v4.05.305 TPLP305 — Imposed temperature bar with X-FEM adiabatic interface

Summary:

This test is the equivalent in stationary linear thermal of the mechanical X-FEM test SSNV173 [V6.04.173]. The objective of this test is to validate two aspects of elementary calculation in the context of solving thermal problems with X- FEM [R7.02.12]:

• the integration of a discontinuous quantity thanks to a sub-division of the element

• the enrichment of shape functions by the Heaviside function

We consider a parallelepipedic bar crossed by an adiabatic interface, the two parts of the bar

thus defined are therefore thermally insulated from one another. Each of these parts is then subjected to a temperature imposed on one of its edges.

All Heaviside enrichment thermal X-FEM elements are tested, the results are compared to an analytical solution.

• 1. Reference problem
  • 1.1. 3D geometry
  • 1.2. 2D geometry
  • 1.3. Material properties
  • 1.4. Boundary conditions and loads
  • 1.5. Initial conditions
• 2. Benchmark solution
  • 2.1. Calculation method
  • 2.2. Reference quantities and results
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
• 7. E modeling
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
• 8. F modeling
  • 8.1. Characteristics of modeling
  • 8.2. Characteristics of the mesh
  • 8.3. Tested sizes and results
• 9. G modeling
  • 9.1. Characteristics of modeling
  • 9.2. Characteristics of the mesh
  • 9.3. Tested sizes and results
• 10. H modeling
  • 10.1. Characteristics of modeling
  • 10.2. Characteristics of the mesh
  • 10.3. Tested sizes and results
• 11. Modeling I
  • 11.1. Characteristics of modeling
  • 11.2. Characteristics of the mesh
  • 11.3. Tested sizes and results
• 12. J modeling
  • 12.1. Characteristics of modeling
  • 12.2. Characteristics of the mesh
  • 12.3. Tested sizes and results
• 13. Summary of results