {(ρ c V)}_{t o t a l} T (t),

A L L H F (t) = {A L L H F |}_{e n d - s t e p 1} + \int_{t_{0}}^{t} q A_{2} d t = {A L L H F |}_{e n d - s t e p 1} + q A_{2} (t - t_{0})

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:

rbisono_1dhtrd_std_cax4t.inp: CAX4T elements.
rbisono_1dhtrd_std_cps4t.inp: CPS4T elements.
rbisono_1dhtrd_std_c3d8t.inp: C3D8T elements.

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:

rbisono_htpatch_std_cax4ht.inp: CAX4HT elements.
rbisono_htpatch_std_c3d8ht.inp: C3D8HT elements.

Temperature-dependent film condition:

rbisono_tempdep_std_cpe4t.inp: CPE4T elements.
rbisono_tempdepfm_std_cps4t.inp: CPS4T elements and the user subroutine FILM.

One-element lumped model:

rbisoyes_heatcap_std_cax4t.inp: CAX4T elements.
rbisoyes_heatcap_std_cpe4t.inp: CPE4T elements.
rbisoyes_heatcap_std_c3d8t.inp: C3D8T elements.

Abaqus/Explicit input files

rbisoyes_heatcap_xpl_sc8rt.inp: SC8RT elements.
rbisoyes_heatcap_xpl_s4rt.inp: S4RT elements.

One-dimensional heat transfer with radiation:

rbisono_1dhtrd_xpl_cax3t.inp: CAX3T elements.
rbisono_1dhtrd_xpl_cax4rt.inp: CAX4RT elements.
rbisono_1dhtrd_xpl_cax6mt.inp: CAX6MT elements.
rbisono_1dhtrd_xpl_cpe3t.inp: CPE3T elements.
rbisono_1dhtrd_xpl_cpe4rt.inp: CPE4RT elements.
rbisono_1dhtrd_xpl_cpe6mt.inp: CPE6MT elements.
rbisono_1dhtrd_xpl_cps3t.inp: CPS3T elements.
rbisono_1dhtrd_xpl_cps4rt.inp: CPS4RT elements.
rbisono_1dhtrd_xpl_cps6mt.inp: CPS6MT elements.
rbisono_1dhtrd_xpl_c3d4t.inp: C3D4T elements.
rbisono_1dhtrd_xpl_c3d6t.inp: C3D6T elements.
rbisono_1dhtrd_xpl_c3d8rt.inp: C3D8RT elements.
rbisono_1dhtrd_xpl_c3d8t.inp: C3D8T elements.

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_1dhtcdc_xpl_s4rt.inp: S4RT 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.
rbisono_1dhtcdf_xpl_s3rt.inp: S3RT 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_2dhtcvc_xpl_c3d8t.inp: C3D8T elements, coarse mesh.
rbisono_2dhtcvc_xpl_c3d6t.inp: C3D6T 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.
rbisono_2dhtcvf_xpl_sc8rt.inp: SC8RT elements, fine mesh.

Patch test for heat transfer:

rbisono_htpatch_xpl_cax3t.inp: CAX3T elements.
rbisono_htpatch_xpl_cax4rt.inp: CAX4RT elements.
rbisono_htpatch_xpl_cax6mt.inp: CAX6MT elements.
rbisono_htpatch_xpl_cpe3t.inp: CPE3T elements.
rbisono_htpatch_xpl_cpe4rt.inp: CPE4RT elements.
rbisono_htpatch_xpl_cpe6mt.inp: CPE6MT elements.
rbisono_htpatch_xpl_cps3t.inp: CPS3T elements.
rbisono_htpatch_xpl_cps4rt.inp: CPS4RT elements.
rbisono_htpatch_xpl_cps6mt.inp: CPS6MT elements.
rbisono_htpatch_xpl_c3d4t.inp: C3D4T elements.
rbisono_htpatch_xpl_c3d6t.inp: C3D6T elements.
rbisono_htpatch_xpl_c3d8rt.inp: C3D8RT elements.
rbisono_htpatch_xpl_c3d8t.inp: C3D8T elements.
rbisono_htpatch_xpl_sc8rt.inp: SC8RT elements.

Temperature-dependent film condition:

rbisono_tempdep_xpl_cpe3t.inp: CPE3T elements.
rbisono_tempdep_xpl_cpe4rt.inp: CPE4RT elements.
rbisono_tempdep_xpl_cpe6mt.inp: CPE6MT elements.
rbisono_tempdep_xpl_cps3t.inp: CPS3T elements.
rbisono_tempdep_xpl_cps4rt.inp: CPS4RT elements.
rbisono_tempdep_xpl_cps6mt.inp: CPS6MT elements.
rbisono_tempdep_xpl_s4rt.inp: S4RT elements.

One-element lumped model:

rbisoyes_heatcap_xpl_cax4rt.inp: CAX4RT elements.
rbisoyes_heatcap_xpl_cax6mt.inp: CAX6MT elements.
rbisoyes_heatcap_xpl_cpe4rt.inp: CPE4RT elements.
rbisoyes_heatcap_xpl_cpe6mt.inp: CPE6MT elements.
rbisoyes_heatcap_xpl_cps6mt.inp: CPS6MT elements.
rbisoyes_heatcap_xpl_c3d8rt.inp: C3D8RT elements.
rbisoyes_heatcap_xpl_c3d8t.inp: C3D8T elements.
rbisoyes_heatcap_xpl_c3d10mt.inp: C3D10MT elements.

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
C3D8T
C3D10MT
SC8RT

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.

Input files

Abaqus/Standard input files

heatcapcfilm_std_dcax4.inp: DCAX4 elements.
heatcapcfilm_std_dc2d4.inp: DC2D4 elements.
heatcapcfilm_std_dc2d8.inp: DC2D8 elements.
heatcapcfilm_std_dc3d6.inp: DC3D6 elements.
heatcapcfilm_std_dc3d8.inp: DC3D8 elements.
heatcapcfilm_std_cax4t.inp: CAX4T elements.
heatcapcfilm_std_cpeg4t.inp: CPEG4T elements.
heatcapcfilm_std_cpeg8t.inp: CPEG8T elements.
heatcapcfilm_std_cps4t.inp: CPS4T elements.
heatcapcfilm_std_cps8rt.inp: CPS8RT elements.
heatcapcfilm_std_c3d8t.inp: C3D8T elements.
heatcapcfilm_std_dcax4e.inp: DCAX4E elements.
heatcapcfilm_std_dc2d4e.inp: DC2D4E elements.
heatcapcfilm_std_dc2d8e.inp: DC2D8E elements.
heatcapcfilm_std_dc2d8e_post.inp: POST OUTPUT analysis.
heatcapcfilm_std_dc3d8e.inp: DC3D8E elements.

Abaqus/Explicit input files

rbisoyes_heatcap_xpl_cax4rt.inp: CAX4RT elements.
rbisoyes_heatcap_xpl_cax6mt.inp: CAX6MT elements.
rbisoyes_heatcap_xpl_cpe4rt.inp: CPE4RT elements.
rbisoyes_heatcap_xpl_cpe6mt.inp: CPE6MT elements.
rbisoyes_heatcap_xpl_cps6mt.inp: CPS6MT elements.
rbisoyes_heatcap_xpl_c3d8rt.inp: C3D8RT elements.
rbisoyes_heatcap_xpl_c3d8t.inp: C3D8T elements.
rbisoyes_heatcap_xpl_c3d10mt.inp: C3D10MT elements.
rbisoyes_heatcap_xpl_sc8rt.inp: SC8RT elements.

Node-based radiation conditions

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. In the tests presented here, element-based radiation conditions are replaced by node-based radiation conditions.

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/Standard input files

onedht_crad_std_dc1d2.inp: DC1D2 elements.
onedht_crad_std_dc1d3.inp: DC1D3 elements.
onedht_crad_std_dcax3.inp: DCAX3 elements.
onedht_crad_std_dcax4.inp: DCAX4 elements.
onedht_crad_std_dcax6.inp: DCAX6 elements.
onedht_crad_std_dcax8.inp: DCAX8 elements.
onedht_crad_std_dc2d3.inp: DC2D3 elements.
onedht_crad_std_dc2d4.inp: DC2D4 elements.
onedht_crad_std_dc2d6.inp: DC2D6 elements.
onedht_crad_std_dc2d8.inp: DC2D8 elements.
onedht_crad_std_dc3d8.inp: DC3D8 elements.
onedht_crad_std_cax8ht.inp: CAX8HT elements.
onedht_crad_std_cpe4t.inp: CPE4T elements.
onedht_crad_std_cpeg4t.inp: CPEG4T elements.
onedht_crad_std_cpeg8t.inp: CPEG8T elements.
onedht_crad_std_c3d8ht.inp: C3D8HT elements.
onedht_crad_std_t2d2t.inp: T2D2T elements.
onedht_crad_std_dc1d2e.inp: DC1D2E elements.
onedht_crad_std_dc2d3e.inp: DC2D3E elements.
onedht_crad_std_dcax6e.inp: DCAX6E elements.
onedht_crad_std_dc3d8e.inp: DC3D8E elements.

Abaqus/Explicit input files

cradiate_1dhtrd_xpl_cax4rt.inp: CAX4RT elements.
cradiate_1dhtrd_xpl_cpe6mt.inp: CPE6MT elements.
cradiate_1dhtrd_xpl_cpe4rt.inp: CPE4RT elements.
cradiate_1dhtrd_xpl_c3d8rt.inp: C3D8RT elements.

Node-based film conditions and concentrated heat fluxes

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
SC6RT

Problem description

The tests are based on the one-element lumped model described earlier. The nodal thermal loads node-based film conditions and concentrated heat fluxes are used for cooling and heating the body, respectively. As with the node-based radiation conditions 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/Standard input files

heatcapcfilm_std_dcax4.inp: DCAX4 element.
heatcapcfilm_std_dc2d4.inp: DC2D4 element.
heatcapcfilm_std_dc2d8.inp: DC2D8 element.
heatcapcfilm_std_dc3d6.inp: DC3D6 element.
heatcapcfilm_std_dc3d8.inp: DC3D8 element.
heatcapcfilm_std_cax4t.inp: CAX4T element.
heatcapcfilm_std_cpeg4t.inp: CPEG4T elements.
heatcapcfilm_std_cpeg8t.inp: CPEG8T elements.
heatcapcfilm_std_cps4t.inp: CPS4T element.
heatcapcfilm_std_cps8rt.inp: CPS8RT element.
heatcapcfilm_std_c3d8t.inp: C3D8T element.
heatcapcfilm_std_dcax4e.inp: DCAX4E element.
heatcapcfilm_std_dc2d4e.inp: DC2D4E element.
heatcapcfilm_std_dc2d8e.inp: DC2D8E element.
heatcapcfilm_std_dc3d8e.inp: DC3D8E element.

Abaqus/Explicit input files

cfilm_cflux_xpl_cax3t.inp: CAX3T element.
cfilm_cflux_xpl_cax6mt.inp: CAX6MT element.
cfilm_cflux_xpl_cpe6mt.inp: CPE6MT element.
cfilm_cflux_xpl_cps4rt.inp: CPS4RT element.
cfilm_cflux_xpl_cps6mt.inp: CPS6MT element.
cfilm_cflux_xpl_c3d6t.inp: C3D6T element.
cfilm_cflux_xpl_c3d10mt.inp: C3D10MT element.
cfilm_cflux_xpl_sc6rt.inp: SC6RT element.

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 and Coupled temperature-displacement analysis: one-dimensional gap conductance and radiation. 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; 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.
field_contactp_std_cps4t_po.inp: POST OUTPUT analysis.
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.