On the treatment of finite element structures in stochastic linear dynamics using a mode-based meta-model

This contribution presents a meta-model of the structural modes, which can be used for efficient dynamic analysis of finite element structures in the presence of uncertainties in the loading and structural parameters. The main goal consists in cutting down the computational time required for the repeated number of analyses in order to assess the impact of the uncertainties. The meta-model allows for an efficient evaluation of the structural modes which are represented as a linear combination of the modes of a reference solution. The calibration of the meta-model is based on the modes of about 30–50 samples of the structure obtained with Monte Carlo simulation. The mode-based meta-model can always be advantageously employed when a limited number of modes are required for analysis, such as, e.g. for mode superposition analysis. The numerical examples show the utilization of the meta-model for various applications such as uncertainty analysis, reliability assessment and design optimization.