Abstract
This paper presents the theory underlying Johnson's recent analogy between upper bound solutions for rigid/perfectly-plastic materials in plane strain and in plate bending theory. This analogy is extended to lower bound and complete solutions. Many exact solutions in plane strain, such as the classical Prandtl punch solution, can be interpreted as exact solutions to plate bending problems. As an illustration of a slip-line field technique which can be taken over into plate theory, Bishop's method of completing slip-line solutions is used to complete a yield-line theory solution for a centrally-loaded simply-supported rectangular plate. Recent solutions to this and similar problems due to Sawczuk and Hodge are shown to be in error.
Published Version
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