CARRYING CAPACITY AND OPTIMIZATION OF THREE-LAYER REINFORCED CIRCULAR PLATE OF DIFFERENTLY RESISTANT MATERIALS, SUPPORTED ON THE INTERNAL CONTOUR

Abstract

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. 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 uniformly distributed over the surface of the plate. It is shown that there are three schemes of limit deformation of the plate, depending on the location of the internal support. 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. The optimum thickness ratio of the upper and lower layers of the plate for a given total thickness is determined, which corresponds to the maximum load limit.

Keywords: rigid-plastic model, hybrid composite plate, differently resistant materials, corner reinforcement, three-layer plate, internal support, rigid insert, limit load, optimal location of support.