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Elastica solution for the hygrothermal buckling of a beam. (English) Zbl 1006.74035

Summary: We present an elliptic integral solution for post-buckling response of a linearly elastic hygrothermal beam fully restrained against axial expansion. Whereas in the classical solutions the extension of the beam can be neglected, a well-posed formulation of the title problem must include the extension. The solution for the limiting case of a string is presented. The present solution shows that the magnitude of compressive axial load is maximal at the onset of buckling, and decreases as the potential for free expansion is increased; this is in contrast to approximate solutions found in the literature.

MSC:

74G60 Bifurcation and buckling
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K05 Strings
74F05 Thermal effects in solid mechanics
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