Abstract
In this chapter, we consider three thermoelastic optimization problems. We look at the optimal thickness distribution for a beam of variable thickness, when the goal is to maximize its resistance to thermoelastic buckling, or in other words, to maximize the critical temperature at which buckling occurs. In the second problem, we allow the beam to be constructed inhomogeneously, looking for an optimal distribution of materials that maximizes the critical temperature. The third and final problem concerns heat conduction in locally orthotropic solid bodies. By locally orthotropic, we mean a particular type of inhomogeneity, where the principal directions (axes of orthotropy) may vary as a function of the space coordinates. We derive a guaranteed double-sided estimate for energy dissipation that occurs in heat conduction in a locally orthotropic body, without assuming anything about the material orientation field. This yields guaranteed lower and upper bounds for energy dissipation that always hold regardless of how the local material orientation is distributed in the solid body.
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References
Albul AV, Banichuk NV, Barsuk AA (1980) Optimization of stability for elastic rods with thermal loads. Izvestiya Akademii Nauk SSSR, Mekhanika Tverdogo Tela (MTT), vol 3, pp 127–133 (in Russian)
Banichuk NV, Ivanova SY, Makeev EV, Ragnedda F (2007) Nonlocal optimization of thermoelastic rod made from discrete set of materials with application of genetic algorithm. Probl Strength Plast (69):38
Banichuk NV (1990) Introduction to optimization of structures. Springer, New York, 300 pages
Banichuk VV (1983) Problems and methods of optimal structural design. Plenum Press, New York, 313 pages
Goldberg DF (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading, MA
Haslinger J, Mäkinen RAE (2003) Introduction to shape optimization: theory, approximation and computations. SIAM, Philadelphia, PA
Holland JH (1975) Adaptation in neural and artificial systems. University of Michigan Press, Ann Arbor, MI
Komkov V (1988) Variational principles of continuum mechanics with engineering applications. Vol 1: critical points theory. Reidel Publishing Co., Dordrecht
Komkov V (1988) Variational principles of continuum mechanics with engineering applications. Vol. 1: introduction to optimal design theory. Reidel Publishing Co., Dordrecht
Landau LD, Lifshitz EM (1970) Teoriya uprugosti (Theory of elasticity, 2nd edn). English 2nd edn. Published by Pergamon Press, Oxford, 1965
Larichev AD (1981) Finding a minimum volume for a beam on an elastic foundation, for a given magnitude of a critical load. In Applied and theoretical research into building structures, Moscow, pp 19–25. Kucherenko TsNIINSK (in Russian)
Love AEH (1944) A treatise on the mathematical theory of elasticity, 4th edn. Dover Publications, New York
Nowacki W (1970) Teoria sprezystosci. Panstwowe Wydawnictwo Naukowe, Warszawa
Skutch Rudolf (1897) Uber die Bewegung eines gespannten Fadens, weicher gezwungen ist durch zwei feste Punkte, mit einer constanten Geschwindigkeit zu gehen, und zwischen denselben in Transversal-schwingungen von gerlinger Amplitude versetzt wird. Annalen der Physik und Chemie 61:190–195
Timoshenko S (1956) Strength of materials, Part II: advanced theory and problems, 3rd edn. D. Van Nostrand Company
Timoshenko S, Goodier J (1987) Theory of elasticity, 3rd edn. McGraw-Hill
Washizu K (1982) Variational methods in elasticity and plasticity. Pergamon, Oxford
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Banichuk, N., Barsuk, A., Jeronen, J., Tuovinen, T., Neittaanmäki, P. (2020). Optimization of Elastic Bodies Subjected to Thermal Loads. In: Stability of Axially Moving Materials. Solid Mechanics and Its Applications, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-030-23803-2_9
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DOI: https://doi.org/10.1007/978-3-030-23803-2_9
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