Impulse deformation of triangular plates based on the classical theory

This article discusses the impulse effects of various loads on triangular, isosceles, elastic, isotropic plates. Analytical solutions of the direct problem of determining the internal moments and deflections of the plate, as well as the numerical results of calculations of specific loading case are presented. Goal. The goal is to develop a method for solving direct problems of determining internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates. Methodology. To solve the direct problem, the Navier method, the classical theory of modeling vibrations of thin plates and the Laplace transform are used. Results. A technique has been obtained that allows one to obtain numerical and analytical dependences for calculating the internal moments and deflections in a triangular plate. Originality. For the first time, a technique was developed for solving direct non-stationary problems to determine the internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates based on the classical theory. Practical value. The obtained analytical dependences can be used to simulate impulse vibrations of square and isosceles rectangular triangular thin isotropic elastic plates, which can be critical structural elements.

Nonparametric Method for Predicting the Trajectory of an Actively Maneuvering Vessel for Unmanned Aerial Vehicle Landing

The article is devoted to the development of algorithms for predicting the trajectory of maneuvering objects based on nonparametric systems theory. The analysis of uncertainties affecting the modeling of the movement maneuvering water objects is presented. An overview of parametric, nonparametric and combined methods for predicting maneuvering water objects trajectory is given. The problem of high-precision autonomous control of the landing unmanned aerial vehicles on the landing vessel in the conditions of its irregular movement caused by meteorological conditions and active maneuvering is being solved. The method for predicting the trajectory of a vessel’s movement based on solving direct problems of dynamics using nonparametric systems theory is proposed. The advantages of the proposed method are that it’s not affected by model errors, due to the fact that it is based only on a retrospective analysis of several consecutive values of the spatial vessel coordinates. The proposed method differs from similar nonparametric methods in that it does not require statistical calculations, own training, or time-consuming tuning. The method does not imply the solution of identification model parameters, state and control actions problems and can be applied with any unknown linearizable input control actions, including when the model of the vessel’s motion dynamics is not identifiable. The results of numerical modeling for solution the problem of predicting the trajectory of an actively maneuvering small-sized landing vessel using a full nonlinear dynamic model with six degrees of freedom are presented. The studies carried out confirm the efficiency, adequacy and very fast adjustment of the developed method under conditions of complete parametric and nonparametric uncertainty. The proposed method can be used to predict the trajectory of any vehicle under the condition of linearizability of its model and control signals over the observed time interval.

Determination of Prestress in Circular Inhomogeneous Solid and Annular Plates in the Framework of the Timoshenko Hypotheses

Determination of prestress fields in structures is of the utmost importance, since they have a significant impact on operational characteristics, and their level and distribution must be strictly controlled. In this paper, we present modeling of bending vibrations of solid and annular round inhomogeneous prestressed plates within the framework of the Timoshenko hypotheses. New inverse problems of prestress identification in plates are studied on the basis of the acoustic response subjected to some probing load. To solve direct problems on calculating oscillations and amplitude-frequency characteristics, a computational Galerkin-method-based scheme has been developed. In order to treat the inverse problems, we use a special projection approach based on the constructed weak problems statements, which makes it possible to determine the desired characteristics in the given classes of functions. The developed techniques for solving direct problems are implemented in the form of software packages realized via Maple. For both solid and annular plates, we estimate the sensitivity of the amplitude-frequency characteristics the values of which are used as the additional data in the inverse problems to a change in the prestress level; we conclude that the most favorable frequency range should be selected in the resonance vicinity. We have conducted a series of computational tests on reconstructing the plate’s prestresses of various levels and distribution patterns (decreasing, increasing, sign-changing laws). The results of computational tests revealed that the technique developed allows for the determination of the prestresses with a low error for two cases: when the cause of prestress formation and its type are known and when arbitrary prestress changing laws are considered.

SYNTHESIS TRENDS OF FORECASTING USING INDUCTIVE MODELING METHODS

Modern development of computer technology and the possibility of implementing calculations in parallel allow to solve increasingly large-scale problems of numerical modeling. The development of multiprocessor computing and parallel computing makes it important to solve problems of optimization analysis. The optimization analysis is based on the mass solution of inverse problems when the defining parameters of the considered class of problems change in certain ranges. Thus, calculations of not only direct problems where it is necessary to model the phenomenon at the known initial data, but also calculations of inverse problems where it is necessary to define on what defining parameters there is this or that phenomenon become more and more demanded. This formulation requires multiple solutions of direct problems and solving the problem of optimization analysis and construction of predictive trends. Sets of multidimensional parametric data in the paper are considered as numerical solutions of the optimization problem. The construction of predictive trends is implemented on the basis of the group method of data handling as a direction of induction modeling. The methodology of visualization of results of calculation of parametric functions is realized. The scheme of Data Mining with application of methods of visualization by means of the Matlab software environment is described

Design and Construction of an Air Quality Monitoring System to Mitigate Virus Spread

Air pollution is one of the most dangerous problems we face in the world today. It causes many illnesses and diseases that affect the immune system of humans and non-human animals and is also a means of propagating the novel COVID-19 or corona virus. Temperature, humidity, and the level of carbon dioxide characterize the air quality in an environment. In addition to abnormal temperatures and humidity causing direct problems to humans like headaches, heatstroke, hypothermia and hyperthermia, death and so on, it could also cause complicated problems like the acceleration of the growth and lifespan of harmful viruses like the corona virus especially in closed spaces like on a drilling rig or a processing facility. Multiple studies show that the influenza virus, coronavirus, and many others spread from host to host faster in areas with low humidity and high temperatures and upon infection, mortality rate is higher in low humidity regions. Inhalation of toxic levels of carbon dioxide has adverse effects ranging from drowsiness to coma and even death. Despite safety measures put in place in offshore facilities, there are still cases of corona virus outbreaks, hence this study aims to combat the facilitated spread of viruses and enhancement of good air quality via the design and construction of a device that measures the temperature, humidity, and carbon dioxide levels, using a DHT11 and MQ135 sensor. The temperature, humidity and carbon dioxide levels of the living area, bedroom, kitchen, and balcony in a facility was captured by the device to determine the quality of air and characterized. The values were then compared with the expected values from a trusted website to determine the accuracy of the device. The device showed a 99.8% accuracy and passed quality check making it a recommendation to enhance air quality in facilities, houses, or offices.

Simulation of Dynamic Processes in Deformable Medium with the Grid-Characteristic Approach

Существует значительное количество прикладных задач, для решения которых применяется математическое моделирование динамических процессов в деформируемых средах. К таким задачам относят моделирование распространения упругих волн в геологических средах, в том числе с учетом ледовых образований, их рассеяния на зонах трещиноватости. Актуальность этих постановок обусловлена важностью решения обратных задач сейсмической разведки, обработки данных сейсмической разведки с целью уточнения запасов углеводородов и определения расположения углеводородов и других полезных ископаемых. Поэтому приобретает важность разработка высокоточных численных методов, позволяющих моделировать упругие волны в деформируемых средах. Одним из этих методов является сеточно-характеристический численный метод, примененный в данной работе. Этот численный метод применяется для решения прямых задач, то есть для расчета распространения упругих волн при известных параметрах рассматриваемой среды. А для решения обратной задачи по восстановлению параметров геологической среды по данным сейсмической разведки можно применять нейронные сети, для обучения которых можно использовать многократное решение прямых задач сеточно-характеристическим методом. В данной работе приведены примеры решения разнообразных прямых задач по распространению упругих волн в неоднородных геологических средах, в том числе в зоне Арктики, а также представлена постановка задачи по обучению нейронных сетей и графики, показывающие эффективность их обучения с использованием двух различных подходов. Many problems can be solved with the simulation of dynamic processes in deformable media. They are the simulation of elastic wave propagation in rocks including ice formations, and wave scattering on rock-fracture zones. Such studies are important for solving inverse problems of seismic exploration and seismic data processing to get a better estimation of hydrocarbon reserves, locate hydrocarbons and other minerals. Therefore, it is necessary to develop high-precision numerical methods used to simulate elastic waves in deformable media. One of such methods is the grid-characteristic approach used in this work. It is suitable for solving direct problems, i.e., to analyze the propagation of elastic waves in a medium with known properties. Neural networks can be applied to solve the inverse problem: reconstructing the geology from seismic survey data. Multiple solving of direct problems by the gridcharacteristic approach is used for network training. This paper contains some examples of solving a range of direct problems on the elastic wave propagation in heterogeneous rocks, also in the Arctic zone, and the problem statement for training neural networks and graphs is proposed to demonstrate the efficiency of training with two approaches.

The structure and features of the software for geophysical geometrical 3D inversions

The structure and features of a software package for 3D inversion of geophysical data are considered. The presented software package is focused on solving direct and inverse problems of electrical exploration and engineering geophysics. In addition to the parameters that determine physical properties of the medium, the software package allows you to restore the geometry parameters of the geophysical model, namely layer reliefs and boundaries of three-dimensional inclusions. The inclusions can be in the form of arbitrary hexagons or prisms with a polygonal base. The software package consists of four main subsystems: an interface, subsystems for solving direct and inverse problems, and a client-server part for performing calculations on remote computing nodes. The graphical interface consists of geophysicist-oriented pre- and postprocessor modules that allow you to describe the problem and present the results of its solution in user-friendly terms. To solve direct problems, the finite element method and the technology for dividing the field into normal and anomalous components are used. At the same time, special methods of discretization of the computational domain are used, which make it possible to take into account both the complex three-dimensional structure of the environment and the presence of man-made objects (wells) in the computational domain. To increase the efficiency of solving direct problems, nonconforming grids with cells in the form of arbitrary hexahedrons are used. Methods for efficient calculation of derivatives (with respect to these parameters) necessary for solving inverse problems by the Gauss-Newton method are also described for the geometry parameters. The main idea for efficient derivatives computation is to identify the effect of changing the value of the parameter (used to compute the value of the generalized derivative) on the problem. The main actions performed by the subsystem for solving inverse problems and the features associated with the processing of geometry parameters are described.

APPLICATION OF CALCULATION REGION DECOMPOSITION IN SOLVING MAGNETOTELLURIC SOUNDING PROBLEMS

Using numerical experiments, possibilities of application the decomposition method of the calculation region in solving direct problems of the magnetotelluric sounding are considered.

Simulation of Fractured Rock Heterogeneity with the Grid Characteristic Method Using Structured Multiblock Grids

Основной задачей, стоящей перед сейсмической разведкой, является восстановление структуры и свойств подповерхностного пространства на основе регистрации колебаний земной поверхности. Для этого необходимо решить обратную задачу, что, в свою очередь, требует решения серии прямых задач с последовательно изменяющейся моделью геологического массива. В связи с открытием нетрадиционных месторождений (например, Баженовская свита), актуальной становится задача интерпретации сейсмического сигнала, обусловленной неоднородной структурой трещиноватых пластов. В настоящей работе была построена трещиноватая модель, отражающая некоторые особенности нефтеносных геологических сред. Проведено численное моделирование распространения сейсмических волн и получены синтетические площадные сейсмограммы. Также был проведен анализ сейсмического отклика. The key objective of seismic exploration is the recreation of the subsoil structure and properties by registering the surface waves. To solve a reverse problem, several direct problems shall be solved as the rock model is gradually changed. As nonconventional deposits are discovered (like the Bazhenov suite), it becomes necessary to interpret the seismic response caused by the heterogeneous structure of the fractured rock. This study presents a fractured rock model that represents some features of oilbearing geology. The seismic waves propagation was simulated, and composed widepatch seismic records were produced. The seismic response was also analyzed.

The mathematical modeling of magnetic systems with rectangular structure for different experiments

Design, construction and operation of the magnetic systems of some electrophysical setups require a preliminary mathematical modeling as well as a constant maintenance of mathematical modeling when debugging and operating the setups. While calculating the fields of the mentioned magnetic systems (on the base of solving a number of the direct problems of magnetostatics), we are concerned with the inverse problem of magnetostatics, namely, an optimal construction of the current elements and ferromagnetic yoke was found resulting in the expected distribution of the magnetic field. This work discusses the results on the numerical modeling of the distributing magnetic field for some modifications of the spectrometric magnet SP-94, SP-40 and the magnet of solenoid type, weach used in some experimental setups.