Neumann expansion for fuzzy finite element analysis

• Published in: Engineering computations Vol. 16; no. 5; pp. 572 - 583
• Main Authors: Lallemand, B., Plessis, G., Tison, T., Level, P.
• Format: Journal Article
• Language: English
• Published: Bradford MCB UP Ltd 01.01.1999; Emerald Group Publishing Limited
• Subjects: Algorithms; Boundary conditions; Composite materials; Computers; Eigenvalues; Engineering; Evaluation; Finite element analysis; Fuzzy logic; Fuzzy sets; International conferences; Mathematical models; Mechanics; Methods; Random variables; Random vibration; Sensitivity; Set theory; Simulation; Structural engineering; Studies; Eigenvalues; Fuzzy sets; Evaluation; Sensitivity; Finite element analysis
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/02644409910277933

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.