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The objective of this paper is to critically review the emerging non-probabilistic approaches for uncertainty treatment in finite element analysis. The paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis. First, the applicability of the non-probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint. The necessary conditions for a useful application of the non-probabilistic concepts are determined, and are proven to be complementary rather than competitive to the classical probabilistic approach. The second part of the paper focuses on numerical aspects of the interval finite element method. It describes two principal strategies for the implementation, i.e. the anti-optimisation and the interval arithmetic approach, and gives a state-of-the-art of the interval finite element algorithms available from literature. It is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output, and the main sources of this conservatism are identified. A numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built-up benchmark structure.

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This paper gives an overview of recent advances in the field of nonprobabilistic uncertainty quantification. Both techniques for the forward propagation and inverse quantification of interval and fuzzy uncertainty are discussed. Also the modeling of spatial uncertainty in an interval and fuzzy context is discussed. An in depth discussion of a recently introduced method for the inverse quantification of spatial interval uncertainty is provided and its performance is illustrated using a case studies taken from literature. It is shown that the method enables an accurate quantification of spatial uncertainty under very low data availability and with a very limited amount of assumptions on the underlying uncertainty. Finally, also a conceptual comparison with the class of Bayesian methods for uncertainty quantification is provided.

This paper describes and analyzes fracture toughness and crack propagation of selective laser molten (SLM) components made from Ti6Al4V powder particles. The main goal of this research is to gain more insight in the fracture mechanisms of this relatively new material and to improve the static and dynamic behavior of cracked SLM‐Ti components. At first, the SLM process parameters are optimized until the relative material density equals 99.7%. This is close to the relative density of vacuum arc remelted mill annealed standard oxygen titanium which is used as a reference for all experiments. A distinctive difference in phase morphology and texture of the microstructure is noticed between the SLM and the reference titanium. The fine acicular martensite phase of the SLM‐Ti results in more brittle behavior and inferior fracture toughness. On the other hand, the fine grained microstructure leads to a large number of grain boundaries acting as obstacle points for crack propagation. Consequently, crack growth properties do not significantly differ between both. Microstructural analysis of the crack growth and final failure areas on the fractured surfaces is performed to study the failure mechanisms in more detail.

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