Node Numbering Optimization in Structural Analysis

An algorithm is presented to produce an optimum node numbering system for a structure to be analyzed by the finite element method, reducing computer time and storage needs if band solution methods are used for solving the system of equations. Only nonzero off-diagonal elements of the connectivity matrix defining the topology of the structure are stored in a rectangular integer array. For every nonzero element causing the largest current bandwidth, the algorithm finds a pair of rows (and columns) to be interchanged in such a way that the bandwidth is either reduced or left unchanged. The process continues until the bandwidth is reduced either to the minimum or to the largest acceptable value, depending on the input parameters. A list of new node numbers is produced. New code numbers (listings of the elements) are also produced and punched in a set of cards ready to replace the old set.