Chinese Journal of Theoretical and Applied Mechani ›› 2011, Vol. 43 ›› Issue (3): 496-504.DOI: 10.6052/0459-1879-2011-3-lxxb2010-382
• Research paper •
Qiu Zhiping,Qi Wuchao
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.
Qiu Zhiping Qi Wuchao. Collocation interval finite element method[J]. Chinese Journal of Theoretical and Applied Mechani, 2011, 43(3): 496-504.
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