Approximate static and dynamic reanalysis techniques for structural optimization

Abstract

This paper presents an approach based on reduced basis approximation concepts for static and dynamic reanalysis of structural systems. In the presented approach, scaling parameters are introduced to increase the range of applicability of local approximation techniques based on Taylor or matrix perturbation series. The terms of the local approximation series are used as basis vectors for constructing an approximation of the perturbed response quantities. The undetermined scalar quantities are then estimated by solving the perturbed equilibrium equations int he reduced basis. This approach was earlier proposed in the context of statistics by Kirsch (1991). This paper presents in brief the reanalysis procedure for statics and a new method based on a similar line of approach is proposed for approximate dynamic reanalysis. The method is applied to approximate dynamic reanalysis of a cantilevered beam structure. Preliminary results for this example problem indicate that high quality approximation of the natural frequencies and mode shapes can be obtained for moderate perturbations in the stiffness matrix elements of the order of 40%.

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