No abstract

One of the a method of formation of triangular networks in the field is investigated. Conditions 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 elements, the possibility of pre-assembly and prestressing. The solution of the problem of one embodiment of a triangular network of accommodation in a compatible spherical triangle and, accordingly, on the sphere. Optimization of triangular geometric network on a sphere on the criterion of minimum sizes of elements can be solved by placing the system in an irregular hexagon inscribed in a circle of minimal size, maximum regular hexagons.

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..

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.

Abstract. The sphere 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 spherewas 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 pre-assembly and prestressing. 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 emplacementinthe system the irregular hexagons inscribed in circles of minimal sizes, the maximum of regular hexagons.