The design of mechanical structures often involves the analysis of several candidate designs before a final selection is made. To avoid the high cost of repetitive analysis, rapid reanalysis methods based on power series expansions have been proposed. While these methods can be effective for small design changes, for larger changes poor convergence or divergence can occur. In this paper a reanalysis method based on rational approximants is presented. The method exploits the superior convergence behavior of rational approximants to gain a substantial improvement in convergence and accuracy. The method is applied to reanalysis problems involving linear equations and eigenproblems and is illustrated through representative examples.

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