Dynamic analysis of grandstands

Abstract

The purpose of this thesis is to provide a systematic approach to the modelling of the crowd-grandstand problem taking into account various sources of randomness in complex FEM-based numerical approach using geometries, material properties and other parameters from the models for the static analysis. Further, to quantify performance and efficiency of this method in comparison with direct Monte Carlo simulation. To this end, stochastic calculus in terms of Itô's integral and Brownian motion process is employed to derive moment equations describing the resulting output quantities which can be subsequently used to asses overall serviceability and reliability of the system. Utilizing various methods which reduce the size of the corresponding mathematical model, the approach becomes tractable and quite efficient. It is demonstrated on several examples that not only the randomness of the induced active crowd forces can be captured, but also a random spatial distribution of a crowd and uncertainties in biodynamic models reflecting passive spectators. Since the approach is in its essence analytical, it illuminates and reveals several relationships between the behavior of the system response and particular sources of randomness.

The purpose of this thesis is to provide a systematic approach to the modelling of the crowd-grandstand problem taking into account various sources of randomness in complex FEM-based numerical approach using geometries, material properties and other parameters from the models for the static analysis. Further, to quantify performance and efficiency of this method in comparison with direct Monte Carlo simulation. To this end, stochastic calculus in terms of Itô's integral and Brownian motion process is employed to derive moment equations describing the resulting output quantities which can be subsequently used to asses overall serviceability and reliability of the system. Utilizing various methods which reduce the size of the corresponding mathematical model, the approach becomes tractable and quite efficient. It is demonstrated on several examples that not only the randomness of the induced active crowd forces can be captured, but also a random spatial distribution of a crowd and uncertainties in biodynamic models reflecting passive spectators. Since the approach is in its essence analytical, it illuminates and reveals several relationships between the behavior of the system response and particular sources of randomness.