Optimal support of rigid-plastic singly and doubly connected polygonal plates

In the model of an ideal rigid-plastic body the general solution of a problem of the limit behavior and dynamic bend is obtained for regular singly and doubly connected polygonal plates, hinge supported on immobile polygonal contour, located inside of the plate. The plate is under a short-term dynamic load of an explosive type with high intensity, uniformly distributed over the surface. It is shown that there are several mechanisms of limit and dynamic deformation of plates depending on the location of the support contour and on the availability of hole. In all schemes the plate deforms as a set of identical rigid areas in the form of a trapezium, separated by linear plastic hinges with normal bending moment equal to the limit value. For each of the mechanisms the governing equations are obtained and the conditions of their implementation are defined. The simple analytic expressions are obtained for the limit load and maximum final deflection of plates. The optimal location of support is determined. The optimal support is a support at which the plate has a maximum limit load. The study shows that the inner support is optimal if a plastic hinge is formed on it. We have defined the locations of the support contour at which the plate with a hole will be more durable than a plate without a hole. The solution of the problem extended to the case of plates with polygon contours, into which you can inscribe the circle. The study obtained that these plates have the same respective limit loads, time of deformation and the maximum final deflection which does not depend on the number of sides of the polygon contours and coincides with the same values for circular and annular plate. Numerical examples are given. The solution can be useful in engineering.