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THEORETICAL STUDIES OF PRECAST SPHERICAL SHELLS

The problem of optimisation of a triangular geometrical network on sphere by criterion of a minimum of standard sizes of elements as it has already been noted, was put by many authors of various systems spherical razrezok [2, 44, 65, 68, 90, 94, 118, 122, 127, 141, 162, 166-168 etc.] In all cases of decisions was one or several schemes razrezok spheres with use, basically, symmetry axes in the form of the main lines (lines of the big circles of sphere), lines of parallel sectional views of sphere, and also compatibility of parts of sides of correct polyhedrons. Various mathematical shchkoly [2, 44, 65, 68, 90, 94, 118, 122, 127, 141, 162, 166-168 etc.] Have convincingly proved, that an optimum triangular network on a plane is the network from equaterial triangles which are combined in different combinations of correct hexagons which, in turn, can be described a network of crossed circles (are captured all triangles) or concerning circles (it is regular through one triangle, see fig. 2.1 and,). Also it has been proved, that if between such systems on a plane and on other surface there is a projective communication sproetsirovannaja the triangular network also will be optimum by criterion of lengths of the parties of triangles.

Placing on sphere of the correct and wrong hexagons entered in circles is obvious, that, i.e. figures flat or the hexagons (pyramids) made in turn from flat triangles (fig. 2.1 and,) with minimum dimensions of ridges, gives the optimum decision of a triangular network on sphere. Besides such network is formed on the basis of circles of the minimum radiuses, i.e. circles on the sphere, three adjacent circles received at a contact which centres are on the least distance from each other [4-14,17-19].

It is possible to present a spherical hexagon as two quadrilaterals with the set parties and it has the maximum area

When it is entered in a circle. The hexagonal panels entered in circles with the minimum radiuses (i.e. concerning), will have minimum dimensions and the maximum areas at the set number of sides of a triangular network of sphere. I.e. elements of a network in the form of radiuses will have the minimum length as represent the shortest distances centre to centre circles, and the contours entered in circles, also will have minimum dimensions. Formation of correct hexagons in this network is possible as a special case. Thus, for each variant razrezki the optimum decision on a material minimum (length of elements) is placing of the hexagons entered in circles, and in the first optimum variant adjacent three circles concern each other. Optimisation of a triangular geometrical network on sphere by criterion of a minimum of standard sizes of elements can be presented placing in system of the wrong hexagons entered in circles of minimum dimensions, a maximum of correct hexagons, for example, in compatible spherical triangles (segments) with radially ring basis, in sectors with one vertex in the centre; and also in compatible spherical triangles (segments) of correct polyhedrons (ikosaedra, an octahedron and a tetrahedron) with use of every possible basic networks for the centres of circles and with schemes razrezok, shown on fig. 2.1, 2.2.

Except variants of application of properties of symmetry of the main things and parallel lines of circles of sphere, in similar razrezkah possibilities of the central symmetry of circles [5, 6] and an effective basic network of the centres of circles should be realised.

2.1.

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A source: Antoshkin Vasily Dmitrievich. is constructive-TECHNOLOGICAL DECISIONS of PRECAST SPHERICAL SHELLS. The dissertation on competition of a scientific degree of a Dr.Sci.Tech. Saransk - 2017. 2017

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