BEARING CAPACITY AND DYNAMIC BEHAVIOR OF RIGID PLASTIC CIRCULAR PLATES WITH FREE CONTOUR SECTIONS UNDER EXPLOSIVE LOADS

Based on the model of an ideal rigid-plastic body, a general solution to the problem of the limit and dynamic behavior of layered circular plates with mixed edge conditions is constructed. Part of the contour is free; the supported part of the plates is simply supported or clamped. A short-term dynamic load of high explosive intensity evenly distributed over the surface of the plate acts. The solution of the problem becomes non-axisymmetric due to the irregular supporting of the contour. It is shown that there are several schemes of limit and dynamic deformation of plates depending on the size of the free part of the contour and on the amplitude of the load. In all schemes, the plate takes the form of a set of ruled surfaces (conical or flat rigid areas) separated by plastic hinges with a normal bending moment equal to the limit value. These hinges can be straight or curved; their position changes in time. The governing equations are obtained on the basis of the virtual power principle in combination with the Dalembert principle. For each of the deformation mechanisms, the conditions for their implementation are defined. Simple analytical expressions for the limit load and the maximum final deflection of the plate are obtained. The proposed approach is extended to the case of circular plates with several sections of a free contour. It is shown that with an increase their number and under the condition of the same length of the total free contour, the limit load increases, but it is always less than the limit load of the plate with the limit deformation scheme in the shape of a cone. Numerical examples are given. It is shown that as the free part of the contour increases, the limit load decreases.