Elastica solution for the hygrothermal buckling of a beam

An elliptic integral solution for the post-buckling response of a linear-elastic and hygrothermal beam fully restrained against axial expansion is presented. 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 the compressive axial load is a maximum at the onset of buckling and decreases as the potential for free expansion is increased; this is in contrast to the approximate solutions found in the literature. (C) 1999 Elsevier Science Ltd. All rights reserved.