Analtical Calculation of the Deflection of a Spatial Hinge-Rod Frame with an Arbitrary Number of Panels

2020 ◽  
pp. 68-77
Author(s):  
М. Н. Кирсанов
Keyword(s):  
Arbitrary Number ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Asymptotic Approximations ◽  
Induction Method ◽  
Symbolic Form ◽  
Regular Type ◽  
Proposed Model ◽  
Different Types ◽  
Independent Parameters

Постановка задачи. Ставится задача получить в символьном виде зависимость прогиба предлагаемой схемы статически определимой пространственной фермы регулярного типа от числа панелей при различных нагрузках, в том числе при нагрузке из плоскости фермы. Ферма имеет два независимых параметра, задающие ее пропорции. Результаты. Для нескольких видов нагружения по формуле Максвелла-Мора выведены аналитические зависимости прогибов конструкции от числа панелей, нагрузки и размеров. При обобщении серии частных решений с заданным числом панелей на произвольное число панелей совместно с операторами системы компьютерной математики Maple использован метод индукции. Получены асимптотические приближения решений. Выводы. Предложенная схема пространственной рамы с двумя независимыми числами панелей, задающими пропорции конструкции, допускает аналитическое решение задачи о прогибе при различных видах нагружения. Выведенные формулы могут быть использованы как тестовые для оценки приближенных численных решений и в задачах оптимизации. Statement of the problem. The task is to obtain in symbolic form the dependence of the deflection of the proposed scheme of a statically definable spatial truss of a regular type on the number of panels under various loads, including the load from the truss plane. A truss has two independent parameters that define its proportions. Results. For several types of loading according to the Maxwell - Mohr formula, analytical dependences of the deflections of the structure on the number of panels, load, and dimensions are derived. When generalizing a series of partial solutions with a given number of panels to an arbitrary number of panels, together with operators of the Maple computer mathematics system, the induction method is used. Asymptotic approximations of solutions are obtained. Conclusions. The proposed model of a spatial frame with two independent numbers of panels that define the proportions of the structure allows an analytical solution of the problem of deflection under different types of loading. The derived formulas can be used as test formulas for evaluating approximate numerical solutions and for optimization problems.

scholarly journals ANALYTICAL CALCULATION OF THE DEFLECTIONOF A SPATIAL HINGE-ROD FRAME WITH AN ARBITRARY NUMBER OF PANELS

2020 ◽  
pp. 65-75
Author(s):  
M. N. Kirsanov
Keyword(s):  
Arbitrary Number ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Analytical Calculation ◽  
Induction Method ◽  
Symbolic Form ◽  
Regular Type ◽  
Proposed Model ◽  
Different Types ◽  
Independent Parameters

Statement of the problem. The task is to obtain in symbolic form the dependence of the deflection of the proposed scheme of a statically definable spatial truss of a regular type on the number of panels under various loads, including the load from the truss plane. A truss has two independent parameters that define its proportions.Results. For several types of loading according to the Maxwell - Mohr formula, analytical dependences of the deflections of the structure on the number of panels, load, and dimensions are derived. When generalizing a series of partial solutions with a given number of panels to an arbitrary number of panels, together with operators of the Maple computer mathematics system, the induction method is used. Asymptotic approximations of solutions are obtained.Conclusions. The proposed model of a spatial frame with two independent numbers of panels that define the proportions of the structure allows an analytical solution of the problem of deflection under different types of loading. The derived formulas can be used as test formulas for evaluating approximate numerical solutions and for optimization problems.

Analytical Calculation of Deformations and Kinematic Analysis of a Flat Truss with an Arbitrary Number of Panels

2021 ◽  
pp. 113-122
Author(s):  
М. Н. Кирсанов ◽  
О. В. Воробьев
Keyword(s):  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Analytical Calculation ◽  
Middle Part ◽  
Asymptotic Approximations ◽  
Induction Method ◽  
Particular Solutions

Постановка задачи. Разыскиваются аналитические зависимости прогиба и смещения опоры плоской фермы решетчатого вида от числа панелей. Ферма имеет сдвоенную решетку, прямолинейный нижний и приподнятый в средней части верхний пояс. Результаты. Для двух видов нагружения по формуле Максвелла-Мора получены аналитические зависимости прогибов конструкции от нагрузки, размеров и числа панелей. Для обобщения серии частных решений с различным числом панелей ферм на произвольный случай использован метод индукции и аналитические возможности системы компьютерной математики Maple. Для некоторых решений получены асимптотические приближения. Показано распределение усилий в элементах фермы. Выводы. Полученные формулы могут быть использованы в задачах оптимизации и как тестовые для оценки приближенных численных решений. Выявлены случаи геометрической изменяемости фермы при числе панелей, кратном трем. Приведен алгоритм выявления соответствующего распределения возможных скоростей шарниров. Statement of the problem. Analytical dependences of the deflection and displacement of the support of a flat lattice truss on the number of panels are being sought. The truss has a double lattice, a rectilinear lower belt and an upper belt raised in the middle part. Results. For two types of loading, according to the Maxwell-Mohr formula, analytical dependences of the deflections of the structure on the load, dimensions and number of panels are obtained. To generalize a series of particular solutions for trusses with different numbers of panels for an arbitrary case, the induction method and the analytical capabilities of the Maple computer mathematics system were used. For some solutions, asymptotic approximations are obtained. The distribution of forces in the rods of the structure is shown. Conclusions. The obtained formulas can be used in optimization problems and as test ones for evaluating approximate numerical solutions. Cases of geometric variability of the truss with the number of panels being a multiple of three are revealed. An algorithm for identifying the corresponding distribution of possible velocities of the joints is presented.

scholarly journals Calculation of deformations of a cantilever-frame planar truss model with an arbitrary number of panels

Vestnik MGSU ◽  
2020 ◽  
pp. 510-517
Author(s):  
Karina Buka-Vaivade ◽  
Mikhail N. Kirsanov ◽  
Dmitrijs O. Serdjuks
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Engineering Practice ◽  
Symbolic Form ◽  
Concentrated Load ◽  
Structural Rigidity ◽  
Truss Model ◽  
Different Types ◽  
Homogeneous Linear ◽  
Independent Parameters

Introduction. By method of induction using three independent parameters (numbers of panels) formulas for deflection under different types of loading are derived. Curves based on the derived formulas are analyzed, and the asymptotic of solutions for the number of panels are sought. The frame is statically definable, symmetrical, with descending braces. The problem of deflection under the action of a load evenly distributed over the nodes of the upper chord, a concentrated load in the middle of the span, and the problem of shifting the mobile support is considered. Materials and methods. The calculation of forces in the truss bars is performed in symbolic form using the method of cutting nodes and operators of the Maple computer mathematics system. The deflection is determined by the Maxwell – Mohr formula. Operators of the Maple computer mathematics system are used for composing and solving homogeneous linear recurrent equations that satisfy sequences of coefficients of the required dependencies. The stiffness of all truss bars is assumed to be the same. Results. All the obtained dependencies have a polynomial form for the number of panels. To illustrate the obtained solutions and their qualitative analysis, curves of the deflection dependence on the number of panels are constructed. Conclusions. A scheme of a statically definable three-parameter truss is proposed that allows an analytical solution of the problem of deflection and displacement of the support. The obtained dependences can be used in engineering practice in problems of structural rigidity optimization and for evaluating the accuracy of numerical solutions.

scholarly journals ANALYTICAL SOLUTION OF THE FREQUENCY OF THE LOAD OSCILLATION AT AN ARBITRARY GIRDER NODE IN THE SYSTEM MAPLE

2019 ◽  
pp. 3-3
Author(s):  
Mikhail N. Kirsanov ◽  
Dmitriy V. Tinkov
Keyword(s):  
Analytical Solution ◽  
Arbitrary Number ◽  
Analytical Form ◽  
Labor Costs ◽  
Induction Method ◽  
Regular Type ◽  
Final Formula ◽  
The Common ◽  
Two Stages ◽  
Elastic Lattice

Introduction. We study the oscillations of a massive load on a planar statically definable symmetric truss of a regular type with parallel belts. Truss weight is not included. Free vertical oscillations are considered. The stiffness of the truss rods is assumed to be the same, the deformations are elastic. Lattice of the truss is double with descending braces and racks. New in the formulation and solution of the problem is the analytical form of the solution, which makes it possible in practice to easily evaluate the frequency characteristics of the structure depending on an arbitrary number of truss panels and the location of the load. Materials and methods. The operators and methods of the system of computer mathematics Maple are used. To determine the forces in the rods, the knotting method is used. The common terms of the sequence of coefficients of solutions for different numbers of panels are obtained from solving linear homogeneous recurrent equations of various order, obtained by special operators of the Maple system. Dependence on two arbitrary natural parameters is revealed in two stages. First, solutions for fixed load positions are found, then these solutions are summarized into one final formula for frequency. Results. By a series of individual solutions to the problem of load oscillation using the double induction method, it was possible to find common members of all sequences. The solution is polynomial in both natural parameters. Graphs constructed for particular cases, showed the adequacy of the approach. The discontinuous non-monotonic nature of the intermittent change depending on the number of truss panels and some other features of the solution are noted. Conclusions. It is shown that the induction method, previously applicable mainly to statics problems with one parameter (number of truss panels), is fully operational to the problems of the oscillations of system with two natural parameters. It should be noted that significant labor costs and a significant increase in the time symbolic transformations in such tasks

scholarly journals Analytical calculation of deformations of a truss for a long span covering

Vestnik MGSU ◽  
2020 ◽  
pp. 1399-1406
Author(s):  
Mikhail N. Kirsanov
Keyword(s):  
Structural Optimization ◽  
Qualitative Analysis ◽  
Arbitrary Number ◽  
Numerical Solutions ◽  
Analytical Calculation ◽  
Linear Recurrence ◽  
Induction Method ◽  
Design Formula ◽  
Long Span ◽  
Final Design

Introduction. The method of induction based on the number of panels is employed to derive formulas designated for deflection of a square in plan hinged rod structure, which has supports on its sides and which consists of individual pyramidal rod elements. The truss is statically determinable and symmetrical. Some features of the solution are identified on the curves constructed according to derived formulas. Materials and methods. The analysis of forces arising in the rods of the covering is performed symbolically using the method of joint isolation and operators of the Maple symbolic math engine. The deflection in the centre of the covering is found by the Maxwell–Mohr’s formula. The rigidity of truss rods is assumed to be the same. The analysis of a sequence of analytical calculations of trusses, having different numbers of panels, is employed to identify coefficients, designated for deflection and reaction at the supports, in the final design formula. The induction method is employed for this purpose. Common members of sequences of coefficients are derived from the solution of linear recurrence equations made using Maple operators. Results. Solutions, obtained for three types of loads, are polynomial in terms of the number of panels. To illustrate the solutions and their qualitative analysis, curves describing the dependence of deflection on the number of panels are made. The author identified the quadratic asymptotics of the solution with respect to the number of panels. The quadratic asymptotics is linear in height. Conclusions. Formulas are obtained for calculating deflection and reactions of covering supports having an arbitrary number of panels and dimensions if exposed to three types of loads. The presence of extremum points on solution curves is shown. The dependences, identified by the author, are designated both for evaluating the accuracy of numerical solutions and for solving problems of structural optimization in terms of rigidity.

scholarly journals Application of Blockchain in Education: GDPR-Compliant and Scalable Certification and Verification of Academic Information

2021 ◽  
Vol 11 (10) ◽  
pp. 4537
Author(s):  
Christian Delgado-von-Eitzen ◽  
Luis Anido-Rifón ◽  
Manuel J. Fernández-Iglesias
Keyword(s):  
Data Protection ◽  
Personal Data ◽  
General Data Protection Regulation ◽  
Certification System ◽  
Proposed Model ◽  
Different Types ◽  
International Regulations ◽  
Innovative Solution ◽  
General Data ◽  
Academic Information

Blockchain technologies are awakening in recent years the interest of different actors in various sectors and, among them, the education field, which is studying the application of these technologies to improve information traceability, accountability, and integrity, while guaranteeing its privacy, transparency, robustness, trustworthiness, and authenticity. Different interesting proposals and projects were launched and are currently being developed. Nevertheless, there are still issues not adequately addressed, such as scalability, privacy, and compliance with international regulations such as the General Data Protection Regulation in Europe. This paper analyzes the application of blockchain technologies and related challenges to issue and verify educational data and proposes an innovative solution to tackle them. The proposed model supports the issuance, storage, and verification of different types of academic information, both formal and informal, and complies with applicable regulations, protecting the privacy of users’ personal data. This proposal also addresses the scalability challenges and paves the way for a global academic certification system.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

Optimization of Cold-Formed Channel Sections Using Imperialist Competitive Algorithm

2012 ◽  
Vol 166-169 ◽  
pp. 493-496
Author(s):  
Roya Kohandel ◽  
Behzad Abdi ◽  
Poi Ngian Shek ◽  
M.Md. Tahir ◽  
Ahmad Beng Hong Kueh
Keyword(s):  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Imperialist Competitive Algorithm ◽  
Computational Method ◽  
Compression Force ◽  
Sqp Method ◽  
Competitive Algorithm ◽  
Different Types ◽  
Formed Channel ◽  
Good Agreement

The Imperialist Competitive Algorithm (ICA) is a novel computational method based on the concept of socio-political motivated strategy, which is usually used to solve different types of optimization problems. This paper presents the optimization of cold-formed channel section subjected to axial compression force utilizing the ICA method. The results are then compared to the Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) algorithm for validation purpose. The results obtained from the ICA method is in good agreement with the GA and SQP method in terms of weight but slightly different in the geometry shape.

scholarly journals Optimization of Consignment-Store-Based Supply Chain with Black Hole Algorithm

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Ágota Bányai ◽  
Tamás Bányai ◽  
Béla Illés
Keyword(s):  
Black Hole ◽  
Supply Chain ◽  
Optimization Problems ◽  
Optimization Method ◽  
Chain Model ◽  
Supply Chain Optimization ◽  
Proposed Model ◽  
Supply Chain Model ◽  
Supply Model ◽  
Black Hole Algorithm

The globalization of economy and market led to increased networking in the field of manufacturing and services. These manufacturing and service processes including supply chain became more and more complex. The supply chain includes in many cases consignment stores. The design and operation of these complex supply chain processes can be described as NP-hard optimization problems. These problems can be solved using sophisticated models and methods based on metaheuristic algorithms. This research proposes an integrated supply model based on consignment stores. After a careful literature review, this paper introduces a mathematical model to formulate the problem of consignment-store-based supply chain optimization. The integrated model includes facility location and assignment problems to be solved. Next, an enhanced black hole algorithm dealing with multiobjective supply chain model is presented. The sensitivity analysis of the heuristic black hole optimization method is also described to check the efficiency of new operators to increase the convergence of the algorithm. Numerical results with different datasets demonstrate how the proposed model supports the efficiency, flexibility, and reliability of the consignment-store-based supply chain.

scholarly journals Truncated Inception Net: COVID-19 Outbreak Screening using Chest X-rays

2020 ◽  
Author(s):  
Dipayan Das ◽  
KC Santosh ◽  
Umapada Pal
Keyword(s):  
Neural Network ◽  
World Wide ◽  
Imaging Techniques ◽  
Imaging Systems ◽  
Ct Scans ◽  
X Rays ◽  
X Ray ◽  
X Ray Imaging ◽  
Proposed Model ◽  
Different Types

Abstract Since December 2019, the Coronavirus Disease (COVID-19) pandemic has caused world-wide turmoil in less than a couple of months, and the infection, caused by SARS-CoV-2, is spreading at an unprecedented rate. AI-driven tools are used to identify Coronavirus outbreaks as well as forecast their nature of spread, where imaging techniques are widely used, such as CT scans and chest X-rays (CXRs). In this paper, motivated by the fact that X-ray imaging systems are more prevalent and cheaper than CT scan systems, a deep learning-based Convolutional Neural Network (CNN) model, which we call Truncated Inception Net, is proposed to screen COVID-19 positive CXRs from other non-COVID and/or healthy cases. To validate our proposal, six different types of datasets were employed by taking the following CXRs: COVID-19 positive, Pneumonia positive, Tuberculosis positive, and healthy cases into account. The proposed model achieved an accuracy of 99.96% (AUC of 1.0) in classifying COVID- 19 positive cases from combined Pneumonia and healthy cases. Similarly, it achieved an accuracy of 99.92% (AUC of 0.99) in classifying COVID-19 positive cases from combined Pneumonia, Tuberculosis and healthy CXRs. To the best of our knowledge, as of now, the achieved results outperform the existing AI-driven tools for screening COVID-19 using CXRs.

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