New perspectives on probabilistic methods for nonlinear transient dynamics in civil engineering

The objective of this thesis is to develop probabilistic methods to perform nonlinear transient analysis in civil engineering applications. The manuscript is divided into two parts. For large-dimensional structures subject to coherent random loads, an asymptotic expansion-based method is used to improve linear evolutionary spectral analysis. Then, this method is extended to equivalent statistical linearization by a multiple timescales approach. The second part of the thesis is focused on small-dimensional systems. It explores the solution of the Fokker-Planck equation with the smoothed particle hydrodynamics method. This meshless Lagrangian method particularly ensures the conservation and the positivity of the probability field. The accuracy and efficiency of both approaches are compared with Monte-Carlo simulations.