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MAGAZINE OF CIVIL ENGINEERING 2021年第7期107卷

作者： Yurchenko, V. V. Peleshko, I. D. Kyiv Natl Univ Construct & Architecture Kiev Ukraine Lviv Polytech Natl Univ Lvov Ukraine

The main research goal is the development of a numerical methodology for solving parametric optimization problems of steel structures with orientation to software implementation in a computer-aided design system. The paper introduces a new mathematical model for parametric optimization problems of steel structures. The design variable vector includes geometrical parameters of the structure (node coordinates), cross-sectional dimensions of the structural members, as well as initial pre-stressing forces introduced into the specified redundant members of the structure. The system of constraints covers load-carrying capacities constraints formulated for all design sections of structural members of the steel structure subjected to all ultimate load case combinations. The displacements constraints formulated for the specified nodes of the steel structure subjected to all serviceability load case combinations have been also included into the system of constraints. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used for solving the parametric optimization problem. A numerical algorithm for solving the formulated parametric optimization problems of steel structures has been developed in the paper. The comparison of the optimization results of truss structures presented by the paper confirms the validity of the optimum solutions obtained using the proposed numerical methodology.

关键词： optimization steel structures nonlinear programming strength buckling stiffness gradient projection method finite element method numerical algorithm

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Fuzzy Optimal Control Problem with Non-linear Functional

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FUZZY INFORMATION AND ENGINEERING 2011年第3期3卷 311-320页

作者： Niftiyev, A. A. Zeynalov, C. I. Poormanuchehri, M. Baku State Univ Inst Appl Math Baku Azerbaijan Naxchivan State Univ Nakhchivan Azerbaijan

In this paper, we introduce a new space of fuzzy numbers equipped with a scalar product defined in this space. The notion of a derivative of a fuzzy function in this space is defined. By employing these notions, an optimal control problem with non-linear functional is formulated and an optimality condition is obtained in the form of maximum principle. Using this result, the numerical algorithm is offered for the solution of such problems.

关键词： Space of fuzzy numbers Fuzzy differential equation Optimality condition Maximum principle numerical algorithm

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Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation

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APPLIED MATHEMATICS AND NONLINEAR SCIENCES 2022年第1期8卷 1167-1176页

作者： Chen, Xuming Zhu, Jianfa Li, Liangxiao Long, Chengwen Jiangxi Coll Appl Technol Ganzhou 341000 Jiangxi Peoples R China

In order to explore the fractional differential equations in accounting informatization financial software, the author proposes a system for fractional diffusion wave equations and fractional differential equations, two numerical algorithms with higher precision are given, and the amount of computation is reduced at the same time. First, based on the equivalent integral form of the time fractional diffusion wave equation, using the fractional echelon method and the Crank-Nicolson method, for the time fractional diffusion wave equation, a finite difference scheme is designed, this format has second-order accuracy in both the temporal and spatial directions and is computationally stable. numerical examples verify the accuracy and effectiveness of this format. Then when dealing with the initial value problem of fractional differential equations with Caputo derivative operator, convert it to the equivalent Voltera integral equation system, an initial approximate solution is obtained by a low-order method, derive the residual and error equations, the idea of applying the stepwise correction of spectral delay correction improves the numerical accuracy of the solution, at the same time, the Richard Askey integral equation is used to reduce the amount of calculation. At last, the high precision and effectiveness of the new method are verified by numerical experiments. Experiments show that: Starting from the equivalent integral form of the fractional diffusion wave equation, a second-order finite-difference scheme of the fractional-order diffusive wave equation is constructed, through numerical experiments, it is verified that the scheme has good accuracy and efficiency. In numerical solution, discrete integral equations have better numerical stability than differential equations, therefore, the format also has better stability. When taking different fractional derivative indices a=1.5 and a=1.8, it can be seen that the difference format constructed by the author, in the ti

关键词： Accounting informatization Financial software Fractional order Differential equation numerical algorithm

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STUDY OF FLOW AND TEMPERATURE IN RESIN TRANSFER MOLDING PROCESS BY numerical MODEL

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Transactions of Nanjing University of Aeronautics and Astronautics 2003年第2期20卷 165-171页

作者：陈仁良李明成南京航空航天大学航空宇航学院

A mathematical model of resin flow and temperature variation in the filling stage of the resin transfer molding (RTM) is developed based on the control volume/finite element method (CV/FEM). The effects of the heat transfer and chemical reaction of the resin on the flow and temperature are considered. The numerical algorithm of the resin flow and temperature variation in the process of RTM are studied. Its accuracy and convergence are analyzed. The comparison of temperature variations between experimental results and model predictions is carried out for two RTM cases. Result shows that the model is efficient for evaluating the flow and temperature variation in the filling stage of RTM and there is a good coincidence between theory and experiment.

关键词： resin transfer molding mathematical modeling numerical algorithm heat transfer

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AI OPTIMIZATION OF THE EXOTHERMIC REACTION OF ETHYLENE OXIDE WITH WATER

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BIOMEDICAL ENGINEERING-APPLICATIONS BASIS COMMUNICATIONS 2021年第5期33卷

作者： Al-Utaibi, Khaled A. Sohail, Ayesha Zafar, Andleeb Talha, Rana Sait, Sadiq M. Univ Hail Comp Sci & Software Engn Dept Hail Saudi Arabia Comsats Univ Dept Math Lahore 54000 Pakistan Geol Survey Pakistan Geosci Adv Res Labs Islamabad Pakistan King Fahd Univ Petr & Minerals Ctr Commun & IT Res Res Inst Dhahran 31261 Saudi Arabia

A computational framework, for the numerical approximation of the exothermic reaction of ethylene oxide (EO) with water, to form ethylene glycol is presented in this paper. Ethylene Glycol also known as Mono-ethylene Glycol (MEG), is a diol with a boiling of 198 degrees C and conventionally produced through hydrolysis of ethylene oxide which is obtained through the oxidation of ethylene. It is used as an excellent automobile coolant as the 1:1 ratio mixture of MEG with Water boils at 129 degrees C and freezes at - 37 degrees C. Other than its use as an antifreeze, it is also used as a reagent during the production of polyester fibers, pharmaceutics, cosmetics, hydraulic fluids, printing inks, explosives, polyesters and paint solvents. The mathematical model presented here, consists of an energy balance and a material balance system, described in an axisymmetric coordinate system. The optimized resulting values using the artificial intelligence approach are summarized in this paper. We derive an analytical solution. The analytical solution for the mathematical model equations is in general not possible for this model but it may be possible to derive an analytical solution to this mathematical model if we consider the equation for the conservation of material (chemical species) as a formulation for plug flow and isothermal conditions. Noteworthy findings are reported in this paper for future research.

关键词： Chemical reaction Energy balance numerical algorithm Optimization

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algorithm for shear flows in arbitrary cross-sections of thin-walled bars

MAGAZINE OF CIVIL ENGINEERING

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MAGAZINE OF CIVIL ENGINEERING 2019年第8期92卷 3-26页

作者： Yurchenko, V Kyiv Natl Univ Construct & Architecture Kiev Ukraine

Development of a general computer program for the design and verification of thin-walled bar structural members remains an actual task. Despite the prevailing influence of normal stresses on the stress-strain state of thin-walled bars design and verification of thin-walled structural members should be performed taking into account not only normal stresses, but also shear stresses. Therefore, in the paper a thin-walled bar of an arbitrary cross-section which is undergone to the general load case is considered as investigated object. The main research question is development of mathematical support and knoware for numerical solution for the shear stresses problem with orientation on software implementation in a computer-aided design system for thin-walled bar structures. The problem of shear stresses outside longitudinal edges of an arbitrary cross-section (including open-closed multi-contour cross-sections) of a thin-walled bar subjected to the general load case has been considered in the paper. The formulated problem has been reduced to the searching problem for unknown shear forces flows that have the least value of the Castigliano's functional. Besides, constraints-equalities of shear forces flows equilibrium formulated for cross-section branch points, as well as equilibrium equation formulated for the whole cross-section relating to longitudinal axes of the thin-walled bar have been taken into account. A detailed numerical algorithm intended to solve the formulated problem has been proposed by the paper. The algorithm is oriented on software implementation in systems of computer-aided design of thin-walled bar structures. Developed algorithm has been implemented in SCAD Office environment by the program TONUS. numerical examples for calculation of thin-walled bars with open and open-closed multi-contour cross-sections have been considered in order to validate developed algorithm and verify calculation accuracy for sectorial cross-section geometrical properties an

关键词： thin-walled bar arbitrary cross-section shear forces flow closed contour graph theory numerical algorithm numerical examples software implementation

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Validity and error analysis of calculating matrix exponential function and vector product

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NONLINEAR ENGINEERING - MODELING AND APPLICATION 2024年第1期13卷

作者： Tu, Lihui Hong, Huanjie NingboTech Univ Sch Comp & Data Engn Ningbo 315100 Peoples R China

In this study, an efficient calculation method of matrix exponential function and vector product is proposed to reduce the calculation error. This method is based on the flexible exponential integral scheme;using B-series theory and two-color tree theory, the numerical series expression is obtained, and the exponential integral of the matrix exponential function is solved. By constructing a specific numerical integration scheme and analyzing its convergence under the theoretical framework of analytic semigroups, the convergence analysis of numerical schemes is studied and perfected. The numerical results show that the proposed method of matrix exponential function and vector product has a small error, which shows obvious advantages in reducing the calculation error.

关键词： matrix exponential function vector product efficient calculation numerical algorithm

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Multiple covering of a closed set on a plane with non-Euclidean metrics

Multiple covering of a closed set on a plane with non-Euclid...

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17th IFAC Technical-Committee-on-Optimal-Control (TC 2.4) Workshop on Control Applications of Optimization (CAO)

作者： Lempert, Anna Le, Quang Mung Russian Acad Sci Siberian Branch Matrosov Inst Syst Dynam & Control Theory Irkutsk Russia Irkutsk Natl Res Tech Univ Irkutsk Russia

The article is devoted to multiple circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Such statements arise in the construction of global navigation systems like GPS and Glonass. A similar problem appears in infrastructure logistics if there is a main servicing system and it is necessary to create a duplicate system to support service in the case of failure of one or more nodes. To solve this problem, we propose a computational algorithm based on a combination of the optical -geometric approach due to Fermat and Huygens principles and Voronoi diagram. A key feature of the algorithm is the ability to deal with non-Euclidean metrics. numerical results and a comparison with known approaches are presented and discussed. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： multiple covering problem k-fold covering problem optical-geometric approach Voronoi diagram non-Euclidean metric numerical algorithm computational experiment

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Research on a Specific Harmonic Elimination Technique for Step Wave of Cascade Type H Bridge Converters

Research on a Specific Harmonic Elimination Technique for St...

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2015 5th International Conference on Computer Sciences and Automation Engineering(ICCSAE 2015)

作者： Anqi Li Department of Electrical Engineering North China Electric Power University

With the rapid development of power electronic technology, power electronic equipments with inverter devices as the main circuit structure are widely used, producing numerous harmonics and having a harmful effect on power grids and electricity equipments. This paper uses the improved genetic algorithm model and least square optimization model to calculate the switch angle when specific harmonic is eliminated and put forward the auxiliary control strategy to achieve power balance in each H bridge converter unit in a certain period.

关键词： selective harmonic elimination the improved genetic algorithm least squares optimization 0-1 planning numerical algorithm

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A new fractional mathematical modelling of COVID-19 with the availability of vaccine

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RESULTS IN PHYSICS 2021年 24卷 104213-104213页

作者： Kumar, Pushpendra Erturk, Vedat Suat Murillo-Arcila, Marina Cent Univ Punjab Sch Basic & Appl Sci Dept Math & Stat Bathinda 151001 Punjab India Ondokuz Mayis Univ Fac Arts & Sci Dept Math TR-55200 Atakum Samsun Turkey Univ Politecn Valencia Inst Univ Matemat Pura & Aplicada Valencia 46022 Spain

The most dangerous disease of this decade novel coronavirus or COVID-19 is yet not over. The whole world is facing this threat and trying to stand together to defeat this pandemic. Many countries have defeated this virus by their strong control strategies and many are still trying to do so. To date, some countries have prepared a vaccine against this virus but not in an enough amount. In this research article, we proposed a new SEIRS dynamical model by including the vaccine rate. First we formulate the model with integer order and after that we generalize it in Atangana-Baleanu derivative sense. The high motivation to apply Atangana-Baleanu fractional derivative on our model is to explore the dynamics of the model more clearly. We provide the analysis of the existence of solution for the given fractional SEIRS model. We use the famous Predictor-Corrector algorithm to derive the solution of the model. Also, the analysis for the stability of the given algorithm is established. We simulate number of graphs to see the role of vaccine on the dynamics of the population. For practical simulations, we use the parameter values which are based on real data of Spain. The main motivation or aim of this research study is to justify the role of vaccine in this tough time of COVID-19. A clear role of vaccine at this crucial time can be realized by this study.

关键词： COVID-19 Vaccine Virus Mathematical model numerical algorithm Atangana-Baleanu fractional derivative

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