Wyniki wyszukiwania - BazTech

1

Probabilistic buckling analysis of the beam steel structures subjected to fire by the stochastic finite element metho

Świta P., Kamiński M.

International Journal of Applied Mechanics and Engineering

|

2016

|

Vol. 21, no. 2

485--510

EN

The main purpose is to present the stochastic perturbation-based Finite Element Method analysis of the stability in the issues related to the influence of high temperature resulting from a fire directly connected with the reliability analysis of such structures. The thin-walled beam structures with constant cross-sectional thickness are uploaded with typical constant loads, variable loads and, additionally, a temperature increase and we look for the first critical value equivalent to the global stability loss. Such an analysis is carried out in the probabilistic context to determine as precisely as possible the safety margins according to the civil engineering Eurocode statements. To achieve this goal we employ the additional design-oriented Finite Element Method program and computer algebra system to get the analytical polynomial functions relating the critical pressure (or force) and several random design parameters; all the models are state-dependent as we consider an additional reduction of the strength parameters due to the temperature increase. The first four probabilistic moments of the critical forces are computed assuming that the input random parameters have all Gaussian probability functions truncated to the positive values only. Finally, the reliability index is calculated according to the First Order Reliability Method (FORM) by an application of the limit function as a difference in-between critical pressure and maximum compression stress determined in the given structures to verify their durability according to the demands of EU engineering designing codes related to the fire situation.

2

Structural stability and reliability of the underground steel tanks with the Stochastic Finite Element Method

Kamiński M., Świta P.

Archives of Civil and Mechanical Engineering

|

2015

|

Vol. 15, no. 2

593--602

EN

The main aim is to present the Stochastic perturbation-based Finite Element Method analysis of the stability and also reliability of the underground steel vertical cylindrical structure of the waste container. This thin walled structure with constant cross-sectional thickness is loaded with subsoil pressure, snow and surface as well as dead loads and we look for the critical pressure value, when stability loss would be observed; it is done to design in the probabilistic context the safety margins. We employ to achieve this goal the Finite Element Method program ROBOT and computer algebra system MAPLE to get the analytical polynomial functions relating the critical pressure and random design parameters – shell thickness and its Young's modulus as well as to provide all probabilistic calculations. We determine up to the fourth order probabilistic characteristics of the structural response assuming that the input random parameters have Gaussian probability functions truncated to the positive values only. Finally, the reliability index is calculated according to the first order method using a difference in-between critical pressure and maximum tensile stress determined in this structure to verify its durability according to the demands of EU engineering codes.

3

Homogenization of fiber-reinforced composites with random properties using the weighted least squares response function approach

Kamiński M.

Archives of Mechanics

|

2011

|

Vol. 63, nr 5-6

479-505

EN

The main aim of the paper is a determination of the basic probabilistic characteristics for the effective elasticity tensor of the periodic fiber-reinforced composites, using the generalized stochastic perturbation technique. An evaluation of the generalized stochastic perturbation method of the analytical formulas and the Monte-Carlo simulation technique is provided for the 1D periodic structure with random material parameters. The higher-order terms are determined using numerical determination of the response functions between the effective tensor components and the given random input variables. It is carried out with the use of the Least Squares Method (LSM), applied for the series of computational experiments consisting of the Finite Element Method (FEM) solutions to the cell problems for the randomized input parameters. The key problem is the weighting LSM procedure worked out to speed up the probabilistic convergence of the homogenization results.

4

Zagadnienie stateczności wybranych konstrukcji inżynierskich o parametrach losowych

Kamiński M., Świta P.

Zeszyty Naukowe. Budownictwo / Politechnika Łódzka

|

2010

|

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.

5

Stochastic reliability in contact problems for composites with spherical particles

Kamiński M.

Journal of Theoretical and Applied Mechanics

|

2001

|

Vol. 39 nr 3

539-562

EN

The application of the stochastic perturbation technique in the classical Hertz contact problem of a composite with spherical particle is presented in the paper. The perturbation approach is used in conjunction with the Weibull-Second Order Third Moment (W-SOTM) reliability model in numerical analysis of the composite. All computational experiments are carried out using symbolic computation package MAPLE, that makes it possible to visualize the deterministic sensitivity gradients as well as to show probabilistic moments of contact stresses. The entire methodology can be applied to analytical solutions of contact problems with a more complicated contact surface geometry and, on the other hand, to computational implementation in the Finite or Boundary Element Method programs for simulations of some contact phenomena.

PL

Stochastyczna analiza niezawodności w zagadnieniu kontaktowym kompozytu ze sferycznymi inkluzjami. Tematem niniejszej pracy jest zastosowanie stochastycznej metody perturbacji w analizie niezawodności materiałów kompozytowych ze sferycznymi inkluzjami. W analizie tej wykorzystano stochastyczną metodę perturbacji drugiego rzędu uwzględniając momenty probabilistyczne rzędu trzeciego. Zastosowane podejście umożliwiło potraktowanie wybranych parametrów materiałowych i geometrycznych jako zmienne losowe i wyznaczenie wartości oczekiwanych oraz odchyleń standardowych naprężeń kontaktowych. Obliczenia numeryczne wykonano przy pomocy matematycznego do obliczeń symbolicznych MAPLE. Dzięki jego zastosowaniu wykonano wizualizację wybranych elementów losowych, a także gradientów wrażliwości naprężeń kontaktowych. Zaproponowane w pracy podejście można rozszerzyć na rozwiązania analityczne zagadnień kontaktowych o bardziej skomplikowanej geometrii, a także w odpowiednich implementacjach numerycznych Metody Elementów Skończonych lub Metody Elementów Brzegowych.