This paper is concerned with a new approach to the solution of the stability problems for plates on an elastic foundation by the Boundary Element method. The use of this method makes it possible to reduce the biharmonical problem to the system of two Poisson's equations. The numerical solution is based on an iteration process. Rayleigh's formula is used here to determine the critical force parameter for a floating plate. The numerical results obtained are compared with analytical solutions and investigations by other authors.
Determination of ice force from the interaction between an ice cover and a hydrodynamics structure is important. Experimental and natural observations show that ice cover destruction takes place because of instability. This phenomenon is known as buckling. In this paper an ice sheet is modeled as a thin plate on an elastic foundation. The plate stability problem is a classical problem, but analytical solution may be found only for very simple cases. For example, solutions for rectangular and round plates with simple loading are well known. In this paper the ice sheet stability problem is solved by the boundary element method. The characteristic feature of the numerical solution of the problem is the necessity to solve it by two steps. At the first step the two-dimensional elasticity problem is solved to determine the stress state of the plate. At the second step the deflection and critical load when the floating plate loses its stability are determined. In the paper the stress tensor σαβ is considered to be Inlown. For such determination, the boundary element method (BEM) (Brebbia, 1984) as well as the finite element method (FEM) (Ciarlet, 1978) may be used. In the paper an iterative process is proposed to determine the critical parameter for plate stability.
