Modified Interval and Subinterval Perturbation Methods for the Static Response Analysis of Structures with Interval Parameters

AbstractTo overcome the drawbacks in the traditional interval perturbation method due to the unpredictable effect of neglecting the higher-order terms of Neumann series, a modified interval perturbation method is presented and used to determine the static response interval of the structure with interval parameters. In the proposed method, the inverse of the interval structural stiffness matrix is approximated by a modified Neumann expansion in which the higher-order terms of Neumann series are considered. For the uncertain structure with large uncertainty levels, the subinterval analysis technique is introduced into the proposed method and the approach to determine the number of subintervals is proposed. The modified interval and subinterval perturbation methods are implemented in the finite-element framework. Numerical results on a six-bar space truss structure and a shell structure with interval parameters verify the accuracy and efficiency of the proposed methods. Hence, the modified interval and subin...

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