Design and Optimization of shell structures with polymorphic uncertain data

• Applicant: Dr.-Ing. Marc Fina
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 511267658

Shell structures can efficiently carry loads due to their curved shape and are widely used structures in civil and aerospace engineering. They are thin-walled and slender structures with low dead weight and high load-bearing capacity. In pressure loading, buckling is usually the governing failure mode. In particular, geometric and material imperfections, such as deviations in the geometric shape and thickness of the shell, residual stresses, variations in boundary conditions and material parameters have a major influence on the buckling behavior. Small variations of the parameters have large effects on the load-bearing behavior. Thus, the robustness of thin-walled shells in particular is very low.The shape of the imperfections is often unknown or only few measurements are available. Therefore, according to traditional deterministic and probabilistic design concepts, enormous safety factors have to be applied. The design of shell structures with deterministic models implies precision. In reality, all data and information are characterized by various types of uncertainty, e.g., natural variability, incompleteness (lack of knowledge), and imprecision (measurement errors). These uncertainties have not been sufficiently considered in traditional design concepts so far. The focus of this project is to develop a new optimization-based design strategy for shell structures in which all uncertainties of the design parameters will be quantified using polymorphic uncertainty models. Particularly in shell buckling, the objective is to formulate a new design concept based on uncertain data. With the help of fuzzy variables, verbal statements about the hazard potential will be numerically determined. The new design concept is intended to initiate a rethinking of the methodology for the numerical design of shells.Following the uncertainty quantification based on experimental data, optimization objectives are formulated on the basis of the newly developed design concept. Thus, the uncertainty is taken into account in the optimization process with the aim of improving the robustness and economy of shell structures. Moreover, imperfections are spatially correlated and are simulated as random fields in probabilistic design concepts. The uncertainty of the parameters for the representation of imperfections as random fields must be taken into account. For this purpose, correlation models with uncertain parameters for fiber composite shells are to be developed.In polymorphic uncertainty modeling an optimization procedure is very computationally expensive. Therefore, this project also includes research on the application of special surrogate models, which can be used to replace complex shell models. The methods are implemented in a powerful simulation environment for high-performance computing.

• DFG Programme: Research Grants
• Co-Investigators: Professor Dr.-Ing. Steffen Freitag; Professor Dr.-Ing. Werner Wagner