Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis

There is a growing awareness of the impact of non-deterministic model properties on the numerical simulation of physical phenomena. These non-deterministic aspects are of great importance when there is a large amount of information to be retrieved from the numerical analysis, as for instance in a numerical reliability study or reliability based optimisation during a design process. Therefore, the non-deterministic properties form a primordial part of a trustworthy virtual prototyping environment. The implementation of such a virtual prototyping environment requires the inclusion of non-deterministic properties in the numerical finite element framework. This articel gives an overview of the emerging non-probabilistic approaches for non-deterministic numerical analysis, and compares them to the classical probabilistic methodology. Their applicability in the context in engineering design is discussed. The typical implementation strategies applied in literature are reviewed. A new concept is introduced for the calculation of envelope frequency response functions. This method is explained in detail and illustrated on a numerical example.[PUBLICATION ABSTRACT]