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Computer analysis of dynamic reliability of some concrete beam structure exhibiting random damping

Bredow R., Kamiński M.

International Journal of Applied Mechanics and Engineering

2021

Vol. 26, no. 1

45--64

An efficiency of the generalized tenth order stochastic perturbation technique in determination of the basic probabilistic characteristics of up to the fourth order of dynamic response of Euler-Bernoulli beams with Gaussian uncertain damping is verified in this work. This is done on civil engineering application of a two-bay reinforced concrete beam using the Stochastic Finite Element Method implementation and its contrast with traditional Monte-Carlo simulation based Finite Element Method study and also with the semi-analytical probabilistic approach. The special purpose numerical implementation of the entire Stochastic perturbation-based Finite Element Method has been entirely programmed in computer algebra system MAPLE 2019 using Runge-Kutta-Fehlberg method. Further usage of the proposed technique to analyze stochastic reliability of the given structure subjected to dynamic oscillatory excitation is also included and discussed here because of a complete lack of the additional detailed demands in the current European designing codes.

Comparative study to assess reliability in the presence of two geometric defect shapes for non-destructive testing

Oudni Zehor, Berkache Azouaou, Mehaddene Hamid, Mohellebi Hassane, Lee Jinyi

Przegląd Elektrotechniczny

2019

R. 95, nr 12

48--52

This study aims at evaluating the reliability for non-destructive eddy currents control. Two geometrical forms of the defect are generated whose dimensions and the electrical conductivity of the studied material are random variables of Gaussian type. The model SSFEM constructs allows the treatment and the post-treatment of the problem posed in a single step. the results of the impedance variation are compared with those of the Monte Carlo simulation and the experimental measurements. The state of reliability is quantified for the two forms of the defect.

Analizowana jest wiarygodność detekcji metodą prądów wirowych. Badana jest obecność dwóch różnych defektów których kształt jest przypadkowy. Wykorzystywano model SSFEM. Metodę porównano z rezultatami przy wykorzystaniu metody |Monte Carlo oraz z eksperymentem.

Time integration of stochastic generalized equations of motion using SSFEM

Poński Mariusz

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 1

37--48

The paper develops an integration approach to stochastic nonlinear partial differential equations (SPDE’s) with parameters to be random fields. The methodology is based upon assumption that random fields are from a special class of functions, and can be described as a product of two functions with dependent and independent random variables. Such an approach allows one to use Karhunen-Lo`eve expansion directly, and the modified stochastic spectral finite element method (SSFEM). It is assumed that a random field is stationary and Gaussian while the autocovariance function is known. A numerical example of onedimensional heat waves analysis is shown.