Systematic prediction of yield-line configurations for arbitrary polygonal plates

In addition to the well-established finite element method in recent years several optimization approaches have been developed concerning the yield-line theory. This paper presents a new systematical algorithm to predict initial yield-line configurations of arbitrary polygonal plates. It contributes a solution to the task of detecting yield-line patterns in advance of an optimization process. For this reason a ciphering of yield-line patterns is proposed and a new application of Catalan numbers and binary trees is demonstrated. After a subsequent refining a triangular element is used in combination with a simplex optimization procedure in order to determine the ultimate load of the considered yield-line configuration. Moreover, further optimization strategies like the direct search method and the conjugate gradient method lead to the final solution of the problem. The use and the efficiency of the new approach are demonstrated with three examples.