Non-probabilistic approaches for non-deterministic dynamic FE analysis of imprecisely defined structures

The objective of this paper is to give a survey on the use of non-probabilistic methods for non-deterministic numerical analysis. It consists of a general theoretical discussion on the use of non-deterministic concepts in numerical analysis, an overview of the basic properties of possible implementations of the non-probabilistic finite element code, and finally a discussion on their possible applications in a typical product design process. In the first part of the paper, a classification of different types of non-deterministic properties is presented. Based on the nature of these different classes of model properties, it is discussed to what degree each of these fits in the framework of either a probabilistic or a non-probabilistic concept. In the second part of the paper, an overview of possible implementations of the non-probabilistic finite element procedure is presented. It is shown how the deterministic finite element procedure is translated to a non-probabilistic counterpart. The paper then focuses on the application of these non-probabilistic concepts for design purposes. The use of the probabilistic and non-probabilistic approaches is projected into a typical design process.