EDUCATIONAL AND APPLIED ASPECTS OF CONSTRUCTION INVOLUTES OF THE TRIAXIAL ELLIPSOID SURFACE

Visnyk LNAU: Architecture and Farm Building 2019 №20: 9-13

EDUCATIONAL AND APPLIED ASPECTS OF CONSTRUCTION INVOLUTES OF THE TRIAXIAL ELLIPSOID SURFACE

Kernytskyi I., Doctor of Engineering
Lviv National Agrarian University
Nikitenko O.,
SGGW, Wydział Budownictwa i Inżynierii Środowiska
Stukalets I., Candidate of Engineering Science
Burtak V., Candidate of Engineering Science
Horodetskyi I. Candidate of Engineering Science
Lviv National Agrarian University

https://doi.org/10.31734/architecture2019.20.009

Annotation

In the present architectural environment, constructions are designed with complicated geometric surfaces for the sake of originality. A triaxial ellipsoid is one of such surfaces. Unlike the ellipsoid of rotation, such surface is not applied in a technique, and its use in architecture is rather rare. The bright examples of triaxial ellipsoid application in architecture are presented by the National Theatre in Beijing and Intercontinental Hotel in Davos.

The article analyzes the existing methods concerning solution of the tasks of construction of the involutes of pyramid, prism, and also surfaces of rotation, i.e. a cone and a cylinder. A particular attention is paid to construction of involutes of a globe and curvilinear surfaces of rotation, applying the method of cylinders or cones that can be described (or entered) round the set surfaces.

The analysis of didactics experience confirms that the academic study of the different methods of involutes construction is an important element of the educational program, professional knowledge, and practical skills of the students of architectural, building and technical specialties. It is argued that the topic «Involute» requires students’ deeper knowledge and skills of the all-round applied use.

The works investigates a triaxial ellipsoid as a complicated geometrical surface. The article describes the established and approved basic principles of construction of the involute of triaxial ellipsoid surface with the set sizes. The involute of ellipsoid was projected according to the methodology of construction of conditional involute of a globe, i. e. its laying out on separate segments. All graphic constructions were executed in the graphics editor AutoCAD. It is practically confirmed, that the geometrical model of involute of the triaxial ellipsoid surface is rather simple for architectural modeling and can be applied for the design of different curvilinear surfaces of the second order, which, unlike the surfaces of rotation, have ellipses, but not circles in their horizontal sections.

Key words

triaxial ellipsoid, development, paper modeling, sectional planes

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