Stochastic Methods Applied to Structural Mechanics

Abstract

Uncertainty modelling with random variables motivates the adoption of advanced PTM for reliability analysis to solve problems of mechanical systems. Probabilistic transformation method (PTM) is readily applicable when the function between the input and the output of the system is explicit. When these functions are implicit, a technique is proposed that combines finite element analysis (FEA) and probabilistic transformation method (PTM) that is based on the numerical simulations of the finite element analysis (FEA) and the probabilistic transformation method (PTM) using an interface between finite element software and Matlab. Structure problems are treated with the proposed technique, and the obtained results are compared to those obtained by the reference Monte Carlo method. A second aim of this work is to develop an algorithm of global optimization using the local method SQP. The proposed approach MSQP is tested on test functions comparing with other methods, and it is used to resolve a structural problem under reliability constraints.