An APDM-based method for the analysis of systems with uncertainties

In this work a novel approach, called the Surface Reference Method (SRM), is proposed for the analysis of discretized systems with uncertain properties. It is based on the result of the Approximated Deformation Principal Modes (APDM) method by Falsone and Impollonia and on a simple property of the uncertain response of systems modeled as specified in this paper, that is: in the space of the random variables the response varies linearly along the straight lines passing by the origin. Using this property, an approximate method is obtained based on some new coefficients that enable to improve the APDM method. This new method enables analyzing systems with very high level of uncertainty with a low computational effort. In order to evidence the goodness of the method, two numerical examples are proposed considering several types of distributions for the uncertain parameters.