Wiener path integrals and multi-dimensional global bases for non-stationary stochastic response determination of structural systems

2019 ◽  
Vol 128 ◽  
pp. 551-571 ◽  
Author(s):  
Apostolos F. Psaros ◽  
Ioannis Petromichelakis ◽  
Ioannis A. Kougioumtzoglou
Keyword(s):  
Path Integrals ◽  
Structural Systems ◽  
Stochastic Response ◽  
Response Determination

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

2015 ◽  
Vol 82 (10) ◽  
Author(s):  
Ioannis A. Kougioumtzoglou ◽  
Alberto Di Matteo ◽  
Pol D. Spanos ◽  
Antonina Pirrotta ◽  
Mario Di Paola
Keyword(s):  
Path Integral ◽  
Computational Cost ◽  
High Dimensional ◽  
System Response ◽  
Stochastic Response ◽  
Mdof Systems ◽  
Low Dimensional ◽  
Response Determination ◽  
Efficiency And Reliability

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” 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 high-dimensional 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.

Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

2014 ◽  
Vol 38 ◽  
pp. 127-135 ◽  
Author(s):  
Alberto Di Matteo ◽  
Ioannis A. Kougioumtzoglou ◽  
Antonina Pirrotta ◽  
Pol D. Spanos ◽  
Mario Di Paola
Keyword(s):  
Path Integral ◽  
Fractional Derivatives ◽  
Nonlinear Oscillators ◽  
Stochastic Response ◽  
Response Determination
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