Wim Verhaeghe

A fuzzy finite element analysis technique for structural static analysis based on interval fields

One of the main shortcomings of current fuzzy and interval nite element procedures is that mutual dependency between multiple uncertain model parameters cannot be included in the analysis. This limit is posed by the classical interval concept, where multi-dimensional interval quantities are generally treated as hypercubes, thus ignoring all possible dependency between vector components. For this reason, most literature on this subject focuses on one-dimensional output quantities. In order to cope with this problem, this work discusses the application of the concept of interval elds for static analysis of uncertain mechanical structures in the context of fuzzy nite element analysis. The theoretic background of the concept is explained, and it is shown how it can be applied to represent dependency between parametric uncertainties. Further, the paper concentrates on the calculation of interval elds resulting from static struc- tural analysis. A procedure that enables the calculation of a joint representation of multiple output quantities of a single interval nite element problem while preserving the mutual dependency between the components of the output vector is introduced. This procedure is based on a projection of the original problem on the space composed by the classical static deformation patterns. This paper in particular introduces a novel projection in which the space of the classical deformation patterns is augmented with deviatoric parts. This novel projection leads to a better approximation of the results without a signicant increase in computation time. Finally, a numerical case study illustrates the procedure and validates the improved accuracy of the results obtained with the novel projection technique.

Probabilistic and Interval Analyses Contrasted in Impact Buckling of a Clamped Column

In this study we contrast two competing methodologies for the impact buckling of a column that is clamped at both ends. The initial imperfection is postulated to be co-configurational with the fundamental mode shape of the column without the axial loading. A solution is also furnished for the case when the initial imperfection is proportional to the Filonenko-Borodich “cosinusoidal polynomial”. Probabilistic and interval analyses are conducted for each case; these are contrasted on some representative numerical data.

Uncertainty assessment in random field representations: An interval approach

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.

Expansion of a random field with interval correlation length using interval fields

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

Analysis of efficient interval field techniques for random field analysis with uncertain correlation length

The representation of uncertainties that give rise to a spatially distributed influence is still a topic of research in the non-probabilistic approach. The authors have developed an interval field framework to deal with multiple dependent uncertainties. Recently, the interval field method was developed to deal with random field expansions with an uncertain correlation length. The base vectors of this interval field come from a number of exact expansions of the random field in the correlation length space (e.g., Karhunen-Loeve expansion). The scaling interval factors are essentially a function of the correlation length. The present paper studies for the first time the convergence of an uncertain FE output (i.e. the interval on the FE output) with respect to the dimension of the base vector space, which is determined by the number of eigenvectors retained in one exact random field expansion and the number of exact random field expansions used to build the interval field representation.Copyright

Non-deterministic finite element analysis with shape uncertainty based on interval fields

This paper discusses the application of interval elds for the analysis of uncertain mechanical structures. More speci cally, this work focuses on shape uncertainty analysis in the context of nite element analysis. First, the theoretic background of the interval eld concept is explained, and it is shown how it can be applied to represent dependent uncertainty in the model de nition phase and in the post-processing phase. An explicit and an implicit form of de ning interval elds is discussed. Next, shape uncertainty is represented as a set of spatially dependent geometric interval properties of a nite element model. The uncertainty of the grid point locations in the nite element model is expressed as a combination of an explicit and implicit interval eld, while dependent FE analysis results are represented by implicit interval elds. Finally, the application of interval elds for shape uncertainty is illustrated using a numerical example.

Interval field implementations for spatial uncertainty processing in non-deterministic FE analysis

This paper discusses the application of interval fields for the analysis of uncertain mechanical structures. More specifically, this work illustrates the use of interval fields to represent uncertainties with spatially distributed uncertain parameters in the context of finite element analysis. Four different mathematical interval field implementations are introduced and their efficieny and accuracy is compared. Finally, these implementations are illustrated and validated using a static stress analysis of a conical shell structure.

Application of Interval Fields for Uncertainty Modeling in a Geohydrological Case

In situ soil remediation requires a good knowledge about the processes that occur in the subsurface. Groundwater transport models are needed to predict the flow of contaminants. Such a model must contain information on the material layers. This information is obtained from in situ point measurements which are costly and thus limited in number. The overall model is thus characterised by uncertainty. This uncertainty has a spatial character, i.e. the value of an uncertain parameter can vary based on the location in the model itself. In other words the uncertain parameter is non-uniform throughout the model. On the other hand the uncertain parameter does have some spatial dependency, i.e. the particular value of the uncertainty in one location is not totally independent of its value in a location adjacent to it. To deal with such uncertainties the authors have developed the concept of interval fields. The main advantage of the interval field is its ability to represent a field uncertainty in two separate entities: one to represent the uncertainty and one to represent the spatial dependency. The main focus of the paper is on the application of interval fields to a geohydrological problem. The uncertainty taken into account is the material layers’ hydraulic conductivity. The results presented are the uncertainties on the contaminant’s concentration near a river. The second objective of the paper is to define an input uncertainty elasticity of the output. In other words, identify the locations in the model, whose uncertainties influence the uncertainty on the output the most. Such a quantity will indicate where to perform additional in situ point measurements to reduce the uncertainty on the output the most.