Structural analysis considering uncertainties with polynomial chaos expansions

A realistic structural analysis requires both a suitable numerical model as well as the consideration of uncertainties in the input data such as material properties. These parameters can be modeled by random variables or spatially correlated random fields. Calculating stochastic attributes such as mean value or variance of a quantity of interest such as a displacement requires a high computational effort when using standard methods such as the Monte-Carlo simulation (MCS). Modern methods such as the polynomial chaos expansions (PCE) allow an efficient approximation of the numerical model based on a few samples. Thereby, the PCE offers the particular advantage that stochastic attributes can be determined directly from the postprocessing of the chaos expansion. In addition, the method offers the possibility of a sensitivity analysis to identify important model parameters. Current research focuses on the application of the PCE in the context of structural analysis with the goal of efficiently replacing the computationally expensive MCS. Besides the sample-based application of the PCE, it can be integrated into the finite element formulation of structural elements directly. The focus is on the application to geometrically non-linear problems. 

Contact Person
Lukas Panther