Joint uncertainty propagation in linear structural dynamics using stochastic reduced basis methods

Uncertainties in the properties of joints produce uncertainties in the dynamic response of built-up structures. Line joints, such as glued or continuously welded joints, have spatially distributed uncertainty and can be modeled by a discretized random field. Techniques such as Monte Carlo simulation can be applied to estimate the output statistics, but computational cost can be prohibitive. This paper addresses how uncertainties in joints might be included straightforwardly in a finite element model, with particular reference to approaches based on fixed-interface (Craig– Bampton) component mode synthesis and a stochastic reduced basis method with two variants. These methods are used to determine the output statistics of a structure. Unlike perturbation-based methods, good accuracy can be achieved even when the coefficients of variation of the input random variables are not small. Undamped as well as proportionally damped components are considered. Efficient implementations are proposed based on an exact matrix identity that leads to a significantly lower computational cost if the number of joint degrees of freedom is sufficiently small compared with the structure’s overall number of degrees of freedom. A numerical example is presented. The proposed formulation is an efficient and effective implementation of a stochastic reduced basis projection scheme. It is seen that the method can be up to orders of magnitude faster than direct Monte Carlo simulation, while providing results of comparable accuracy. Furthermore, the proposed implementation is more efficient when fewer joints are affected by uncertainty