Static Response Analysis of Uncertain Structures With Large-Scale Unknown-But-Bounded Parameters

This paper proposes an interval finite element method based on function decomposition for structural static response problems with large-scale unknown-but-bounded parameters. When there is a large number of uncertain parameters, it will lead to the curse of dimensionality. The existing Taylor expansion-based methods, which is often employed to deal with large-scale uncertainty problems, need the sensitivity information of response function to uncertain parameters. However, the gradient information may be difficult to obtain for some complicated structural problems. To overcome this drawback, univariate decomposition expression (UDE) and bivariate decomposition expression (BDE) are deduced by the higher-order Taylor series expansion. The original structure function with n-dimensional interval parameters is decomposed into the sum of several low-dimensional response functions by UDE or BDE, each of which has only one or two interval parameters while the other interval parameters are replaced by their midpoint values. Therefore, solving the upper and lower bounds of the n-dimensional function can be converted into solving those of the one- or two-dimensional functions, which savethe calculation costs and can be easily implemented. The accuracy and efficiency of the new method are verified by three numerical examples.