Extremal Thermoelastic Buckling Analysis of Fixed Slender Beams

Publication Type:
Conference Proceeding
Procedia Engineering: The Proceedings of the Twelfth East Asia-Pacific Conference on Structural Engineering and Construction - EASEC12, 2011, pp. 256 - 263
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The thermal expansions and rotations of a fixed slender beam that result from a linear temperature gradient field are fully restrained at the beam ends. These restrained expansions and rotations will produce internal bending and compressive actions in the beam, and these actions increase with an increase of the temperature differential and average temperature of the linear temperature gradient field. When these actions reach critical values, the fixed beam may bifurcate from its primary equilibrium configuration to a buckled equilibrium configuration. In previously-reported studies of the thermoelastic buckling of a member or structure, the material and geometric properties of the structure are predetermined. However, in practice, these properties are always subjected to a certain amount of uncertainty due to inaccurate measurement, and manufacture and construction errors. For example, a material manufactured by the same process may demonstrate differences in its elastic properties. A more realistic thermoelastic buckling analysis should be carried out by accounting for the variations of the material and geometry of the structure. This paper uses convex sets to model these uncertainties and derives the upper and lower critical temperatures for the thermoelastic in-plane buckling of fixed slender beams
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