Numerical dynamic analysis of uncertain mechanical structures based on interval fields

Moens, David; Munck, Maarten De; Desmet, Wim; Vandepitte, Dirk

doi:10.1007/978-94-007-0289-9_6

Cited by 39 publications

(51 citation statements)

References 4 publications

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“…From a physical point of view, the uncertain Young's modulus may be represented by any function ranging between the LB and UB, E(x) and E(x). The interval field concept has been first introduced by Moens et al [2] to provide a more realistic description of spatially varying uncertain-but-bounded parameters. Recently, the first two authors proposed a novel interval field model [6,7] based on the so-called improved interval analysis (IIA) via extra unitary interval (EUI) (see [5] and Appendix A).…”

Section: Interval Young's Modulus Fieldmentioning

confidence: 99%

“…Starting from the pioneering work by Moens et al [2], more recently a novel interval field model based on the so-called improved interval analysis via extra unitary interval (IIA via EUI) [5] has been proposed [6,7]. The IIA via EUI is a very effective tool to limit the overestimation of the interval solution width due to the dependency phenomenon [8] affecting the CIA.…”

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confidence: 98%

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Static response bounds of Timoshenko beams with spatially varying interval uncertainties

2015

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Response variability of Timoshenko beams with uncertain Young's modulus subjected to deterministic static loads is analyzed. The uncertain material property is idealized within a non-probabilistic context by using an interval field model recently proposed by the first two authors. Such a model is able to quantify the dependency between adjacent values of an interval uncertainty by means of a real, deterministic, symmetric, nonnegative, bounded function conceived as the non-probabilistic counterpart of the autocorrelation function characterizing random fields. In order to analyze the effects of Young's modulus uncertainty on the static response of the Timoshenko beam, a finite difference discretization of the coupled interval ordinary differential equations of equilibrium is performed. Then, approximate explicit expressions of the lower bound and upper bound of the interval response are derived. Numerical results showing the effects of interval material uncertainty on the static response of a simply supported beam under uniformly distributed load are presented.

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Section: Interval Young's Modulus Fieldmentioning

confidence: 99%

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confidence: 98%

Static response bounds of Timoshenko beams with spatially varying interval uncertainties

2015

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“…To cope with this problem, Moens et al (2011) introduced the so-called interval field as a natural extension of the random field concept. An interval field is able to define a form of dependency between adjacent interval values that cannot differ as much as values that are further apart.…”

Section: Interval Field Model Based On Improved Interval Analysismentioning

confidence: 99%

Static Analysis of Timoshenko Beams with Interval Young's Modulus

Sofi¹,

Muscolino²,

Elishakoff³

2014

Vulnerability, Uncertainty, and Risk

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An original procedure for the static analysis of Timoshenko beams with uncertain Young's modulus is presented. Within a non-probabilistic framework, the uncertain material property is modeled as an interval field according to the definition recently introduced by the first two authors. The key idea is to account for the dependency between interval values of the Young's modulus at various locations by means of a deterministic symmetric non-negative function playing the same role of the autocorrelation function in random field theory. After performing a finite difference discretization of the interval ordinary differential equations of equilibrium, approximate closed-form expressions of the bounds of beam response are obtained. For validation purposes, numerical results concerning a simply supported Timoshenko beam are presented.

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“…The authors have developped an interval field framework [2]. In this framework an explicit and implicit description are developped.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty assessment in random field representations: An interval approach

Verhaeghe

Desmet

Vandepitte

et al. 2011

2011 Annual Meeting of the North American Fuzzy Information Processing Society

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This paper discusses the application of interval fields for the analysis of uncertain mechanical structures. More specifically, this work focuses on representing uncertainties with a spatially distributed influence in the context of finite element analysis. First, the concept of interval fields is briefly reviewed. Next, random fields are presented, with a focus on the influence of an uncertain correlation length on its discretization. The methods for applying the interval field framework to represent the uncertain correlation length are explained in the next section. Finally, the application of interval fields for representing a random field expansion in the uncertain correlation length space is illustrated using a numerical example.

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Numerical dynamic analysis of uncertain mechanical structures based on interval fields

Cited by 39 publications

References 4 publications

Static response bounds of Timoshenko beams with spatially varying interval uncertainties

Static response bounds of Timoshenko beams with spatially varying interval uncertainties

Static Analysis of Timoshenko Beams with Interval Young's Modulus

Uncertainty assessment in random field representations: An interval approach

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