Practical fuzzy finite element analysis of structures

Abstract

A practical approach for analyzing the response of structures with fuzzy parameters is developed. The methodology involves integrated finite element modelling, response surface analysis and fuzzy analysis. The uncertainties in the material, loading and structural properties are represented using convex normal fuzzy sets. Vertex solution methodology that is based on α-cut representation is used for the fuzzy analysis. Response surface methodology is used to approximate the fuzzy finite element response quantity at the normal point. Combinatorial optimization is then performed on the response surface approximate quantity to determine the binary combinations of the fuzzy variables that result in extreme responses at an α-level. The true values of the extreme responses at an α-level are obtained by applying the binary combinations of the fuzzy variables that result in extreme responses to the finite element model. The merit of the proposed methodology is computational efficiency without compromise on accuracy and this is demonstrated through some example problems.