Analysis of Regular Structures with Member Irregularity Using the Equilibrium Equations and the Singular Value Decomposition

Abstract

In this paper an efficient method is presented for the analysis of those structures which can be formed by addition some members to regular structures. This method is also applicable when some members are reduced from regular structures. If a model is the union of a regular structure and some additional members, then these members are separated from the structure, and their effect is introduced through equilibrium matrix and added to that of the regular structure. For models which lack some members, pairs of hypothetical elements with positive and negative modulus of elasticity are added, and the members with negative modulus are separated from the structure resulting in a regular structure.