Analysis of the Effect of Uncertain Clamping Stiffness on the Dynamical Behaviour of Structures Using Interval Field Methods

Abstract

In uncertainty calculation, the inability of interval parameters to take into account mutual dependency is a major shortcoming. When parameters with a geometric perspective are involved, the construction of a model using intervals at discrete locations not only increases the problem dimensionality unnecessarily, but it also assumes no dependency whatsoever, including unrealistic parameter combinations leading to results that probably overestimate the true uncertainty. The concept of modelling uncertainty with a geometric aspect using interval fields eliminates this problem by defining basis functions and expressing the uncertain process as a weighted sum of these functions. The definition of the functions enables the model to take into account geometrically dependent parameters, whereas the coefficients in a non-interactive interval format represent the uncertainty. This paper introduces a new type of interval field specifically tailored for geometrically oriented uncertain parameters, based on a maximum gradient condition to model the dependency. This field definition is then applied to a model of a clamped plate with uncertain clamping stiffness with the purpose of identifying the effects of spatial variability and mean value separately.

Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty

“…Local interval field decomposition was introduced by the authors in [101,100] and starts also from the explicit formulation of the interval field, as introduced in eq. ( 19).…”

“…In practice, this achieved by defining the base functions ψ i (r) as identically shaped, piecewise second order polynomial functions for each separate element, which are located at the element midpoints [101,100].…”

“…As an example, when applying the inverse distance weighting interpolation technique, subjectivity is present in the selection of the control points and the exponent of the distance weighting. Moreover, the application of interval fields to practical problems is still very scarce in literature (see e.g., [130,202,204,100]). This is however also partially explained by the relatively recent introduction of these techniques as compared to the well-established framework of random fields.…”

Transient landing dynamics analysis for a lunar lander with random and interval fields

“…The definition as such can be based either on engineering judgment, or on direct [36] or indirect [37,38,39] measurement data. In the context of the explicit interval field formulation, two techniques exist for the construction of ψ i (r): Inverse Distance Weighting interpolation [39] and Local Interval Field Decomposition (LIFD) [40,41]. In this paper LIFD is applied for the comparison to random field approaches.…”

Multivariate dependent interval finite element analysis via convex hull pair constructions and the Extended Transformation Method

“…with IR n b the domain of real-valued interval vectors of dimension n b . This framework for the modelling of spatial uncertainty modelling was recently applied in the context of inverse uncertainty quantification [6,7] and the modelling of various dynamic phenomena [8,9,10], as well as additively manufactured plastic components [11]. Also alternative formulations for modelling spatial uncertainty in an interval context have been proposed by other authors [12,13].…”