Approximate structural reanalysis based on series expansion

Abstract In most optimal design procedures the analysis of the structure must be repeated many times. This operation, which involves much computational effort, is one of the main difficulties in applying optimization methods to large systems. This study deals with approximate reanalysis methods based on series expansion. Both design variables and inverse variables formulations are presented. It is shown that a Taylor series expansion of the nodal displacements or the redundant forces is equivalent to a series obtained from a simple iteration procedure. The series coefficients can readily be computed, providing efficient and high-degree polynomial approximations. To further improve the quality of the approximations, a modified nonpolynomial series is proposed. To reduce the amount of calculations, the possibility of reanalysis along a given line in the variables space is demonstrated. All the proposed procedures require a single exact analysis to obtain an explicit behaviour model along a line. The relationship between the various methods is discussed and numerical examples demonstrate applications. The results obtained are encouraging and indicate that the proposed methods provide efficient and high quality approximations for the structural behavior. This may lead to a wider use of optimization methods in the design of large structural systems.