Reliability Problems with Implicit Response Functions

This paper deals with a Probabilistic Transformation Method (PTM) for structures that require Finite Element Analysis to evaluate their response. The Probabilistic Transformation Method (PTM) is an efficient reliability method to solve problems of mechanical systems with uncertain parameters. This method 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. In this paper, we propose technique that combines Finite Element Analysis (FEA), and Probabilistic Transformation Method (PTM) to evaluate the Probability Density Function (PDF) of response where the expression between input and output of the considered structure is implicit. This technique is based on the numerical simulations of the Finite Element Analysis (FEA) and the Probabilistic Transformation Method (PTM) by making an interface between the software ANSYS and Matlab. Some problems of structures are treated in order to demonstrate the applicability of the proposed technique.