A direct topological reanalysis algorithm based on updating matrix triangular factorization

Abstract

Purpose The purpose of this paper is to establish and implement a direct topological reanalysis algorithm for general successive structural modifications, based on the updating matrix triangular factorization (UMTF) method for non-topological modification proposed by Song et al. [Computers and Structures, 143(2014):60-72]. Design/methodology/approach In this method, topological modifications are viewed as a union of symbolic and numerical change of structural matrices. The numerical part is dealt with UMTF by directly updating the matrix triangular factors. For symbolic change, an integral structure which consists of all potential nodes/elements is introduced to avoid side effects on the efficiency during successive modifications. Necessary pre- and post processing are also developed for memory-economic matrix manipulation. Findings The new reanalysis algorithm is applicable to successive general structural modifications for arbitrary modification amplitudes and locations. It explicitly updates the factor matrices of the modified structure and thus guarantees the accuracy as full direct analysis while greatly enhancing the efficiency. Practical implications Examples including evolutionary structural optimization and sequential construction analysis show the capability and efficiency of the algorithm. Originality/value This innovative paper makes direct topological reanalysis be applicable for successive structural modifications in many different areas.