Abstract
A new mathematical model is introduced to describe the moisture-induced deformation in an elastic panel. The problem for the stresses is found to be singularly perturbed in the aspect ratio squared, the domain being split into four asymptotic regions. Determination of the matching constants is made possible by the introduction of a stress function in the boundary layer. Explicit expressions are derived for the stress and deformation in the three-dimensional problem. The predictions for deformation are compared with experimental results; the agreement is reasonable. The moment of the moisture concentration is found to be the crucial factor in determining panel warp. A model, which consists of two coupled parabolic equations, is also proposed for moisture transport in exterior applications. The disparate time-scales allow the system to be reduced to a single partial differential equation. In one parameter régime, a multiple-scale analysis further reduces this partial differential equation to an averaged equation which only requires solution over the long moisture-diffusion time-scale.
Similar content being viewed by others
References
O. Suchland, Y. G. Feng, and D. P. Xu. The hygroscopic warping of laminated panels. Forest Prod. J. 45 (1995) 57–63.
S. P. Timoshenko and J. N. Goodier, Theory of Elasticity. New York: McGraw-Hill (1982) 567 pp.
A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity. Cambridge: Cambridge University Press (1927) 643 pp.
P. V. Kaprielian, T. G. Rogers, and A. J. M. Spencer, Theory of laminated elastic plates. I. isotropic laminae. Phil. Trans. R. Soc. London A 324 (1988) 565–594.
K. O. Friedrichs and R. F. Dressler, A boundary-layer theory for elastic plates. Comm. Pure Appl. Math. 14 (1961) 1–33.
D. Chandra, H. J. J. Gramberg, T. Ivashkova, W. R. Smith, A. Suryanto, J. H. M. ten Thije Boonkkamp, T. Ulicevic, and J. C. J. Verhoeven, Modelling of moisture induced warp in panels containing wood fibres. In: Proceedings of the Thirty-sixth European Study Group with Industry, 2000.
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids. Oxford: Clarendon Press (1959) 510 pp.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Smith, W., Gramberg, H. Mathematical modelling of moisture-induced panel deformation. Journal of Engineering Mathematics 43, 347–366 (2002). https://doi.org/10.1023/A:1020339728020
Issue Date:
DOI: https://doi.org/10.1023/A:1020339728020