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Structural Engineering and Mechanics Volume 43, Number 2, July25 2012 , pages 211-223 DOI: https://doi.org/10.12989/sem.2012.43.2.211 |
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Analytical approximate solutions for large post-buckling response of a hygrothermal beam |
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Yongping Yu and Youhong Sun
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| Abstract | ||
| This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton\'s method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to \"reference\" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach. | ||
| Key Words | ||
| buckling; approximation method; large deformation; Chebyshev polynomials | ||
| Address | ||
| Yongping Yu and Youhong Sun: College of Construction Engineering, Jilin University, Changchun 130021, P.R. China | ||