Decision making in structural engineering problems under polymorphic uncertainty : a benchmark proposal

The treatment of diverse uncertainties is an important challenge in structural engineering problems, especially from the viewpoint of realistic analysis. Inaccuracy and variability are always present and have to be quantified by either probabilistic, possibilistic, polymorphic or other uncertainty approaches. Regardless to the applied uncertainty quantification method, the numerical predictions have to be useful for structural assessment and decision making. The authors propose in this contribution a benchmark example of a portal frame structure including various uncertainties. The goal of this benchmark study is to compare justifications and decisions provided by probabilistic and non-probabilistic methods with respect to clear challenges of decision making with and without measurements and data assimilation. The engineering problem itself is simple enough to understand and complex enough not to be reduced to a simple formula with uncertain parameters.DFG, 273721697, SPP 1886: Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukture

Acquisition of polymorphic uncertain data based on computer tomographic scans and integration in numerical models of adhesive bonds

Since commercial wind turbines were introduced around 1980, the length of rotor blades has increased substantially up to 80m with consequently higher demands on availability and failure prevention. One of the typical failure mechanisms of rotor blades in operation are fatigue cracks in adhesive bonds often caused by air voids with a-priori unknown properties, which results from the manufacturing process. In this contribution, the usage of computer tomography as non-destructive testing (NDT) on a representative sub-component, called the Henkel beam, is proposed for air void detection and quantification. By using the NDT data, structural failure is simulated by means of a finite element approach under polymorphic uncertainties to consider diverse uncertainty sources in the data acquisition. On the one hand, aleatory irreducible uncertainties are described with stochastic variables and on the other hand, interval and fuzzy variables are used for epistemic reducible uncertainties. For solving the problem under polymorphic uncertainties, different computational methods within a MATLAB framework called PolyUQ are used and compared with regard to accuracy and efficiency.DFG, 273721697, SPP 1886: Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukture

Parameterization of arbitrary hole shapes using non-destructive testing and resulting stress concentration in a 2D plate with finite dimensions

Air void inclusions are mostly unavoidable in many different materials resulting from manufacturing processes or environmental conditions. In this contribution, non-destructive testing (NDT) like computer tomography (CT) is used for air void detection and quantification. The air voids lead to stress concentrations around them which influence significantly the structural integrity and at worst, lead to structural failure. By nature, air voids exhibit arbitrary shapes on which circular, elliptical, slotted and rounded rectangular holes are fitted by a least-square optimization algorithm to reduce the amount of necessary shape parameters. The mentioned shapes are compared in relation to the arbitrary one and with regard to the resulting stress concentration factor as well as the location of the maximum first principal stress in a 2D plate with finite dimensions under uniaxial tension. Finally, aleatory and epistemic uncertainties are derived from the conducted CT analysis which leads to a problem under polymorphic uncertainties. The problem is solved by a surrogate model based on cubic spline interpolation and points out the importance of the consideration of different hole shapes for analyzing the stress concentration.DFG, 273721697, SPP 1886: Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukture

Decision making in structural engineering problems under polymorphic uncertainty : a benchmark proposal

The treatment of diverse uncertainties is an important challenge in structural engineering problems, especially from the viewpoint of realistic analysis. Inaccuracy and variability are always present and have to be quantified by either probabilistic, possibilistic, polymorphic or other uncertainty approaches. Regardless to the applied uncertainty quantification method, the numerical predictions have to be useful for structural assessment and decision making. The authors propose in this contribution a benchmark example of a portal frame structure including various uncertainties. The goal of this benchmark study is to compare justifications and decisions provided by different uncertainty models with respect to clear challenges of decision making with and without measurements, data assimilation and design. The engineering problem itself is simple enough to understand and complex enough not to be reduced to a simple formula with uncertain parameters.DFG, 273721697, SPP 1886: Polymorphe Unschärfemodellierungen für den numerischen Entwurf von Strukture

Comparison of monomorphic and polymorphic approaches for uncertainty quantification with experimental investigations

Unavoidable uncertainties due to natural variability, inaccuracies, imperfections or lack of knowledge are always present in real world problems. To take them into account within a numerical simulation, the probability, possibility or fuzzy set theory as well as a combination of these are potentially usable for the description and quantification of uncertainties. In this work, different monomorphic and polymorphic uncertainty models are applied on linear elastic structures with non-periodic perforations in order to analyze the individual usefulness and expressiveness. The first principal stress is used as an indicator for structural failure which is evaluated and classified. In addition to classical sampling methods, a surrogate model based on artificial neural networks is presented. With regard to accuracy, efficiency and resulting numerical predictions, all methods are compared and assessed with respect to the added value. Real experiments of perforated plates under uniaxial tension are validated with the help of the different uncertainty models

Global stability failure of a 3D composite structure accompanied by unavoidable polymorphic uncertainties

In this study, a non-linear stability analysis of a carbon fiber reinforced plastic (CFRP) considering unavoidable polymorphic uncertainties is conducted. For the realistic incorporation of the uncertainties in the finite element model, thickness variations and geometrical inaccuracies have been detected in advance by non-destructive testing. For that, a structure made of CFRP has been designed. Additionally, the material parameters have been defined as dependent stochastic variables based on reference studies in the literature. The distinction in aleatory and epistemic uncertainties leads to different uncertainty models and to a computationally costly fuzzy-stochastic analysis. Strains and displacements have been measured in a symmetric three-point bending test and compared to the numerical predictions. In addition to the present uncertain parameters, a case study shows that the fiber volume content and a small pre-deformation should be taken into account to minimize the deviation from the experimental results