• Research paper •

### Collocation interval finite element method

Qiu Zhiping,Qi Wuchao

1. Institute of Solid Mechanics, Beihang University, Beijing 100191, China
• Received:2010-06-03 Revised:2010-12-16 Online:2011-05-25 Published:2011-05-16
• Contact: Qiu Zhiping

Abstract: Based on shortcoming analysis of `point approximation' interval finite element method with Taylor expansion, collocation interval finite element method based on the first Chebyshev polynomials which can approach objective function in global domain is proposed in this paper. The method does not require the sensitivities of the objective function with respect to uncertain variables and the assumption of narrow interval is also not needed. The method is suitable for solving the case that the objective function is strongly nonlinear with respect to the uncertain variables. The orthogonal expansion coefficients of the objective function are obtained from Gauss-Chebyshev quadrature formula. So Gauss integration points are collocated in the intervals of uncertain variables. The main computational effort is to calculate the values of objective function at Gaussian integration points. When the number of the uncertain variables is $m$ and the ten-point Gauss integral method is introduced, it is needed to analyze the system with 12m times. Examples show that the collocation interval finite element method can still obtain almost exact interval bounds in the case that other interval finite element methods are invalid.

Key words: function approximation

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