An inequality model for solving interval dynamic response of structures with uncertain-but-bounded parameters

Qiu, Zhiping; Ni, Zao

doi:10.1016/j.apm.2009.10.028

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…The uncertainty analysis of time response of structures has received relatively less attention in comparison with evaluation of eigenvalues. The common interval analysis methods include mathematical programming methods [20][21][22][23], perturbation methods [24][25][26] and polynomial series expansion methods [6,27], etc. Qiu and Wang [24,25] presented first-order perturbation methods to estimate the range of the dynamic response of structures.…”

Section: Introductionmentioning

confidence: 99%

Time Response and Natural Frequency Analysis for Structures with Interval Parameters

2023

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This paper deals with the evaluations of lower and upper bounds of dynamic responses and natural frequencies for structures with uncertain interval parameters. The structural physical parameters, geometric dimensions and initial conditions can be considered as interval parameters. The modified Chebyshev interval method (MCIM) is presented to handle the uncertainties. In comparison with the Chebyshev interval method (CIM), MICM provides with tighter bounds of the time responses and natural frequencies without a significant increase in computation time. Monte Carlo method is also used to provide with exact bounds. MICM, CIM and Monte Carlo method are applied for structures with interval parameters, and the efficiency and accuracy of CIM and MCIM are verified.

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Section: Introductionmentioning

confidence: 99%

Time Response and Natural Frequency Analysis for Structures with Interval Parameters

2023

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“…Chen et al [13] and Qiu and Wang [14] discuss the lower and upper bounds of the dynamic response of structure based on the first-order matrix perturbation theory and the first-order parameter perturbation method, respectively. Qiu et al [15] change the above problem into lots of linear programming problems by interval inequality model. Then they obtain the interval of the dynamic response by solving the linear programming problems.…”

Section: Introductionmentioning

confidence: 99%

The exact extreme response and the confidence extreme response analysis of structures subjected to uncertain-but-bounded excitations

Han

Yang

et al. 2020

Applied Mathematical Modelling

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“…In particular, we study the dynamics of elastic structures with uncertain load, geometric and material properties. Uncertain structural parameters are modelled by intervals, and the system response is evaluated by means of the Interval Finite Element Method (IFEM) (Hu and Qiu, 2010;Qiu and Ni, 2010;Xia et al, 2010). From now on, non-italic bold letters are used to denote interval variables.…”

Section: Introductionmentioning

confidence: 99%

Structural dynamic problems in time domain under uncertainty: an interval finite element approach

Xiao

Fedele

Muhanna

2018

IJRS

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An analysis of the structural dynamic response under uncertainty is presented. Uncertainties in load and material are modelled as intervals exploiting the interval finite element method (IFEM). To reduce overestimation and increase the computational efficiency of the solution, we do not solve the dynamic problem by an explicit step-by-step time integration scheme. Instead, our approach solves for the structural variables in the whole time domain simultaneously by an implicit scheme using discrete Fourier transform and its inverse (DFT and IDFT). Non-trivial initial conditions are handled by modifying the right-hand side of the governing equation. To further reduce overestimation, a new decomposition strategy is applied to the IFEM matrices, and both primary and derived quantities are solved simultaneously. The final solution is obtained using an iterative enclosure method, and in our numerical examples the exact solution is enclosed at minimal computational cost.

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An inequality model for solving interval dynamic response of structures with uncertain-but-bounded parameters

Cited by 10 publications

References 13 publications

Time Response and Natural Frequency Analysis for Structures with Interval Parameters

Time Response and Natural Frequency Analysis for Structures with Interval Parameters

The exact extreme response and the confidence extreme response analysis of structures subjected to uncertain-but-bounded excitations

Structural dynamic problems in time domain under uncertainty: an interval finite element approach

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