r3.11.01 Formulation of a thermal model for thin shells

Summary:

The model presented here is the result of the asymptotic analysis of thermal equations when the thickness of the structure tends to zero.

The temperature is described by 3 fields defined on the average surface of the shell.

A few examples show the capabilities of the model with reference to 3D solutions.

The applications targeted are thermomechanical shell calculations, wall thermal restoration for the thermohydraulics of pipes, and identification problems.

Table of Contents

• 1. Introduction
• 2. Presentation of the model
  • 2.1. Position of the thermal problem in shells
  • 2.2. Summary of the results of asymptotic development
  • 2.3. Formulation of the stationary thermal shell model
• 3. Validation of the model on a few examples
  • 3.1. The infinite cylinder subjected to a uniform internal flow
  • 3.2. The infinite plate under a pair of antisymmetric flows
  • 3.3. The infinite plate under a pair of symmetric flows
  • 3.4. The infinite cylinder subjected to horizontal stratification
• 4. Notes on digital discretization
  • 4.1. Finite element resolution
  • 4.2. Numerical blocking of a finite thermal shell element
• 5. Conclusion
• 6. References
• 7. Description of document versions