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Home Industrial Technologies Analytical R-Functions-Based Design of Complex Constructions

Analytical R-Functions-Based Design of Complex Constructions


The work is based on fundamental research in the R-functions theory developed by V.L. Rvachev, Academician of the National Academy of Sciences of Ukraine. The R-functions theory has allowed solving the inverse problem of analytical geometry formulated first by Descartes: given a geometrical object, it is necessary to write down its equation. The R-functions theory allows describing geometric objects with the help of continuously differentiable functions whose values define the boundary, the interior part and other properties of the simulated object. These functions allow accounting for geometrical information analytically, and they are convenient for executing different integro-differential computations.

Innovative Aspect and Main Advantages

New technologies have been developed for synthesis and analysis of complex constructions in analytical design systems with computer-based building of multiparameter normalized equations in 2D and 3D space for mechanical engineering objects. Methods have been developed for building normalized equations of boundaries of geometrical objects possessing translational, cyclic and helical-type symmetry. Methods of translation for finite intervals have been developed. It is first proposed to construct equations of complex geometrical objects using standard primitives. This is a technological basis for automating the process of constructing these equations. Representing a geometric object as an analytical formula dramatically reduces the volume of data describing the type and spatial orientation of the object. To construct a complex geometric object, one needs but parameters that describe its constructional elements instead of huge FEM data arrays. Collections of elements (primitives) can represent a wide spectrum of geometric forms that depend on the subject domain.

Areas of Application

Mathematicians and scientists in many countries of the world use the theory of R-functions for solving problems in geometrical design, solid-state modeling, pattern recognition and research in physico-mechanical fields in complex-shape objects. It can be used for building solution structures, which precisely satisfy all boundary conditions in a boundary- value problem. Such structures can be combined further with many numerical methods for finding approximate solutions of a problem without dividing fields into grids.

Stage of Development

Computer implementation of fluid dynamics, electromagnetic, thermal, strain and other field problems is done using the POLYE system developed at the Podgorny Institute for Mechanical Engineering Problems of NASU. Representation of geometrical and physical information with alphabetic parameters allows for multivariant computations. 3D visualization of constructed equations of geometrical objects is done with the RANOK system developed at the Zaporozhye National University.

Contact Details

A.N. Podgorny Institute for Mechanical Engineering Problems NAS of Ukraine
Contact person: Prof., Academician of NAS of Ukraine Sheyko T.I.
Address: 2\10, Pozharsky str., 61046, Kharkiv, Ukraine
Tel: (+38 0572) 942 774
Fax: (+38 0572) 944 635, 942 744
E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

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