Polymorphic uncertainty modelling for numerical design of structures

Abstract

The numerical analysis and design of structures are currently dominated by deterministic thinking and methods. Deterministic modelling of the reality indicates preciseness and safety, while on contrast all available information and data are characterized by uncertainty (variability, imprecision, incompleteness), which cannot be neglected to represent a holistic point of view. Main goal of the DFG Priority Programme “Polymorphic uncertainty modelling for numerical design of structures” (SPP 1886) is the development of methods for the numerical simulation and design of structures under consideration of uncertainty in data and information. On the basis of polymorphic uncertainty modelling, the description of different kinds of uncertainty is realized. Engineering solutions are designed with respect to inherent robustness and flexibility as essential features for a faultless life of structures and systems at uncertain and changing conditions. An implementation of these features in a structure or system requires a comprehensive consideration of uncertainty in the model parameters and environmental and man imposed loads as well as other types of intrinsic and epistemic uncertainties. Numerical design of structures should be robust with respect to (spatial and time dependent) uncertainties inherently present in resistance of materials, boundary conditions etc. This feature requires the availability of a reliable numerical analysis, assessment, and prediction of the lifecycle of a structure taking explicitly into account the effect of unavoidable uncertainties. Challenges in this context involve, for example, limited information, human factors, subjectivity and experience, linguistic assessments, imprecise measurements, dubious information, unclear physics etc. Because of the polymorphic nature and characteristic of the available information, both probabilistic and set-theoretical approaches are relevant for solutions. SPP 1886 brings together researchers, scholarly persons, and practicing engineers concerned with various forms of advanced engineering designs. Recent developments of numerical methods in the field of engineering design, which include a comprehensive consideration of uncertainty and associated efficient analysis techniques, such as advanced Monte Carlo simulation, meta-model approximations, and high performance computing strategies are explicitly promoted. These approaches may involve imprecise probabilities, interval methods, fuzzy methods, and further concepts. The contributions may address specific technical or mathematical details, conceptual developments and design strategies, individual solutions, and also provide overviews and comparative studies. Particular attention is paid to practical applicability of the methods in engineering. Besides the application of the involved engineering sciences, “real world” scenarios are considered. The distinction between early stage of design and final design is significant. Starting in September 2016 by a kick-off-meeting at Technische Universität Dresden, 2 years of intensive research, programming, networking, and presenting are accomplished by in total 24 projects and over 60 involved researchers. Selected results of the successful joint work are presented in these two special issues. With the help of these publications, opportunities of interand transdisciplinary shall be stimulated for the generation of synergies between mathematics and engineering sciences. In fruitful cooperation with the international journal “Surveys for Applied Mathematics and Mechanics (GAMM-Mitteilungen)”, results jointly found by the research projects and discussions during the workshops, Summer school and the annual meetings are documented.