v7.02.311 HPLP311 - Murakami 11.17 Fissure in the center of a thin rectangular plate obstructing uniform heat flow in an isotropic medium

Summary:

It is an isotropic linear thermo-elastic static calculation.

It is a basic test in \(\mathrm{2D}\) plane for a stationary thermal loading calculated by finite elements on the same mesh with an isotropic material in \(\mathrm{II}\) mode.

Objective:

• basic test in \(\mathrm{2D}\) plane, for a stationary thermal loading calculated by finite elements on the same mesh, with isotropic material, in \(\mathrm{II}\) mode,

• validation of the calculation of \({K}_{\mathrm{II}}\),

• variability of \(G\) depending on the topology (sectors, crowns) of the radiating mesh. Verification of the invariance of the fracture mechanics results, at one end of the crack, in relation to the mesh at the other end of the same crack.

The calculation is tested on a full mesh and a half-mesh. Parameters \(L/W\) and \(\mathrm{2A}/W\) are fixed.

A relative difference is measured on \({K}_{\mathrm{II}}\), but the precision is not well defined.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loading
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty about the solution
  • 2.4. Bibliographical references
• 3. A, B, C, D, E, and F models
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
• 4. Results of A, B, C, C, D, E and F models
  • 4.1. Tested values
  • 4.2. notes
• 5. G modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. Summary of results