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Zagadnienie stateczności wybranych konstrukcji inżynierskich o parametrach losowych

Kamiński M., Świta P.

Zeszyty Naukowe. Budownictwo / Politechnika Łódzka

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2010

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Z. 62

7-20

PL

Tematem niniejszej pracy jest zastosowanie probabilistycznej analizy numerycznej opartej na uogólnionej metodzie perturbacji stochastycznej do wyznaczenia probabilistycznych momentów obciążenia krytycznego. Obciążenia te wyznaczono za pomocą Stochastycznej Metody Elementów Skończonych dla losowo określonych parametrów geometrycznych przekroju. Wykorzystując metodę funkcji odpowiedzi wyznaczono wartości oczekiwane i odchylenia standardowe sił krytycznych dla płaskiej oraz przestrzennej ramy stalowej, które następnie będzie mozna wykorzystać do wyznaczenia ich wskaźników niezawodności.

EN

The main aim of this paper is the stability analysis of elastic frame systems with random parameters using the Generalized Stochastic Finite Element Method. The Taylor expansion with random coefficients of nth order is used to express all random functions and to determine the basic probabilistic moments of the critical load. The Response Function Method assists to determine higher order partial derivatives of the structural response instead of the Direct Differentiation Method employed widely before and is sufficient to assure high quality of the resulting moments. This approach is examined on the examples of 2 and 3D steel frames with some geometrical parameters defined as the Gaussian variables. Further application of this methodology is of course in the reliability analysis and reliability-based optimization of the steel engineering structures.

2

On Some Stability Properties of Monomial Functions

Budzik D.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2003

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Vol. 9

17--23

EN

A map M defined on a semigroup (group, Banach space etc.) and taking values in an Abelian group is called monomial of degree at most n whenever [formula]. We deal with the following stability problem for monomial mappings: given two functions F and ƒ satisfying the inequality [formula], we are looking for conditions admitting the existence of a nonnegative constant α such that [formula].

3

Stochastic parametric instability of thin cylindrical shell using various shell theories

Tylikowski A.

Mechanics and Mechanical Engineering

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2000

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Vol. 4, nr 2

281--290

EN

The dynamic stability problem is solved for thin cylindrical shells compressed by time-dependent deterministic or stochastic membrane forces using three common thin shell theories, namely Donnell's, Love's and Fliigge's shell theories. The asymptotic stability and almost sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov's direct method. The present paper compares effects of the use of the various shell theories on the dynamic stability regions.

4

Nonlinear interfacial instability of two electrified miscible fluids

Mahmoud Y. D., Moatimid G. M., El-Dib Y. O.

Mechanics and Mechanical Engineering

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2000

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Vol. 4, nr 2

225--249

EN

In a previews paper [1], a simplified formulation was presented to deal with the intcrfacial linear stability problem with mass and heat transfer, considering the presence of a periodic electric field. The present paper treats the same problem with a nonlinear approach. This approach is achieved by considering the multiple time scale method. The analysis reveals the existence of both resonant and non - resonant cases. Three types of nonlinear Schődinger equations are derived . The necessary and sufficient stability of conditions in obtained and the results are confirmed numerically. Graphs are drawn to illustrate the stability regions.