The Problem Optimization Triangular Geometric Line Field

Antoshkin, Vasilij Dmitrievich; Травуш, Владимир; Erofeev, Vladimir; Rimshin, Vladimir; Kurbatov, Vladimir Leonidovich

doi:10.5539/mas.v9n3p46

Cited by 34 publications

(17 citation statements)

References 4 publications

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“…From figure 2 it is seen that the optimal triangular network on the sphere is obtained if these are right spherical triangles hexagons inscribed in circles of the smallest radius [1] and placed in the first two rows are compatible spherical triangles sphere b-90-90 о .…”

Section: Resultsmentioning

confidence: 99%

“…The problem of the emplacement of regular and irregular hexagons on the sphere, inscribed in a circles, i.e., flat figures or composed ones of spherical triangles (See Figure 1) with minimum dimensions of the ribs, has an effective solution in the form of a network, formed on the basis of minimum radii circles, i.e., circles on a sphere obtained by the touch of three adjacent circles whose centers are at the shortest distance from each other. [1][2][3][5][6][7][8].However, sometimes there is a possibility of emplacement of two evenly alternating rows of regular hexagons, starting from the equator (Figure 1). …”

Section: Introductionmentioning

confidence: 99%

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To the problem 6 of emplacement of triangular geometric net on the sphere

Травуш¹,

Antoshkin

Erofeyeva

2017

MATEC Web Conf.

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Abstract.Thesphere creates the minimal surface of enclosing structures and has unique resource saving qualities which makes it indispensable in the construction of "smart buildings». One of the methods of formation of triangular networks in the sphere was investigated. Conditions of the problem of locating a triangular network in the area were established. The evaluation criterion of solution effectiveness of the problem is the minimum number of type-sizes of dome panels, the possibility of preassembly and pre-stressing. The solution of the problem of the triangular network emplacement in a compatible spherical triangle on the sphere variant was provided. The problem of the emplacement of regular and irregular hexagons on the sphere, inscribed in a circles, i.e., flat figures or composed ones of spherical triangles with minimum dimensions of the ribs, has an effective solution in the form of a network, formed on the basis of minimum radii circles, i.e., circles on a sphere obtained by the touch of three adjacent circles whose centers are at the shortest distance from each other. The optimization of triangular geometric network on a sphere on the criterion of minimum sizes of elements can be solved by emplacementin the system the irregular hexagons inscribed in circles of minimal sizes, the maximum of regular hexagons.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

To the problem 6 of emplacement of triangular geometric net on the sphere

Травуш¹,

Antoshkin

Erofeyeva

2017

MATEC Web Conf.

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“…However, in case of building vertical extension even with only one storey, strengthening of floor structure raises many questions concerning reliability and light weight of the new structure, as well as stability of the existing one. Provision of solutions for these questions will substantially help to strengthen the structure and extend its service life without need for regular repairs [5][6][7].…”

Section: Methodsmentioning

confidence: 99%

Application of composite reinforcement for modernization of buildings and structures

Cherkas

Rimshin

2017

MATEC Web Conf.

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Abstract. Properties of new reinforcing element -composite reinforcement, are considered. Feasibility study of using this material for modernization of buildings, namely for vertical extension with additional storey, is carried out. Comparative analysis of performance is conducted for metal and composite reinforcement, as well as calculations are performed which results will be used for determination of advantages and disadvantages of this innovative reinforcing method. An important factor for development of projects of building vertical extension after quite a long operation period is a proper selection of construction materials and strength analysis considering the structures to be erected. Calculation of a floor slab erected with using composite fiberglass reinforcement is represented. Results obtained in the calculation and the analysis of the data prove high efficiency of this reinforcing method through the decrease of loads on lower storeys of the building, economic feasibility and other factors.

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“…На схемах рисунков 1 и 2 приведено размеще-ние описанных окружностями пятиугольника и шестиугольника в сферическом треуголь-нике (совместимом сегменте [1][2][3][4][5][6][7][8][9] сфери-ческого икосаэдра) с внутренними углами 36, 90 и 60 о . Указанное размещение центров окружностей, описывающих неправильные и правильные шестиугольники, выполним для разрезки в виде 320-гранника (рис.…”

Section: решениеunclassified

The Problem of Emplacement of Triangular Geometric Net on the Sphere With Nodes on the Same Level

Antoshkin

2017

IJCCSE

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Мордовский государственный университет им. Н.П. Огарева, г. Саранск, РОССИЯ Аннотация: Исследован один из методов образования треугольных сетей на сфере. Поставлены условия задачи размещения треугольной сети на сфере. Критерием оценки эффективности решения задачи явля-ется минимальное число типоразмеров панелей купола, возможность укрупнительной сборки и предва-рительного напряжения. Приведено решение одного варианта задачи размещения треугольной сети в сов-местимом сферическом треугольнике и, соответственно, на сфере. Размещение на сфере правильных и неправильных шестиугольников, вписанных в окружности, т.е. фигур плоских или составленных в свою очередь из сферических треугольников с минимальными размерами ребер, имеет эффективное решение в виде сети, образованной на основе окружностей минимальных радиусов, т.е. окружностей на сфере, полу-ченных при касании двух смежных окружностей, центры которых находятся на наименьшем расстоянии друг от друга. Задача выравнивания опор на одном уровне может быть решена размещением в системе правильных шестиугольников и пятиугольников неправильных шестиугольников, вписанных в окружно-сти минимальных размеров.Ключевые слова: сборная сферическая оболочка, треугольная геометрическая сеть, описанная окружность, правильный шестиугольник, разрезка, купол, оптимизация THE PROBLEM OF EMPLACEMENT OF TRIANGULAR GEOMETRIC NET ON THE SPHERE WITH NODES ON THE SAME LEVEL Vasilij D. Antoshkin Mordovian State University, Saransk, RussiaAbstract: One of the methods of formation of triangular networks in the field is investigated. Conditions of the problem of locating a triangular network in the area are delivered. The criterion for assessing the effectiveness of the solution of the problem is the minimum number of sizes of the dome panels, the possibility of pre-assembly and pre-stressing. The solution of the problem of one embodiment of a triangular network of accommodation in a compatible spherical triangle and, accordingly, on the sphere. Placing on the area of regular and irregular hexagon inscribed in a circle, ie, flat figures or composed in turn of spherical triangles with minimum dimensions of the ribs, is an effective solution in the form of a network formed by circles of minimum radii, ie, circles on a sphere obtained at the touch of three adjacent circles whose centers are at the shortest distance from each other. Task align the supports at one level can be resolved by placement in the regular hexagons and irregular pentagons hexagons inscribed in a circle of minimum size..

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The Problem Optimization Triangular Geometric Line Field

Cited by 34 publications

References 4 publications

To the problem 6 of emplacement of triangular geometric net on the sphere

To the problem 6 of emplacement of triangular geometric net on the sphere

Application of composite reinforcement for modernization of buildings and structures

The Problem of Emplacement of Triangular Geometric Net on the Sphere With Nodes on the Same Level

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