Assessment of the numerically calculated robustness of structures

Robustness is an important design criteria for structures. It denotes the property of a structural response to be independent of the (large) fluctuations in the input parameters. The structure which is designated as robust ensures error-free safe usage over a defined period of time. The assessment of the robustness on one hand requires the consideration of uncertainty in the geometry, material and load parameters and on the other hand  an appropriate formulation of the robustness measure. The concept of robustness as defined by Genichi Taguchi follows:

"Not just strong. Flexible! Idiot Proof! Simple! Efficient! A product/process that produces consistent, high level performance despite being subjected to a wide range of changing client and manufacturing conditions."

The quantification of robustness requires a comprehensive description of the uncertainty. In most cases, this is not a random property of structures and therefore cannot always be modelled using stochastic methods. Sound and widely developed theory of fuzzy data with stochastic properties is further used in numerous research works as basics for the assessment of informal and lexical uncertainty. In addition to stochastic, mathematical approaches also offer Fuzzy Set theory
which allows the interval variables and deterministic values to treated as special cases and the usage of theory of Fuzzy Randomness which contains usual random numbers as special cases. The generalized models and algorithms for uncertainty which are developed  in  SFB 528 will be further modified for other structure classes which also have significant data uncertainty. The transfer project should contribute to fill the scientific gap between mathematics and engineering sciences which exists in the application of all uncertainty models.

An assessment of the individual design variants should be made in view of robustness. For their evaluation, a new definition of robustness is introduced. This definition is based on the uncertainty assessment with the help of Shannon's entropy. The suitability of other fuzzy measurements, e.g. energy measures, is investigated in the transfer project.