Use of the Probability Transformation Method in Some Random Mechanic Problems

Abstract

This work addresses the use of the probability transformation method (PTM) and of some of its extensions for solving mechanical and structural systems for which the response is modeled as random fields or variables that cannot be well-approximated as Gaussian. In particular, the static and dynamic stochastic analyses of linear structural systems excited by non-Gaussian excitations were considered. Moreover, the stochastic structures, the geometric and/or material properties of which are random, were analyzed by coupling the PTM with another approach introduced by one of the authors, the approximated principal deformation mode (APDM) method. Some of the results were reported in other works, and some results are shown here for the first time. This work gathered all the typologies of stochastic structural analyses in which the PTM can be advantageously applied, both in terms of accuracy and in terms of efficiency.