Eigenfrequency and deflection analysis of layered structure using uncertain elastic properties – a fuzzy finite element approach

Abstract

This is the first-time a higher-order fuzzy finite element model has been proposed and implemented to compute the laminated structural responses (modal frequency and static deflection) numerically including the uncertain elastic properties. The composite structure is modelled via a higher-order mid-plane theory which accounts the parabolic variation of the shear stress in conjunction with the fuzzified properties. The fuzzy arithmetic steps are implemented for the composite property evaluation via the triangular membership functions (α-cut method) and solved numerically via finite element techniques. The variational technique and the classical Hamilton's principle are utilized to derive the necessary structural governing equation of the laminated structure including the fuzzified properties. Subsequently, the frequency and the static deflection values are obtained computationally via an efficient home-made computer code (MATLAB environment) with the help of current higher-order finite element model. Further, different kinds of numerical examples are solved using the current higher-order fuzzified model to demonstrate the convergence and comparison behaviour. The differences between the available deterministic (3D-FEM and exact solution) and the uncertain (fuzzified) structural responses indicate the necessity of the current model including the accuracy level. Lastly, the influence of the individual and the combined effect of the material (fuzzified elastic property) and the geometrical parameters on the final structural responses are computed and inferred in details.