scholarly journals Octahedron-based spatial bar structures - the form of large areas covers

2018 ◽  
Vol 174 ◽  
pp. 03007
Author(s):  
Dominika Pilarska
Keyword(s):  
Static Analysis ◽  
Equilateral Triangle ◽  
Regular Octahedron ◽  
Regular Polyhedra ◽  
Geodesic Domes ◽  
Paper Method

The large areas covers may be designed as the spatial dome constructions where the basis of their shaping are regular polyhedra. The paper presents eight new designed spatial bar structures as geodetic domes with a span of 50 m. The basis of their shaping is the regular octahedron. This polyhedron has not been recognized in detail as the basis for geodesic domes designing. Using second method of the division of the initial equilateral triangle proposed by professor Fuliński, bar domes generated from 2904-hedron, 3456-hedron, 4056-hedron, 4704-hedron, 5400-hedron, 6144-hedron, 6936-hedron and 7776-hedron were obtained. The designed eight bar structures were subjected to thorough geometric and static analysis showing the behaviour of the geodesic bar domes generated according to the presented in the paper method of the division of original face of regular octahedron. Own formulas were developed to determine the number of nodes and bars. The designed eight bar systems in the form of geodesic domes, which the basis of shaping is regular octahedron can be used as the covers of large areas without the necessity of the internal supports usage.

Two subdivision methods based on the regular octahedron for single- and double-layer spherical geodesic domes

2020 ◽  
Vol 35 (4) ◽  
pp. 160-173
Author(s):  
Dominika Pilarska
Keyword(s):  
Double Layer ◽  
Geometric Analysis ◽  
Single Layer ◽  
Geometric Parameters ◽  
Final Decision ◽  
Regular Octahedron ◽  
Space Frames ◽  
Geodesic Domes ◽  
Number Of Faces ◽  
Spherical Triangles

The paper presents the topological–geometric analysis of a selected number of space frames configurations for geodesic domes which are generated from the regular octahedron. Two subdivision methods for spherical triangles, proposed by Fuliński, were used to create two families of structures. The first family consists of six single-layer and six double-layer geodesic domes shaped on the basis of the first method of subdivision, while the second family contains six single-layer and six double-layer geodesic domes shaped on the basis of the second method of subdivision. The calculated results of the geometric parameters of the analyzed structures were used to create original formulas that allow for more advanced structures to be achieved, that is, with a larger number of nodes and struts. The geometric results were also used to create nomograms showing the range of struts of the same length for double-layer geodesic domes. In both single-layer and double-layer domes, the number of groups of struts of equal lengths and the number of faces with different areas are smaller for structures created according to the first method of subdivision. The comparison of the resulting element quantities of two methods shows that the largest differences appear between the domes with a larger number of struts (up to 67%). Here, the analysis might help the designer reach a final decision on the better choice of topology, in particular, when this aspect is combined with other design goals, such as efficiency, economy, utility, and elegance in the design of the structure and the cover of large areas.

scholarly journals Geometric shaping of chosen two-layered bar domes

2014 ◽  
Vol 13 (3) ◽  
pp. 033-040
Author(s):  
Dominika Pilarska
Keyword(s):  
Layered Structure ◽  
Layered Structures ◽  
Light Weight ◽  
Regular Octahedron ◽  
Regular Polyhedra ◽  
And Topology

The covering of large areas, such as sport areas, trade halls, warehouses and others, may be designed by using forms of spherical domes. Such constructions, especially bars ones, have undoubtedly big superiority in comparison to other structures, thanks to their light-weight or easy montage and dismantle system of particular elements. Regular polyhedra may constitute the basis for bar domes generating. Octahedron, one of the mentioned polyhedra, is for the author the basis for consideration the bar structures creation. The geometry and topology of nodes allow for the obtainment of different and interesting forms created on starting regular octahedron. The joint of two one-layered structures, using the jointing-bars, enables to obtain a two-layered structure, which is much more stable. Using different distance between two layers that is using different radiuses R1 and R2 describing spheres of each structure, we can receive models with different geometry. Thanks to that, it is appropriate to analyze different geometry parameters of researched domes. The results can be used by designers as the basis for the proper architectural spherical construction choice.

n-dimensional enrichment for Further Mathematicians

2004 ◽  
Vol 89 (516) ◽  
pp. 409-416 ◽  
Author(s):  
Martin Griffiths
Keyword(s):  
Higher Dimensions ◽  
Three Dimensions ◽  
Regular Tetrahedron ◽  
Regular Polygons ◽  
Regular Polytopes ◽  
Platonic Solids ◽  
Mathematical Objects ◽  
Regular Octahedron ◽  
Regular Polyhedra

There are infinitely many regular polygons, but we find, on extending the idea of polygons to three dimensions, that there are only five regular polyhedra, the Platonic solids. What happens then if we try to extend this idea beyond three dimensions? It turns out that, of the five Platonic solids, just the regular tetrahedron, cube and regular octahedron have analogues in all higher dimensions, the so-called regular polytopes. Brief descriptions of these mathematical objects are to be found in [1], for example.

COGNITIVIZATION — THE NEXT STAGE OF INFORMATIZATION OF EDUCATION

2018 ◽  
pp. 5-11
Author(s):  
A. S. Christochevskaya ◽  
S. A. Christochevsky
Keyword(s):  
Comparative Analysis ◽  
Learning Resources ◽  
Technical Base ◽  
Initial Stage ◽  
New Knowledge ◽  
Good Material ◽  
E Learning ◽  
New Material ◽  
High Level ◽  
Paper Method

Informatization of education has been going on for 30 years. During this time, a good material and technical base appeared in schools, there are repositories of e-learning resources to which teachers have access. However, it is difficult to use these e-learning resources due to their too large number and not always high level. It is advisable to introduce a system of reviews and recommendations, to conduct a comparative analysis, as well as to make reviews of resources on a particular subject/topic. In addition, the demand for e-learning resources is affected by the fact that education authorities encourage not so much the use of e-learning resources as their development by the teacher himself. In general, the load on teachers has increased instead of the promised saving of time and effort when using the e-learning resources. At the same time, many e-learning resources are not very effective, since they do not meet the requirements of cognitiveness (they contribute not to learning, but to simple memorization of the material). It is necessary to explore the process of learning new material: this will allow you to create cognitive e-learning resources and other resources that would help you with equal probability to successfully acquire new knowledge for students belonging to different psycho-types. At the initial stage of the study of any subject, it is more expedient to use the usual “paper” method, that is, a textbook and not overload the student’s brain with excessive information. Only when he has mastered the basic provisions, we can turn to e-learning resources, bearing in mind that they must be cognitive, that is, they are aimed at logical perception and rapid intuitive learning, only in this case e-learning resources can be considered effective. The conclusion is formulated that cognitiveness is the next stage of informatization of education after the stage of electronization.

Effects of openings on the seismic behavior and performance level of concrete shear walls

2019 ◽  
Author(s):  
Hossein Alimohammadi ◽  
Mostafa Dalvi Esfahani ◽  
Mohammadali Lotfollahi Yaghin
Keyword(s):  
Static Analysis ◽  
Cross Section ◽  
Seismic Behavior ◽  
Shear Walls ◽  
Shear Wall ◽  
Constant Cross Section ◽  
Added Resistance ◽  
Different Shapes ◽  
And Performance ◽  
Abaqus Software

In this study, the seismic behavior of the concrete shear wall considering the opening with different shapes and constant cross-section has been studied, and for this purpose, several shear walls are placed under the increasingly non-linear static analysis (Pushover). These case studies modeled in 3D Abaqus Software, and the results of the ductility coefficient, hardness, energy absorption, added resistance, the final shape, and the final resistance are compared to shear walls without opening.

Static Analysis Based Correctness Verification for Mandatory Access Control Framework

2009 ◽  
Vol 32 (4) ◽  
pp. 730-739 ◽  
Author(s):  
Xin-Song WU ◽  
Zhou-Yi ZHOU ◽  
Ye-Ping HE ◽  
Hong-Liang LIANG ◽  
Chun-Yang YUAN
Keyword(s):  
Access Control ◽  
Static Analysis ◽  
Mandatory Access Control ◽  
Control Framework

Regional and industry characteristics of trade and economic cooperation of the EEU countries

2018 ◽  
Vol 35 (3) ◽  
pp. 140-148
Author(s):  
P. M. Taranov ◽  
A. N. Gerasimov
Keyword(s):  
International Trade ◽  
Static Analysis ◽  
Economic Cooperation ◽  
Regional Structure ◽  
Trade Study ◽  
Structure Of Trade

In the paper, trends and patterns of development of trade and economic cooperation of the EEU countries are analyzed. The authors, based on the economic-static analysis of international trade, study the features of the transformation of the commodity and regional structure of trade. Conclusions are drawn about the reasons for the existing features and trends in the development of intraregional economic cooperation.

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