Stress Triaxial Constraint and Fracture Toughness Properties of X90 Pipeline Steel

The X90 pipeline steel with high-strength and high-toughness become the most popular pipeline steel. Due to the stress triaxial constraint and fracture toughness properties are the key factors for the stable work of pipeline steel, the research on the fracture toughness of X90 is a great significance to promote the engineering application of high-strength pipeline steel. In order to investigate the stress triaxial constraint and fracture toughness properties of X90 pipeline steel, the experimental rules with different grooves size are proposed using the common toughness experiment and the corresponding numerical models are established in this paper. The resistance curves and fracture toughness of each type of specimens are obtained and compared with that of finite element analysis. Furthermore, the stress distribution, J-integral distribution and stress triaxial constraint of the specimen are analyzed, as well as the influence of side grooves size on the determination of fracture toughness is also discussed. The results obtained from the study will provide a reference to the fracture toughness evaluation research and application of X90 pipeline steel.

КОКУС ЧОҢДУКТАРДЫН ЫКТЫМАЛДУУЛУКТАРЫН БӨЛҮШТҮРҮҮ ФУНКЦИЯСЫН ОКУТУУНУН ЫКМАЛАРЫ

Аннотация: Бөлүштүрүү функциясын, үзгүлтүксүз кокус чоңдуктардын ыктымалдуулуктарын бѳлүштүрүүнүн жиктелиш функциясы (ыктымалдуулуктун тыгыздыгы), ыктымалдуулуктарды бир калыпта бѳлуштүрүү законун аныктоо. Бөлүштүрүү функциясынын касиеттерин окутуу, далилдөө. X кокус чоңдугунун кабыл алууга мүмкүн болгон маанилери (a,b) интервалында жаткандыгынын ыктымалдуулугу бөлүштүрүү функциясынын өсүндүсүнө барабар. Түйүндүү сѳздѳр: Бөлүштурүү функциясы, үзгүлтүксүз кокус чоңдуктардын ыктымалдуулуктары, дискреттик кокус чоңдук, бөлүштүрүүнүн интегралдык функциясы, баштапкы функция. Аннотация: Определять вид непрерывной случайной величины, находить вероятность попадания случайной величины в заданный интервал по заданной функции распределения, уметь находить плотность распределения и равномерное распределения. Еще одно отличие характеристики случайных величин непрерывного действия-включение функции классификации распределения вероятностей, обнаружение первого производного функции последовательности. Следовательно, характеристика распределения вероятностей дискретных случайных величин. Свойства функции распределения обучения и доказательства. Х может быть, чтобы принять параметры диапазона значений (а, б), что функция распределения вероятностей равна приращению. Ключевые слова: Функция распределения, вероятность непрерывной случайной величины, дискретная случайная величина, интегральная функция распределения, первообразная. Annotation: Determine the type of random variable, find the probability of a random variable falling into a given interval by a given distribution function, be able to find the distribution density and uniform distribution. Properties of learning distribution function and evidence. X maybe to take the parameters of the range of values (a, b), that the probability distribution function is equal to the increment. Another difference in the characterization of continuous random variables is the inclusion of the classification function of the probability distribution, the detection of the first derivative of the sequence function. Hence, the characteristic of the probability distribution of discrete random variables Non-decreasing functions, ∫ _ (- ∞) ^ ∞▒ 〖P (x) ax = 1〗. In the case of an individual, if the values of a random variable (a, b) are located within ∫_a ^ b▒ 〖P (x) ax = 1〗 Keywords: Distribution function, probability of continuous random variable, discrete random variable, integral distribution function, antiderivative. DOI: 10.35254/bhu.2019.50.1 ВЕСТНИК БИШКЕКСКОГО ГОСУДАРСТВЕННОГО УНИВЕРСИТЕТА. No4(50) 2019 169 Аннотация: Бөлүштүрүү функциясын, үзгүлтүксүз кокус чоңдуктардын ыктымалдуулуктарын бѳлүштүрүүнүн жиктелиш функциясы (ыктымалдуулуктун тыгыздыгы), ыктымалдуулуктарды бир калыпта бѳлуштүрүү законун аныктоо. Бөлүштүрүү функциясынын касиеттерин окутуу, далилдөө. X кокус чоңдугунун кабыл алууга мүмкүн болгон маанилери (a,b) интервалында жаткандыгынын ыктымалдуулугу бөлүштүрүү функциясынын өсүндүсүнө барабар. X кокус чондугу PP(xx < xx1) ыктымалдуулукта x ден кичине маанилерди кабыл алат; X кокус чондугу xx1 ≤ xx < xx2барабарсыздыктын ыктымалдуулугу PP(xx1 ≤ xx < xx2) түрүндө канааттандырат. Үзгүлтүксүз кокус чоңдуктарды мүнөздөөнүн дагы бир башкача жолу ыктымалдуулукту бөлүштүрүүнүн жиктелиш функциясын киргизүү, тутамдык функциясынын биринчи туундусун табуу. Демек,тутамдык функция жиктелиш функциясынын баштапкы функциясы болорун, дискреттик кокус чондуктардын ыктымалдуулуктарынын бөлүштүрүүсүн мунөздөө. Жиктелиш функциясы кемибөөчү функция, ∫ ff(xx)dddd = 1 ∞ −∞ . Жекече учурда, эгерде кокус чоңдуктардын мүмкүн болгон маанилери (a,b) аралыгында жайгашса, анда � ff(xx)dddd = 1 bb aa Түйүндүү сѳздѳр: Бөлүштурүү функциясы, үзгүлтүксүз кокус чоңдуктардын ыктымалдуулуктары, дискреттик кокус чоңдук, бөлүштүрүүнүн интегралдык функциясы, баштапкы функция. Аннотация: Определять вид непрерывной случайной величины, находить вероятность попадания случайной величины в заданный интервал по заданной функции распределения, уметь находить плотность распределения и равномерное распределения. Еще одно отличие характеристики случайных величин непрерывного действия-включение функции классификации распределения вероятностей, обнаружение первого производного функции последовательности. Следовательно, характеристика распределения вероятностей дискретных случайных величин. Ключевые слова: Функция распределения, вероятность непрерывной случайной величины, дискретная случайная величина, интегральная функция распределения, первообразная. Annotation: Determine the type of random variable, find the probability of a random variable falling into a given interval by a given distribution function, be able to find the distribution density and uniform distribution. Properties of learning distribution function and evidence. X maybe to take the parameters of the range of values (a, b), that the probability distribution function is equal to the increment. Another difference in the characterization of continuous random variables is the inclusion of the classification function of the probability distribution, the detection of the first derivative of the sequence function. Keywords: Distribution function, probability of continuous random variable, discrete random variable, integral distribution function, antiderivative.

Adoption of Managerial Decisions for a Small Number of Input Data

Existing methods of statistical analysis of data and the registration of a small number of observations or tests lead to the need for an organization unnecessarily large number of experiments. In case of the impossibility of conducting the required number of experiments, the results of the analysis are insufficiently reliable. In this paper, statistical methods of increasing the efficiency of processing a small number of experiments and observations for the adoption of sound managerial decisions and the use of appropriate corrective actions are considered. The method of calculating the mathematical expectation and dispersion of the error of construction of the integral distribution law (IDL) based on the method of compression of the region of its existence, as well as the construction of the corresponding nomograms for solving a large number of practical tasks of object management, processes, research and testing is proposed. In the described method of compression of the area of the existence of IDL to consider a priori, the whole set of possible IDLs is introduced. This translates the analysis from a two-dimensional to three-dimensional probability space by introducing concepts such as the probability density of IRAs, probably as a model of a population of IARs that changes after the registration of the results of each subsequent experiment, the section of the probability, and some others. The analysis made it possible to detect the objectively existing area of a small number of tests and specify the number of tests required to obtain the desired result. Compared with the estimates obtained from the inequality of PL Chebyshev, the required number of tests can be reduced in 2% times and at least 4 times in the analysis of the variance of the error of constructing the IDR. Based on the results obtained, new convergence criteria are introduced which begin to work with n = 3.

On the evaluation of storage facilities on the dustiness of the urban environment

Examined the classification of dust from different storage facilities. Were considered different samples of dust (construction, textile, food), generated in storage facilities. Studied the influence of anti-dust coverage on dustiness of storage facilities as the pollution source. This paper presents the results of chemical analysis, studied dustiness, determined classification of studied dust. Constructed integral distribution curves of mass particles by equivalent diameter.

Chapter 1. Research methods

The first chapter presents methods for analyzing nonstationary physiological signals. Among them are 1) the method of continuous wavelet analysis, which allows obtaining the local and integral distribution of the energy of the wavelet spectrum of the signal over frequencies in a certain time interval, as well as providing information on the cross-wavelet spectrum and wavelet coherence of two signals; 2) methods for assessing the multifractality of a signal by searching for the maxima of the wavelet transform modulus maxima and by analyzing fluctuations relative to the trend; 3) the method of recurrent analysis, which allows to identify the quantitative parameters of the evolution of the signal in time, 4) the method of bifurcation analysis, which allows finding the values of the system parameters at which a qualitative change in the solution of the system occurs, for example, a change in the mode of impulse activity of a neuron.

An Improved Non-Gaussian Statistical Theory of Rubber Elasticity for Short Chains

The mechanical behavior of polymers has long been described by the non-Gaussian statistical model. Non-Gaussian models are generally based on the Kuhn-Grün (KG) distribution function, which itself is derived from the first order approximation of the complex Rayleigh’s exact Fourier integral distribution. The KG function has gained such a broad acceptance in the field of polymer physics that the non-Gaussian theory is often used to describe chains with various flexibility ratios. However, KG function is shown to be only relevant for long chains, with more than 40 segments. Here, we propose a new accurate approximation of the entropic force resulted from Rayleigh distribution function of non-Gaussian chains. The approximation provides an improved version of inverse Langevin function which has a limited error value with respect to the exact entropic force. The proposed function provides a significantly more accurate estimation of the distribution function than KG functions for small and medium-sized chains with less than 40 segments.

STRESS INDEX IN UKRAINE’S MARKET OF NEGOTIABLE FINANCIAL INSTRUMENTS

Market of negotiable financial instruments is an immanent component of the financial system and is in a two-way relationship with other financial institutions and real sector of the economy in terms of ensuring its stable functioning. Possible market shocks can adversely affect state of the economy; therefore regulators should carry out constant market surveillance to detect and prevent early possible market violations, by calculating (in particular) the composite stress index. To construct a composite index, correlation analysis, generalized autoregressive conditional heteroscedasticity model, standardization based on the integral distribution function, seasonal adjustment and determination of a long-term trend based on filtering are used. It is proposed to calculate the stress index of Ukraine’s market of negotiable financial instruments on the basis of market data by balanced averaging of the following sub-indices: (i) stocks (UX stock yield volatility, CMAX indicator, market efficiency coefficient); (ii) debt securities (sovereign spread and CDS spread); and (iii) derivatives (indicator of the change in the number of open futures positions for the UX stock). Aforementioned were standardized using the integral distribution function. The author’s analysis of the proposed composite stress index shows that dominant factors affecting the situation in Ukraine’s market of securities and derivatives are intra-national ones, which have become dominant since 2014. At present, the stress index of Ukraine’s market of negotiable financial instruments is still of little importance to reflect economic situation in the state, given weak development of the market and its meager role for financing and reflecting the corporate activity.

Analytical solution of some delamination scenarios in thick structural sandwich plates

The first-, second- and third-order shear deformation plate theories are applied in this work to model thick rectangular sandwich plates with through-width delamination. The models are based on the concept of the four equivalent single layers and the system of exact kinematic conditions. Three different scenarios are considered: the failure of the core, the delamination between the top facesheet and the core, and finally, the case when the delamination takes place in the local midplane of the top facesheet. A general model is derived and applied to sandwich plates with Lévy type boundary conditions. The governing equations are summarized and the state-space model of the system is created. The mechanical fields are calculated and compared to finite element results. The comparison shows that the first-order sandwich plate model is inaccurate, on the other hand, the second- and third-order theories capture very well the mechanical fields compared to finite element results. The J-integral distribution is also calculated along the delamination front and it is concluded that the third- and second-order models give very good approximations of the results by finite element analysis and the virtual crack closure technique.