Uncertain static plane stress analysis with interval fields

Abstract

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.

An interval finite element method for the analysis of structures with spatially varying uncertainties

“…. Notice that the proposed stress bounds, obtained by applying the response surface approximation (34) in conjunction with the combinatorial procedure, are very close to the ones provided by the vertex method. Very accurate estimates, herein omitted for conciseness, are also provided by the sensitivity-based procedure described in Section 3.…”

“…(10) and the proposed response surface approximation of the interval displacements (27) into Eq. (12b), the following explicit relationship between the interval stress field within the h -th FE and the EUIs is obtained: (34) where () II  U e U is the vector collecting the interval displacements defined in Eq. (27).…”

“…This circumstance may lead to high overestimation of the interval stress range unless suitable approaches are adopted to predict sharp bounds. Based on the knowledge of the approximate functional dependence (34) of the stress components on the EUIs, two main strategies are herein proposed to address this issue: the first one relies on a sensitivity analysis, while the second approach is conceived as an enhancement of the classical combinatorial procedure. It is worth remarking that, when applying these strategies, the use of the IIA [25] allows us to keep track of uncertainties throughout calculations by means of the EUIs and thus reduce the overestimation due to the dependency phenomenon.…”

“…The normalized interval displacement of the central node A (see Figure 11b) in the load direction, components even when the degree of uncertainty increases. Very accurate results, herein omitted for conciseness, are also obtained by using the proposed response surface approximation (34) of the stress components in conjunction with the combinatorial procedure, as described in Section 3. It is worth mentioning that, also for this case study, if the uncertain Young's modulus were assumed TSD ( B l ), the stress would not be affected by uncertainty and the nominal stress would be obtained for any value of the TSD Young's modulus.…”

“…Faes and Moens [32] presented a novel methodology for the identification and quantification of spatial uncertainty modelled as an interval field, based on a large set of measurement data, by extending a recently proposed method to identify interval scalars [33]. So far, very few studies have been devoted to the incorporation of the interval field model into the standard FEM (see e.g., [27], [34]- [36]). Furthermore, the development of specialized software, able to interact with powerful third-party software for the analysis of large-scale problems with uncertain properties modeled either as interval variables or interval fields, has not been addressed in the scientific literature.…”