Fuzzy Finite Element Method for Frequency Response Function Analysis of Uncertain Structures

Abstract

A concept is presented for incorporating fuzzy uncertainties in dynamic finite element analyses of uncertain structures. The objective is twofold. The first goal is to clarify and extend the classical fuzzy finite element (FFE) method as it was introduced for static analyses. The shortcomings of the classical approach are described, and an extension to a generalized approach is proposed. This generalized approach is proven to be a more realistic and therefore more reliable concept for taking uncertainty into account. The second goal is to illustrate the applicability of the method for dynamic analyses. The classical and the generalized approach are compared using an eigenvalue analysis of a simple numerical example. The FFE method is also applied to the calculation of the total envelope frequency response function (FRF) using the modal superposition principle. This method requires safe approximations of the individual mode envelope frequency response functions. For this purpose a number of safe approximate optimization strategies are introduced. The numerical example shows that useful results are obtained using this FFE approach for FRF calculations.

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