Fuzzy Finite Element Approach for Analysis of Fiber-Reinforced Laminated Composite Beams

Abstract

The modeling, analysis, and design of large and complex composite structures involve the use of the finite element approach. In most practical applications the structural and material parameters vary considerably and are subject to uncertainties, mainly because of the uncontrollable aspects associated with the manufacturing and assembly of composite materials. In many cases, the probabilistic methods cannot be applied because the probability distributions of the uncertain parameters are not usually known. Also, in some situations the parameters are known only in linguistic form. In this work, the uncertainties encountered in composite structures, which can be described in linguistic terms or in imprecise form, are modeled as fuzzy parameters. A fuzzy finite element analysis technique is developed for the analysis of laminated beams, involving fuzziness, possibly in the boundary conditions as well. The fuzzy beam element can undergo axial, bending, and transverse shear deformations. Using the basic concepts of the deterministic finite element theory, as well as fuzzy computations and fuzzy matrix operations, a fuzzy beam element is developed. The fuzzy beam element is used for the static and eigenvalue analysis of beams involving imprecise data and/or information. A numerical example is presented to demonstrate the feasibility and applicability of the methodology presented.