v4.19.203 TTLA203 - Cylinder at imposed temperatures with adiabatic crack

Summary

The objective of this test is to validate the axisymmetric thermal elements X- FEM in transient linear thermics.

We consider a full cylinder, cracked at the level of the section located halfway up. The crack is a crown with an inner radius the half radius of the cylinder, and an outer radius the radius of the cylinder. The load is transitory and consists of a temperature gradient imposed by the application of Dirichlet conditions at both ends of the cylinder. An adiabatic crack is hypothesized (zero flow on the lips of the crack and discontinuous temperature across the crack)

Four models are considered:

• modeling \(A\): \(\text{FEM AXIS}\) (mesh crack)

• modeling \(B\): \(\text{X-FEM AXIS}\), crack in the middle of the elements

• modeling \(C\): \(\text{FEM 3D}\) (mesh crack)

• modeling \(D\): \(\text{X-FEM}\mathrm{3D}\), crack in the middle of the elements

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. 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. Summaries of results