UPPER BOUNDS TO LOAD FOR TRANSVERSE BENDING OF FLAT RIGID-PERFECTLY PLASTIC PLATES .I. USING HODOGRAPHS - A NEW AND SIMPLE APPROACH .2. AN ANALOGY - SLIP LINE FIELDS FOR ANALYSING BENDING AND TORSION OF PLATES

In Part 1, with the help of the notion of a plastic hinge as used in the plastic analysis of beams, a trivial hodograph for the collapse mechanism of a built-in beam is drawn. The idea is extended to provide a hodograph for a simple collapse mechanism for a square plate and, later, to plates of various shape, each subject to a variety of edge support. Using a proposed system of hinges, together with the hodograph, bounds to collapse loads are easily found. In Part 2, a similarity is pointed out as between the hodographs for certain plane strain extrusion and piercing operations and for proposed kinematic modes of plastic deformation in plates. This makes possible a new analogy and, in particular, the use of known slip-line field solutions for application to the bounding of the collapse load in plates. By utilizing known indentation (or forging) solutions for plane strain metal working, solutions for a class of plate torsion problems are made available. © 1969.