Static response bounds of Timoshenko beams with spatially varying interval uncertainties

Sofi, Alba; Muscolino, G.; Elishakoff, Isaac

doi:10.1007/s00707-015-1400-9

Cited by 49 publications

(19 citation statements)

References 10 publications

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“…In , the idea of interval field, as an analogy of random field, has been proposed and implemented to model the spatially dependent uncertainty of the system output within the context of static finite element analysis. Basing on the proposition of the concept of interval field, Sofi and Muscolino and Sofi have proposed computational methods to determine the static responses of Euler–Bernoulli and Timoshenko beams subjected to the one‐dimensional (1D) spatially varying uncertain Young's modulus, respectively. Moreover, the contrast between the stochastic and interval approaches on modelling 1D spatially dependent uncertain parameters has been comprehensively illustrated in .…”

Section: Introductionmentioning

confidence: 99%

Uncertain static plane stress analysis with interval fields

Gao

2016

Int. J. Numer. Meth. Engng

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Summary Uncertain static plane stress analysis of continuous structure involving interval fields is investigated in this study. Unlike traditional interval analysis of discrete structure, the interval field is adopted to model the uncertainty, as well as the dependency between the physical locations and degrees of variability, of all interval system parameters presented in the continuous structures. By implementing the flexibility properties of some common structural elements, a new computational scheme is proposed to reformulate the uncertain static plane stress analysis with interval fields into standard mathematical programming problems. Consequently, feasible upper and lower bounds of structural responses can be effectively yet efficiently determined. In addition, the proposed method is adequate to deal with situations involving one‐dimensional and two‐dimensional interval fields, which enhances the pertinence of the proposed approach by incorporating both discrete and continuous structures. In addition, the proposed computational scheme is able to establish the realizations of the uncertain parameters causing the extreme structural responses at zero computational cost. The applicability and credibility of the established computational framework are rigorously justified by various numerical investigations. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Uncertain static plane stress analysis with interval fields

Gao

2016

Int. J. Numer. Meth. Engng

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“…Opposed to random fields, where the description of the spatial variability is inherently embedded within the probabilistic framework, the definition and discretization of spatial uncertainty in an interval context is more challenging since intervals are by construction independent. Therefore, interval field [18,19] approaches were recently introduced to model parameters x that are subjected…”

Section: Interval Field Casementioning

confidence: 99%

Hybrid spatial uncertainty analysis for the estimation of imprecise failure probabilities in Laser Sintered PA-12 parts

Faes

Sabyasachi

Moens

2019

Computers & Mathematics with Applications

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This paper presents the application of non-determinstic modelling techniques for the quantification of imprecise failure probabilities in PA-12 parts produced via Laser Sintering (LS). Specifically, a modelling approach consisting of a combination of interval and random fields is applied, and the effect hereof on the resulting polymorphic uncertainty in the mechanical performance of the LS parts is studied. A link with the underlying process physics is given, relating the spatial porosity distributions that are inherently present in LS PA12 parts to a spatial distribution in the apparent Young's modulus. Furthermore, uncertainty on the final dimensions of other parts that are constructed in the same build envelope as the designed part is linked to uncertainty in the cross-sectional area of the designed part. The effect of these sources of uncertainty is studied in three case studies, illustrating the need for a well-thought production process planning given the influence on the resulting mechanical performance of the designed structure. Especially the effect of epistemic uncertainty on the design process is shown to be significant.

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“…The main idea of the interval field approach is to expand globally defined intervals over the model domain using an priori defined set of basis functions. Also, other methods for modeling interval fields have been introduced more recently by other authors based on affine arithmetic, a spatial averaging method, or set‐theoretical approaches for time‐domain problems . Recently, fuzzy fields were also introduced .…”

Section: Introductionmentioning

confidence: 99%

On auto‐ and cross‐interdependence in interval field finite element analysis

Faes

Moens

2020

Numerical Meth Engineering

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Summary This paper discusses the concepts of auto‐ and cross‐interdependence in interval field finite element analysis. In classic interval analysis, independent intervals are used to construct hyper‐rectangular input spaces that correspond to the bounded uncertainty that is present on some model parameters. This is a direct result from the inability of modeling interdependence. Such assumption of complete independence might prove in some cases to be highly over‐conservative. A first example is the modeling of spatial uncertainty, where the interdependence is governed by allowable spatial gradients of field realizations. Secondly, interdependence can also occur in case uncertainty in several structural quantities has the same root cause (eg, the manufacturing process). Recent work by the authors introduced concepts for modeling dependence between intervals in a spatial and multivariate context. However, it is unclear how an analyst has to deal with multiple quantities that have a spatial uncertainty component and are furthermore interdependent. This paper presents an approach to link multiple interval fields using recently introduced convex hull pair constructions and inverse distance weighting interpolation. Two case studies to illustrate the new methodology are included, proving the flexibility of the methodology in the modeling of auto‐ and cross‐interdependence between multiple interval scalars and/or interval fields.

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Static response bounds of Timoshenko beams with spatially varying interval uncertainties

Cited by 49 publications

References 10 publications

Uncertain static plane stress analysis with interval fields

Uncertain static plane stress analysis with interval fields

Hybrid spatial uncertainty analysis for the estimation of imprecise failure probabilities in Laser Sintered PA-12 parts

On auto‐ and cross‐interdependence in interval field finite element analysis

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