Products: ABAQUS/Standard ABAQUS/Explicit
CAX3T CAX4HT CAX4RT CAX4T CAX6MT CAX8HT
CPE3T CPE4RT CPE4T CPE6MT CPE8T
CPS3T CPS4RT CPS4T CPS6MT CPS8T
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:
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
T2: One-dimensional heat transfer with radiation, Section 4.3.2 of the ABAQUS Benchmarks Manual;
T3: One-dimensional transient heat transfer, Section 4.3.3 of the ABAQUS Benchmarks Manual;
T4: Two-dimensional heat transfer with convection, Section 4.3.4 of the ABAQUS Benchmarks Manual;
Temperature-dependent film condition, Section 1.3.41, respectively.
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.
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.
CAX4T elements.
CPS4T elements.
C3D8T elements.
CAX4T elements, coarse mesh.
CAX8HT elements, fine mesh.
CPE4T elements, coarse mesh.
CPE8T elements, fine mesh.
CPS4T elements, coarse mesh.
CPS8T elements, fine mesh.
C3D8T elements, coarse mesh.
CAX4HT elements.
C3D8HT elements.
CPE4T elements.
CPS4T elements and the user subroutine *FILM.
CAX4T elements.
CPE4T elements.
C3D8T elements.
CAX3T elements.
CAX4RT elements.
CAX6MT elements.
CPE3T elements.
CPE4RT elements.
CPE6MT elements.
CPS3T elements.
CPS4RT elements.
CPS6MT elements.
C3D4T elements.
C3D6T elements.
C3D8RT elements.
CAX3T elements, coarse mesh.
CAX4RT elements, coarse mesh.
CAX6MT elements, coarse mesh.
CPE3T elements, coarse mesh.
CPE4RT elements, coarse mesh.
CPE6MT elements, coarse mesh.
CPS3T elements, coarse mesh.
CPS4RT elements, coarse mesh.
CPS6MT elements, coarse mesh.
CAX3T elements, fine mesh.
CAX4RT elements, fine mesh.
CPE3T elements, fine mesh.
CPE4RT elements, fine mesh.
CPS3T elements, fine mesh.
CPS4RT elements, fine mesh.
CPE3T elements, coarse mesh.
CPE4RT elements, coarse mesh.
CPE6MT elements, coarse mesh.
CPS3T elements, coarse mesh.
CPS4RT elements, coarse mesh.
CPS6MT elements, coarse mesh.
C3D6T elements, coarse mesh.
C3D8RT elements, coarse mesh.
CPE3T elements, fine mesh.
CPE4RT elements, fine mesh.
CPS3T elements, fine mesh.
CPS4RT elements, fine mesh.
C3D6T elements, fine mesh.
C3D8RT elements, fine mesh.
CAX3T elements.
CAX4RT elements.
CAX6MT elements.
CPE3T elements.
CPE4RT elements.
CPE6MT elements.
CPS3T elements.
CPS4RT elements.
CPS6MT elements.
C3D4T elements.
C3D6T elements.
C3D8RT elements.
CPE3T elements.
CPE4RT elements.
CPE6MT elements.
CPS3T elements.
CPS4RT elements.
CPS6MT elements.
CAX4RT elements.
CAX6MT elements.
CPE4RT elements.
CPE6MT elements.
CPS6MT elements.
C3D8RT elements.
C3D10MT elements.
DCAX4 DC2D4 DC2D8 DC3D6 DC3D8 DC3D8
CAX4T CPS4T CPS8RT C3D8T
DCAX4E DC2D4E DC2D8E DC3D8E
The test is based on the one-element lumped model described in the previous section.
DCAX4 elements.
DC2D4 elements.
DC2D8 elements.
DC3D6 elements.
DC3D8 elements.
CAX4T elements.
CPEG4T elements.
CPEG8T elements.
CPS4T elements.
CPS8RT elements.
C3D8T elements.
DCAX4E elements.
DC2D4E elements.
DC2D8E elements.
DC3D8E elements.
CAX4RT elements.
CAX6MT elements.
CPE4RT elements.
CPE6MT elements.
CPS6MT elements.
C3D8RT elements.
C3D10MT elements.
DC1D2 DC1D3 DCAX3 DCAX4 DCAX6 DCAX8 DC2D3 DC2D4
DC2D6 DC2D8 DC3D8
CAX8HT CPE4T CPEG4T CPEG8T C3D8HT T2D2T
DCAX6E DC1D2E DC2D3E DC3D8E
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.
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.
DC1D2 elements.
DC1D3 elements.
DCAX3 elements.
DCAX4 elements.
DCAX6 elements.
DCAX8 elements.
DC2D3 elements.
DC2D4 elements.
DC2D6 elements.
DC2D8 elements.
DC3D8 elements.
CAX8HT elements.
CPE4T elements.
CPEG4T elements.
CPEG8T elements.
C3D8HT elements.
T2D2T elements.
DC1D2E elements.
DC2D3E elements.
DCAX6E elements.
DC3D8E elements.
CAX4RT elements.
CPE6MT elements.
CPE4RT elements.
C3D8RT elements.
DCAX4 DC2D4 DC2D8 DC3D6 DC3D8 CAX3T CPS4RT C3D6T
CAX4T CPS4T CPS8RT C3D8T
DCAX4E DC2D4E DC2D8E DC3D8E
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.
DCAX4 element.
DC2D4 element.
DC2D8 element.
DC3D6 element.
DC3D8 element.
CAX4T element.
CPEG4T elements.
CPEG8T elements.
CPS4T element.
CPS8RT element.
C3D8T element.
DCAX4E element.
DC2D4E element.
DC2D8E element.
DC3D8E element.
CAX3T element.
CAX6MT element.
CPE6MT element.
CPS4RT element.
CPS6MT element.
C3D6T element.
C3D10MT element.
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.
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.
CPE4T elements as rigid bodies; *GAP CONDUCTANCE test.
CPS4T elements as rigid bodies; *GAP RADIATION test.
CPS4T elements, with field variable-dependent friction; pressure-dependent *GAP CONDUCTANCE.
CPS4T elements, without field variable-dependent friction; pressure-dependent *GAP CONDUCTANCE.
CPS4RT elements and an analytical rigid surface; *GAP CONDUCTANCE test.
CPE4RT elements as rigid bodies; *GAP CONDUCTANCE test.
CPE6MT elements as rigid bodies; *GAP CONDUCTANCE test.
CPE4RT elements and an analytical rigid surface; *GAP RADIATION test.
CPE6MT elements and an analytical rigid surface; *GAP RADIATION test.
CPS4RT elements as rigid elements; *GAP RADIATION test.