Institute of Fundamental Technological Research

Full limit analysis is preseted of a thin plate under plane stress, perforated with circular holes arranged in a regular penetration pattern. The material is assumed to be elastic–perfectly plastic and to obey the Huber–Mises yield condition together with its associated flow law. The finite element tangential stiffness method is employed. Triangular constant-strain elements are used, the load being generated by means of constant edge displacements at the periphery of a suitably selected subregion. Load-displacement diagrams are obtained for various edge displacement programs and then an interaction curve is constructed for the perforated plate considered. Each computational step is associated with a certain plastic zone which develops until the limit state configuration is reached. The plate is provided with equilateral triangular configuration of holes with arbitrary cutout coefficients. The interaction curves are plotted against the Huber–Mises yield condition for the plate without openings.

It is known from experiments that the actual load-carrying capacities of plates are larger than those predicted by the limit analysis theory. The behavior of plastic structures beyond the bending collapse load is influenced by the changes in geometry of a structure during the process of plastic deformation. In the present paper, an investigation of the load-deflection relationship for simply supported rectangular reinforced concrete plates is presented. The tensile membrane action is found to be localized in zones of bending yield hinges. The zones of pure membrane response consequently develop as the load increases. The paper presents a kinematical method of analysis of plastic plates beyond the bending collapse load. Kinematically admissible collapse modes are studied and the associated dissipation functions are derived. Load-deflection relationships are obtained for various yield patterns. The theoretical results are compared with experimental data following from model tests.