Approximate Solution of the Structural Problems Using Probabilistic Transformation
The aim of this paper is to present a new methodology for the evaluation of the statistical proprieties of the response of structures, based on The Finite Element Analysis (FEA) coupled with the Probabilistic Transformation Method (PTM). Uncertainty modelling with random variables motivates the adoption of advanced PTM for reliability analysis to solve problems of mechanical systems. The PTM is readily applicable in the case where the expression between input and output of structures are available in explicit analytical form. However, the situation is much more involved when it is necessary to perform the evaluation of implicit expression between input and output of structures through numerical models. For this we propose technique that combines the FEA software, and the PTM program to evaluate the Probability Density Function (PDF) of the response where the expression between input and output of structures is implicit. This technique is based on the numerical simulations of the FEA and the PTM by making an interface between Finite Element software and Matlab. Some problems of structures are treated in order to demonstrate the applicability of the proposed technique.
S. Ouhimmou et al., "Approximate Solution of the Structural Problems Using Probabilistic Transformation", Key Engineering Materials, Vol. 446, pp. 91-99, 2010