Numerical determination of the bearing capacity of reinforced annular plates resting on an incompressible liquid base and differently resistant to tension and compression

Abstract

Based on the principle of virtual power, an extreme problem is formulated to determine the upper (kinematic) limit of the load-bearing capacity of bendable annular reinforced plates that are in contact along one of the obverse planes with an incompressible fluid. The internal openings of the structures are closed with absolutely rigid inserts. The reinforcement structure has radial and axial symmetry. The deformed state of the plates is described by the kinematic relations of the classical theory of bending. A rigid-plastic model of the mechanical behavior of the materials of the composition components was used. Plastic flow in them is associated with piecewise linear yield criteria. Phase materials may have different tensile and compressive yield strengths. The binder matrix material may have cylindrical orthotropy. The plastic flow of compositions is determined on the basis of a structural model that takes into account the occurrence of a plane stress state in all components. A two-layer bending plate model was used. The posed axisymmetric problem was discretized along the polar radius. To solve it numerically, the simplex-method of linear programming theory was used. Using examples for homogeneous and isotropic plates, the convergence of the numerical solution and good agreement of the calculation results with previously obtained analytical solutions are demonstrated. A parametric analysis of the influence of the directions and densities of reinforcement of plates on the maximum permissible value of the transverse force acting on a rigid insert was performed. Options for laying fibers along rectilinear radially symmetrical trajectories and logarithmic spirals, as well as radial-circumferential reinforcement structures, are considered. It has been demonstrated that the design with a rigidly clamped outer edge and rigid fastening to the inner insert in the presence of a radial-circular structure has the greatest load-bearing capacity. In this case, the total reinforcement density at each point of the plate must be constant and equal to the maximum permissible (technologically) value. The case of a non-traditional boundary condition on the outer edge of the plate -- a pinching movable in the vertical direction -- has been studied.