| Abstract: | The need for multiple repeated analyses, which usually involve much computational effort, is one of the main difficulties in the optimization of large structures. This study deals with approximate structural reanalysis along a line in the design space, a problem common to many optimal design procedures. The problem is first stated in terms of a single independent variable. Explicit polynomial approximations for the nodal displacements are then presented. It is shown that Taylor series expansion of the displacements and a series based on a simple iteration procedure are equivalent. Furthermore, the series coefficients can readily be computed, providing efficient and high-degree polynomial approximations. To improve the quality of the approximations, two nonpolynomial series are proposed. The relationship between the various methods is discussed and simple numerical examples demonstrate applications. All the proposed procedures require only a single exact analysis to obtain the explicit expressions for any given line. The results obtained are very close to the exact solution and indicate that the proposed methods provide efficient and high-quality approximations for the nodal displacements. |
