Mathematical modelling of moisture-induced panel deformation

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 regime, 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.