Neumann expansion for fuzzy finite element analysis

Abstract

This paper presents a new framework to predict a structure’s effective properties and sensitivities to multiple simultaneous uncertain endogenous parameters. The methodology is based on the use of fuzzy sets and this paper extends the fuzzy set theory to a dynamic finite element analysis of engineering systems containing uncertainty on material properties. A general algorithm, which can resolve the uncertain eigenvalue problem by using a Neumann expansion, is studied. This algorithm is applied to the study of the modal behavior of structures presenting uncertain material properties. Finally, the entropy and the specificity of fuzzy responses lead to the identification of a plate structure’s most sensitive eigenvalue to uncertain sources.