Limit analysis and optimal support of reinforced three-layer circular plates of different resistant materials under non-uniform loading

Within the model of an ideal rigid-plastic body the limit behavior of the hybrid composite circular plates is considered. The exact solution of the problem of bending is built for three-layer reinforced circular plates having different angular structure reinforcement at the top and bottom layer. The material of the middle layer and the binder in the upper and lower layers has a yield stress in compression much greater than in tension. In this case the condition of plasticity for the main moments that are based on the structural model of the reinforced layer with one-dimensional states of stress in the fibers has the form of a rectangle of type Johansen condition. The plates are hinge supported along the internal annular contour and have the rigid circular insert in the central part. The plates are under load non-uniformly distributed over the surface of the plate. It is shown that there are a few schemes of limit deformation of the plate, depending on the location of the internal support and on distribution of load. The conditions of implementation are defined for all schemes. The main moments and the velocities of the deflections of the plate are defined at different locations of the internal support. The simple analytic expressions are obtained for the limit load. The optimal location of support is determined. The optimal support is such support, at which the plate has a maximum limit load. It is shown that the optimal position of the support corresponds to the formation of plastic hinge on it. It is obtained that with increase in the applied distributed load in several times, the limit loads will be reduced in the same times and the optimal location of the support will not change. Numerical examples are given. The solution can be useful in engineering practice to evaluate the bearing capacity of three-layer reinforced concrete plates.