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To eliminate the errors caused by the conventional interval perturbation finite element method due to classic interval arithmetic and neglect of higher-order terms, we propose a novel univariate dimension-reduction based interval finite element method to predict the static response bounds of structures with uncertain but bounded parameters. First, a univariate dimension-reduction algorithm is derived using the generalized Taylor expansion. The global stiffness matrix is expressed as the sum of the median and the univariate disturbance radius. Compared with Taylor expansion approximation, the univariate dimension-reduction approximation has higher accuracy and does not increase the amount of calculation. Then the inverse of the interval global stiffness matrix is approximated as an improved Neumann series. Higher-order terms are included by summing up the geometric terms in the Neumann series. Finally, the improved interval algorithm is used to solve the upper and lower bounds of the structural displacement response and the element stress response. The dependence between the interval parameters is accounted in comparison with the classic interval algorithm. The accuracy and effectiveness of the new method are validated by numerical cases on 2D truss, 3D frame and truck frame with multiple interval parameters.

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A prediction method for the ultimate load of composite corrugated sandwich structures (CCSS) was established based on the dimension-reduction method and Chebyshev polynomial. First, an ultimate load response function of the CCSS was reduced in dimension on basis of the univariate method. The original response function was converted to the sum of univariate functions of all random variables. Chebyshev polynomial was used to fit all univariate functions, and the univariate Chebyshev approximate model (UCAM) of the response function was obtained. Second, the fitting accuracy of the UCAM was analytically compared with the Kriging model, radial basis function, and response surface methodology. Finally, the effect of the order on the fitting accuracy of UCAM was studied. The UCAM has higher fitting accuracy and calculation efficiency compared with the other three approximate models. When the order of UCAM is lower than ninth-order, the larger the order, the higher the fitting accuracy. And the order and the fitting accuracy are no longer positively correlated when the order exceeds ninth-order. The order is recommended to choose an odd-order when using UCAM to solve the uncertainty problem.