Analysis of internally cooled structures using a higher order theory

Steven M. Arnold*, Brett A. Bednarcyk, Jacob Aboudi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper presents the results of a study on the thermo-mechanical behavior of internally cooled silicon nitride structures. Silicon nitride is under consideration for elevated temperature aerospace engine applications, and techniques for lowering the operating temperature of structures composed of this material are under development. Lowering the operating temperature provides a large payoff in terms of fatigue life and may be accomplished through the use of thermal barrier coatings (TBCs) and the novel concept of included cooling channels. Herein, an in depth study is performed on the behavior of a flame-impinged silicon nitride plate with a TBC and internal channels cooled by forced air. The analysis is performed using the higher order theory for functionally graded materials (HOTFGM), which has been developed through NASA Glenn Research Center funding over the past several years. HOTFGM was chosen over the traditional finite element approach in order to facilitate examination of functionally graded silicon nitride structures for which HOTFGM is ideally suited. To accommodate the analysis requirements of the internally cooled plate problem, two crucial enhancements were made to the two-dimensional Cartesian-based version of HOTFGM, namely, incorporation of internal boundary capabilities and incorporation of convective boundary conditions. Results indicate the viability and large benefits of cooling the plate via forced air through cooling channels. Furthermore, cooling can positively impact the stress and displacement fields present in the plate, yielding an additional payoff in terms of fatigue life. Results illustrating the benefits associated with particular cooling channel arrangements and functionally grading the silicon nitride material are also presented. Finally, a spin off capability resulted from inclusion of internal boundaries within HOTFGM; the ability to simulate the thermo-elastic response of structures with curved surfaces. This new capability is demonstrated, and through comparison with an analytical solution, shown to be viable and accurate.

Original languageEnglish
Pages (from-to)659-688
Number of pages30
JournalComputers and Structures
Issue number7-8
StatePublished - Mar 2004


  • Ceramics
  • Deformation
  • Elasticity
  • Parametric study
  • Thermal analysis


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