Neumann expansion for fuzzy finite element analysis

This paper presents a new framework to predict a structure's effective prop erties and sensitivities to multiple simultaneous uncertain endogenous para meters. The methodology is based on the use of fuzzy sets and this paper ex tends the fuzzy set theory to a dynamic finite element analysis of engineer ing systems containing uncertainty on material properties. A general algori thm, which can resolve the uncertain eigenvalue problem try using a Neumann expansion, is studied This algorithm is applied to the study of the modal behavior of structures presenting uncertain material properties. Finally, t he entropy and the specificity of fuzzy responses lead to the identificatio n of a plate structure's most sensitive eigenvalue to uncertain sources.