An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems

Abstract

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multidegreeoffreedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for lowdimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively highdimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localizationâ€‌ capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF. It is shown that, for the case of relatively highdimensional systems, the herein proposed implementation can drastically decrease the associated computational cost by several orders of magnitude, as compared to both the standard WPI technique and an MCS approach. Several numerical examples are included, whereas comparisons with pertinent MCS data demonstrate the efficiency and reliability of the technique.