Load-bearing capacity of ice weakened plates of curvilinear shape with variable thickness

A method is developed for determining the load-bearing capacity of weakened ice plates, which are modeled by an ideal rigid-plastic plate located on an incompressible foundation. The plate is simply supported or clamped on arbitrary piece-wise smooth curvilinear external contour. The central part of the plate contains a free opening with an arbitrary contour. The thickness of the plate decreases when approaching the boundary of the opening. The plate is subject to a load distributed locally around the opening in the region of an arbitrary shape. The load is an arbitrary function of coordinates. The property of ice with different a resistance in tension and compression is taken into account. The solution is made based on the principle of virtual work. Two variants of kinematically admissible deformations are considered in dependence on the geometric parameters of the plate. In both deformation schemes, the central part of the plate (under loading) moves in the direction of the load; while the area near the external contour (due to the foundation incompressibility) moves in the opposite direction. An orthogonal curvilinear coordinate system associated with curvilinear external contour of the plate is considered. In this system, it is convenient to calculate double integrals describing the solution of the problem. Analytical expressions for the limit loads are obtained. Two integral characteristics of the load are determined; and it is shown that in case the plate is affected by differently distributed surface loads (in which these two characteristics coincide) the plate will have the same limit load. А simply supported and clamped plate shaped as an ellipse with a linear function of thickness under the action of several types of local surface loads is considered as an example. The proposed method allows calculating the load-bearing capacity of weakened curvilinear ice plates on an incompressible foundation and estimating the possibility to increase the load-bearing capacity by increasing the loaded area and by redistributing the load on the area of loading.