Stochastic Finite Element Analysis of Beam with Statistical Uncertainties

Abstract

The eigenvalue problem of a beam with uncertain cross-sectional area is described. The cross-sectional area of the beam is expressed in a form containing stochastic variables, and the stochastic finite element method is applied to evaluate the influence of this uncertainty on the eigenvalue and the eigenvector. The formulation is carried out under the condition that the beam has a circular section. Numerical analysis is carried out with respect to the uniform beam and the optimal beam. The optimal beam has the maximum eigenvalue of first mode. The influence of the uncertainty of the beam cross-sectional area on the eigenvalue and the eigenvector is shown.

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