Abstract
The design of thermal structures in the aerospace industry, including exhaust structures on embedded engine aircraft and hypersonic thermal protection systems, poses a number of complex design challenges. These challenges are particularly well addressed by the material layout capabilities of structural topology optimization; however, no topology optimization methods are readily available with the necessary thermoelastic considerations for these problems. This is due in large part to the emphasis on cases of maximum stiffness design for structures subjected to externally applied mechanical loads in the majority of topology optimization applications. In addition, while limited work in the literature has investigated thermoelastic topology optimization, a direct treatment of thermal stresses is not well documented. Such a treatment is critical in the design of thermal structures where excessive thermal stresses are a primary failure mode. In this paper, we present a method for the topology optimization of structures with combined mechanical and thermoelastic (temperature) loads that are subject to stress constraints. We present the necessary steps needed to address both the design-dependent thermal loads and accommodate the challenges of stress-based design criteria. A relaxation technique is utilized to remove the singularity phenomenon in stresses and the large number of stress constraints is handled using a scaled aggregation technique that has been shown previously to satisfy prescribed stress limits in mechanical problems. Finally, the stress-based thermoelastic formulation is applied to two numerical example problems to demonstrate its effectiveness.
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Acknowledgments
This work has been funded by the U.S. Air Force Research Laboratory (AFRL) through contract FA8650-09-2-3938, the Collaborative Center for Multidisciplinary Sciences (CCMS). The views and conclusions contained herein are those of the authors and should not be interpreted as representing official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government. We would also like to thank the reviewers. Their insightful comments undoubtedly helped increase the clarity and technical rigor of this paper.
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Deaton, J.D., Grandhi, R.V. Stress-based design of thermal structures via topology optimization. Struct Multidisc Optim 53, 253–270 (2016). https://doi.org/10.1007/s00158-015-1331-z
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DOI: https://doi.org/10.1007/s00158-015-1331-z