Interval Estimation of Eigenvalue Problem Based on Finite Element Sensitivity Analysis and Convex Model

Abstract

A formulation is presented for interval analysis of eigenvalue problem on the basis of the finite element sensitivity analysis and representation of uncertainty involved in a structural system by a convex model. The first-order approximation obtained by the sensitivity analysis is employed to express the response change due to the uncertainty that is assumed to be confined in a convex hull. The maximum and minimum of responses, by which the interval is bracketed, are searched on the convex boundary by the Lagrange multiplier method. The validity of the present formulation is demonstrated by a numerical example of the axial buckling load of an elastic straight column in the case of spatially uncertain Young's modulus.