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1

Abruptly autofocusing property of circular Pearcey vortex beams with different initial launch angles in harmonic potentials

Liu Xianglian, Zhang Di, Zhao Lijiao, Li Pu, Zhang Jianguo, Liu Yi

Optica Applicata

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2022

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Vol. 52, nr 3

417--428

EN

We have studied and explored the influence of different launch angles on the circular Pearcey beams (CPBs) without vortex or with vortex for the first time. Although launch angles can manipulate the focal length and the contrast of peak intensity of the CPBs, the shape and propagation trajectory of the CPBs maintain invariant. When the vortex is considered, the focal pattern and the contrast of peak intensity of the circular Pearcey vortex beams (CPVBs) can be changed by adjusting the magnitude of topological charges and the position of vortex. In addition, we have deliberated the propagation of the CPVBs under the action of double opposite optical vortices.

2

Uncertainty propagation in structural reliability with implicit limit state functions under aleatory and epistemic uncertainties

Zhou Shuang, Zhang Jianguo, You Lingfei, Zhang Qingyuan

Eksploatacja i Niezawodność

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2021

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Vol. 23, no. 2

231--241

EN

Uncertainty propagation plays a pivotal role in structural reliability assessment. This paper introduces a novel uncertainty propagation method for structural reliability under different knowledge stages based on probability theory, uncertainty theory and chance theory. Firstly, a surrogate model combining the uniform design and least-squares method is presented to simulate the implicit limit state function with random and uncertain variables. Then, a novel quantification method based on chance theory is derived herein, to calculate the structural reliability under mixed aleatory and epistemic uncertainties. The concepts of chance reliability and chance reliability index (CRI) are defined to show the reliable degree of structure. Besides, the selection principles of uncertainty propagation types and the corresponding reliability estimation methods are given according to the different knowledge stages. The proposed methods are finally applied in a practical structural reliability problem, which illustrates the effectiveness and advantages of the techniques presented in this work.

3

Structural reliability analysis based on fuzzy random uncertainty

You Lingfei, Zhang Jianguo, Li Qiao, Ye Nan

Eksploatacja i Niezawodność

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2019

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Vol. 21, no. 4

599--609

EN

To address the fuzzy random uncertainty in structural reliability analysis, a novel method for obtaining the membership function of fuzzy reliability is proposed on the two orders four central moments (TOFM) method based on envelope distribution. At each cut level, the envelope distribution is first constructed, which is a new expression to describe the bound of the fuzzy random variable distribution. The central moments of the bound distribution are determined by generating samples from the envelope distribution, and they are used to calculate the central moments of the limit state function based on the first two orders of the Taylor expansion. Thereafter, the modern approximation method is used to approximate the polynomial expression for the limit state function probability density function (PDF) by considering the central moments as constraint conditions. Thus, the reliability boundaries can be calculated under the considered cut level, and the membership function of the fuzzy reliability is subsequently obtained. Three examples are evaluated to demonstrate the efficiency and accuracy of the proposed method. Moreover, a comparison is made between the proposed method, Monte Carlo simulation (MCS) method, and fuzzy first-order reliability method (FFORM). The results show the superiority of the proposed method, which is feasible for the analysis of structural reliability with fuzzy randomness.

PL

W pracy przedstawiono metodę, która pozwala na uwzględnienie rozmytej niepewności losowej w strukturalnej analizie niezawodności. Zaproponowana metoda określania funkcji przynależności niezawodności rozmytej wykorzystuje cztery momenty centralne dwóch rzędów czy czwarte momenty centralne drugiego rzędu obliczane w oparciu o rozkład obwiedni. Dla każdego poziomu cięcia, najpierw konstruuje się rozkład prawdopodobieństwa obwiedni, za pomocą którego opisuje się granice rozkładu rozmytych zmiennych losowych, a momenty centralne rozkładu ograniczonego wyznacza się poprzez generowanie prób z rozkładu obwiedni. Następnie, stosując nowoczesną metodę optymalnej aproksymacji, otrzymuje się aproksymowane wyrażenie wielomianowe funkcji gęstości prawdopodobieństwa rozkładu obwiedni, gdzie momenty centralne stanowią warunki ograniczające, które pozwalają aproksymować niezawodność za pomocą rozwinięcia Taylora drugiego rzędu funkcji stanu granicznego. W ten sposób granice niezawodności oblicza się na rozważanym poziomie cięcia, a następnie otrzymuje się funkcję przynależności niezawodności rozmytej. W artykule przeanalizowano trzy przykłady, na podstawie których wykazano skuteczność i trafność proponowanej metody. Przeprowadzono także porównanie z metodą symulacji Monte Carlo oraz metodą analizy rozmytej niezawodności pierwszego rzędu. Wyniki wskazują na wyższość omawianej metody, która pozwala analizować niezawodność strukturalną w warunkach losowości rozmytej.

4

Study of anisotropic strength properties of shale

Zheng Danzhu, Miska Stefan, Ziaja Małgorzata, Zhang Jianguo

AGH Drilling, Oil, Gas

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2019

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Vol. 36, no. 1

93--112

EN

Shale has been known to be the source of wellbore instability during the drilling process. Organic rich shales are anisotropic due to their laminated structure and chemical properties. The goal of this study is to evaluate anisotropic mechanical properties of shale by triaxial tests, and predict shale anisotropic properties by well logging data interpretation. Shale samples were prepared with bedding plane inclination angles equal to 0 degrees, 45 degrees, and 90 degrees. Young's modulus, shear modulus, and Poisson’s ratio in different directions were measured for a sample with 0 degrees bedding plane inclination angle. Parameters of the stiffness tensor were calculated by mechanical properties. Compressive strength was measured under different confining pressures of 0 psi, 500 psi, 1000 psi, and 1500 psi. The strength properties of shale samples were evaluated by both compressive strength and tensile strength. Simple Plane of Weakness and Modified Cam Clay failure criteria were applied to describe shear failure mechanisms. A scanning electron microscope method was used for the comparison of micro structures between the intact shale sample and failed sample with different bedding plane inclination angles. Well logging data was used to connect experimental lab data and field data. Compressional wave velocity was predicted with different inclination angles by stiffness parameters. The predicted compressional wave velocity for a 45-degree inclination angle showed a perfect fit with the field logging data. Steps of inverse sonic log data to stiffness parameters were shown by a flow chart. The UCS strength for 0 degrees and 45 degrees was predicted by several empirical relations using sonic logging data. The safe mud window for this special shale formation is predicted by experimental data. As shown in experimental results, our shale sample has a weak direction for both failure criteria. Well logging data and experimental data can be connected, especially by sonic log data. However, to predict shale anisotropic strength through well logging still requires more effort. The novelty of the process which connects experimental results and well logging data will be helpful for solving instability problems occurring in shale formation.