Comparison between sparse stiffness matrix and sub‐structure methods

Recent publications have emphasized the advantages of the sparseness of the over‐all stiffness matrix of a structure. An alternative to setting up the over‐all stiffness matrix is to use sub‐structures. The main purpose of this paper is to show that there is equivalence between these two approaches when rows are not interchanged. It follows that a sparse matrix method can never be more efficient than the sub‐structure method, if a suitable choice of sub‐structures is assumed. However when identical sub‐structures are contained within a structure the repetition can be utilized by the sub‐structure method. In such cases the sub‐structure method will often be quicker than the best sparse matrix solution.