Abstract
The paper proposes a mathematical model describing behavior of ice cover under loading. Not taking into account the chemical characteristics, and considering it a solid continuous medium on an elastic base, the role of which is played by water, to simulate the deflection of the ice cover under loading, it is possible to use the theory of thin shells and plates. Thus, the proposed mathematical model is based on the partial differential equation of the bending of a thin plate on an elastic base. Boundary conditions are set depending on the method of fixing the edges. Delivered the boundary value problem is solved in the class of almost-periodic functions by means of a generalized discrete Fourier transform, which allows us to move from the partial differential equation to the ordinary differential equation. The graph of the function of deflection of the ice plate is constructed.
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