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# Probabilistic Analysis of Transient Problems by the Least Squares Stochastic Perturbation-Based Finite Element Method

M.M. Kaminski

Department of Steel Structures, Faculty of Civil Engrg., Arch. & Env. Engrg., Technical University of Lodz, 90-924 Lodz, Al. Politechniki 6, Poland, Marcin.Kaminski@p.lodz.pl

Computer Modeling in Engineering & Sciences 2011, 80(2), 113-140. https://doi.org/10.3970/cmes.2011.080.113

## Abstract

The main aim of this work is to demonstrate a solution to the transient problems for the statistically homogeneous media with random physical parameters. This is done with the use of the stochastic perturbation technique based on the general order Taylor series expansions and the additionally modified implementation of the Finite Element Method. Now, both the Direct Differentiation Method as well as the Response Function Method are employed to form and solve up to the nth order state equations. Computational implementation of both approaches is illustrated using two examples - by determination of the probabilistic moments of the temperature histories in the heated rod with the constant prismatic cross-section as well as for the two degrees of freedom elastic system subjected to the forced vibrations. The proposed numerical technique may also find an application in the transient heat transfer or elastodynamics in the large scale structures, for both homogeneous and heterogeneous media modelling, where physical parameters may be defined as the stochastic processes like time series, for instance.

## Keywords

APA Style
Kaminski, M. (2011). Probabilistic analysis of transient problems by the least squares stochastic perturbation-based finite element method. Computer Modeling in Engineering & Sciences, 80(2), 113-140. https://doi.org/10.3970/cmes.2011.080.113
Vancouver Style
Kaminski M. Probabilistic analysis of transient problems by the least squares stochastic perturbation-based finite element method. Comput Model Eng Sci. 2011;80(2):113-140 https://doi.org/10.3970/cmes.2011.080.113
IEEE Style
M. Kaminski, "Probabilistic Analysis of Transient Problems by the Least Squares Stochastic Perturbation-Based Finite Element Method," Comput. Model. Eng. Sci., vol. 80, no. 2, pp. 113-140. 2011. https://doi.org/10.3970/cmes.2011.080.113

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