Analysis of Irregular Structures Composed of Regular and Irregular Parts Using Graph Products

Abstract

The inverse of the stiffness matrices of a large group of repeated and regular structures were previously obtained using graph products. Considering the importance of increasing the speed of the computing process and decreasing the amount of computation and dimension of matrices, this paper presents an efficient algorithm that swiftly solves irregular structures composed of regular and irregular parts. The present method is based on generalizing the solution of regular forms to irregular ones. Here, the irregular structure is a regular structure with some additional nodes (irregular part), in comparison with another kind of irregularity concerned with additional members that was discussed previously. The algorithm is subsequently combined with the algorithm of additional members to allow solving all kinds of irregularity. In addition to irregular structures, the method is practical for design and reanalysis of structures, analyzing the existing structures to which new stories or degrees of freedom are added, and solving constructional imperfection problems.