DETERMINATION OF THE UPPER LIMIT OF THE LOAD-LOADING CAPACITY OF BENDING REINFORCED METAL-COMPOSITE RING PLATES IN CONTACT WITH A LIQUID INCOMPRESSIBLE MEDIUM 1. PROBLEM FORMULATION AND CALCULATION METHOD

Abstract

The problem of determining the load-bearing capacity of a bendable reinforced annular plate resting on an incompressible liquid base is considered. The internal opening of the structure is closed with a continuous, absolutely rigid insert. The connection between the insert and the plate can be rigid or hinged. The structure is supported on the outer edge, and it is possible to move the support in the vertical direction, for example in the case of a movable jamming. In the limiting state, liquid flow from one front surface of the plate to another surface is not allowed. The materials of the components of the composition are isotropic and rigid-plastic, having the same yield limits in tension and compression. Plastic flow in the phases of the composition is associated with piecewise linear yield criteria (such as the Tresk's or Ishlinsky - Ivlev's yield conditions). The limit state of such a composite plate is described within the framework of the classical theory of transverse bending. Reinforcement structures have axial and radial symmetry. Two reinforcement options are considered: laying two families of fibers along radially symmetrical spiral trajectories and reinforcement in the radial and circumferential directions. The rein-forcing fibers are assumed to be continuous and have constant cross sections along their length, which gives rise to significant heterogeneity of the structures under consideration in the radial direction. The plastic flow of a metal-composition is calculated using a structural model that takes into account the presence of a plane stress state in all substructural elements. Structural formulas have been written that make it possible to determine the coordinates of corner points on piecewise linear yield curves of the compositions under consideration, taking into account their dependence on non-uniform reinforcement parameters: angles and densities. An extremal principle has been formulated that makes it possible to obtain an upper (kinematic) estimate of the maximum load for this type of structure. The formulated problem is discretized along the polar radius. Nodal values of the sagging speed and mechanical energy dissipation were used as unknown grid functions. A numerical algorithm for solving the formulated discretized problem has been developed, based on the application of the simplex method of linear programming theory.