Floating Ice Plate Research Articles

Floating sea ice plates and the significance of the dependence of the Poisson ratio on brine content

This article investigates the influence of the temperature profile in ice plates on the plate characteristic coefficients for a dynamical theory of flexible plates that accounts for such effects as the variation of the Poisson ratio across the thickness of the plate. The mathematical solution of two simple problems is constructed, dealing with the response of an infinite plate on a Winkler foundation to static line loads and with the propagation of plane waves in a system consisting of a liquid layer and floating ice plate. The static problem is solved by means of the Green function technique, while the wave propagation problem follows the usual lines of harmonic analysis. Numerical results prove that the effects emerging from the dependence of the Poisson ratio on the microstructure are negligible for both fresh water ice and sea ice. On the basis of the plate theory, it should thus be extremely difficult to experimentally detect the dependence of the Poisson ratio on brine content for sea ice.

The deformations and stresses in floating ice plates

In the past, the analyses of floating ice plates subjected to static or dynamic loads were based on the theory of a thin homogeneous plate, although in actual floating ice plates Young's modulus may vary strongly with depth. Recently,A. Assur concluded, on the basis of a heuristic argument, that the solutions obtained for homogeneous plates may be used for floating ice plates, if a modified flexural rigidity is used. The purpose of the present paper is to study this question, by establishing a mathematically consistent formulation for the dynamic plate equation, utilizing Hamilton's Principle in conjunction with the three dimensional theory of elasticity. It is proven that for a variable Young's modulus and a constant Poisson's ratio the resulting formulations for plates and beams are the same as those for the corresponding homogeneous problems, if a modified flexural ridigity is used; thus confirmingAssur's conclusion. It is shown that the stress distribution is not linear and that the stress formula\(\sigma _{\max } = M{{z_0 } \mathord{\left/ {\vphantom {{z_0 } I}} \right. \kern-\nulldelimiterspace} I}\) used by a number of investigators for the determination of the carrying capacity of a floating ice plate, as well as for the computation of failure stresses from tests on floating ice beams, is not applicable. Correct formulas are derived, corresponding stress distributions are presented and the consequences of the findings discussed.

Dynamics of a Floating Ice Sheet

Civilian and military operations are frequently conducted on the surface of floating ice sheets. For reasons of safety and operational reliability it is often required to predict the deformation and stresses in such floating ice plates due to surface loading. The present dynamic analysis considers the deformation of a floating ice sheet of infinite extent subjected to rapidly applied surface loads. Solutions are obtained within the framework of both improved and classical theories.