Efficient models for high quality approximations of forces in structural systems are presented. Four approximate reanalysis models are developed and compared. These are First Order Approximations (FOA), Binomial Series Approximations (BSA), Improved First Order Approximations (IFOA), and Improved Binomial Series Approximations (IBSA) models. Each of these models is based on results of a single exact analysis. Relationships among the models are derived and some of them are shown to be equivalent under certain assumptions. The improved versions are obtained by a procedure that employs scaling and norm minimization of certain matrices. This is also extended into explicit approximations in terms of a single variable introduced along a line in the design space.

It is shown that poor results might be obtained by the FAO, BSA, and IFOA models. High quality approximations of forces are introduced by the IBSA model even for large and random changes in design variables. In most cases only the first two terms of the series are sufficient to obtain excellent results. Numerical examples are given to illustrate the performance of the proposed approximation models.

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