Static response of sparsely probabilistic systems

Abstract

A formal matrix inversion procedure is developed which enables the evaluation of the static response of mechanical and structural systems composed of sparsely nondeterministic component parts. The methodology provides the determination of the mean, standard deviation as well as the various higher order statistical moments of the system output response, namely of the deflections, forces, stresses, strain, etc. This includes the capability to handle any form of statistical component variation. Due to the generality of the formalism, solution conditioning can be established via a priori qualitative and quantitative convergence criteria. Because of the development of efficient recursive algorithms, the computational effort associated with the calculation of the various statistical moments is ordered by the inverse of the traditional system stiffness martrix. In this context, the scheme can handle large scale lumped, finite element and difference type simulations. To demonstrate the methodology, the results of several benchmark problems are presented.