An efficient structural reanalysis model for general design changes and based on the flexibility method

Abstract

Approximate structural reanalysis methods have long been pursued in quest for efficiency so as to enhance their practical' application in the assessment and verification of designs following design modifications, These have been of significant practical importance with particular emphasis on design optimization of large-scale structural systems in which thousands of design modifications need to be carried out during the search operation to identifY optimal systems, However, the consequential problems of accuracy and reliability call for the development of better-quality mathematical models that enhance computational quality while keeping the computational effort at afraction of what might be required if complete and exact analysis would be carried out. This paper presents an efficient structural reanalysis mathematical model that is based on the flexibility method and exhibits high approximation qualities in evaluating structural responses of a newly proposed design from those of an initial trial design, The mathematical model to be presented here is a flexibility-method based binomial-series approximation of structural responses for a general and unconditional change. in design, coordinates. It makes use of one set of results from a single exact analysis usually carried out for the initial trial design. Novel concepts of scaling and norm minimization have been introduced to gain accuracy, efficiency, and reliability. The proposea model has been compared with existing ones and also with exact analysis outputs and it has shown excellent approximating qualities even under significantly large design modifications. A numerical example has been presented to show potential capabilities of the proposed model.