The problem 4 of placement triangular geometric line field

Antoshkin

Erofeyeva

2017

MATEC Web Conf.

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.

Section: Resultsmentioning

confidence: 99%

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

Antoshkin

Erofeyeva

2017

MATEC Web Conf.

“…Similarly, we find the value of . The scheme of figure 4 shows the placement of circles of the same radius, which allows to create an effective design of the dome of two independent systems of frames in the form of the same arches [14][15][16][17][18][19][20][21].…”

Section: Decisionmentioning

confidence: 99%

“…us transform the system of equations (1 and 2) using the formulas[14][15][16][17][18][19][20][21][22] …”

mentioning

confidence: 99%

Network from the circles of the same radius for sustainable energy-efficient roof structures

Antoshkin

Svyatkina³

2019

E3S Web Conf.

In this research paper, we investigated one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra. The variants of cutting sustainable energy-efficient coatings of buildings in the form of spherical domes are proposed. The task conditions of placing the specified network on the sphere are set. The criterion for evaluating the effectiveness of solving the problem is the minimum number of standard sizes of segments of the dome arches, the possibility of using pre-assembly technologies. The solution of one variant of the problem as placing the network on a spherical icosahedron and, accordingly, on a sphere is given. The placement of arches of one radius on the sphere, different from the location in the form of meridians, has an effective solution in the form of a network with minimal dimensions of arch segments and with nodes of paired arches comprised on the basis of circles of the same radii formed on the ground of regular spherical polyhedra. The problem is solved by constructing and combining in a system of regular spherical polyhedral with independent frameworks of arches of the same radius on the basis of paired circles of equal radius.

“…cos O 11 = tg ‫ݔ‬ tg 2ρ 1 (22) where the internal angle O 11 = СO 11 O 12 = МO 11 Е. All sizes in this expression are determined, excepting the angletgܽ 1 .…”

Section: Remarkmentioning

confidence: 99%

“…For a given position of the center of the first rows of hexagons inscribed in a circle, the angles change, and hence, the optimization are possible only for centered hexagons О 2 -О 3 [8,9,[16][17][18][19][20][21][22].…”

Section: Remarkmentioning

confidence: 99%

To the problem 5 of emplacement of triangular geometric net on the sphere

Antoshkin²,

Konovalov³

2017

MATEC Web Conf.

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.