1.5.8 Patch test for heat transfer elements

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

DC1D2 DC1D3

DC2D3 DC2D4 DC2D6 DC2D8

DC3D4 DC3D6 DC3D8 DC3D10 DC3D15 DC3D20

DCAX3 DCAX4 DCAX6 DCAX8

DS3 DS4 DS6 DS8

C3D4T C3D6T C3D8RT C3D10MHT C3D10MT

CAX3T CAX4RHT CAX4RT CAX6MT CGAX4RHT CGAX4RT

CPE3T CPE4RHT CPE4RT CPE6MHT CPE6MT

CPEG4RHT CPEG4RT CPEG6MHT CPEG6MT

CPS3T CPS4RT CPS6MT

Problem description

The meshes used for the heat transfer tests are the same as those used for the corresponding stress elements, except that the axisymmetric heat transfer elements use a larger radius.

For coupled temperature-displacement elements dummy mechanical properties are prescribed to complete the material definition.

The total simulation time for the ABAQUS/Explicit analysis is 20 units. This provides enough time for the transient solution to reach steady-state conditions in this problem.

Boundary conditions:

, where T is the temperature, through are arbitrary constants, and x, y, z denote spatial location. Temperatures are prescribed at every node along the boundary of the mesh. For shell elements z denotes the normal direction to the shell surface.

Reference solution

Fluxes: Since the temperature field is chosen to be linear, it has constant spatial gradients and, thus, has constant fluxes at every integration point.