VYUŽITÍ BÉZIEROVÝCH ENTIT V MECHANICE

BÉZIER ENTITIES USING IN THE MECHANICS

journal article - other

Czech

Bézierovy entity, zejména křivky, plochy a tělesa jsou v současné době používány zejména v CAD-ovských systémech jako podpůrný grafický prostředek při kreslení. V úlohách mechaniky je jejich aplikace poměrně málo častá. V článku je uveden obecný popis entit do řádu 3, včetně derivací, které jsou nutné pokud se Bézierovy entity využívají při řešení parciálních diferenciálních rovnic. Dále je v článku pro ilustraci uvedeno jejich využití v úlohách mechaniky kontinua, termomechaniky a hydromechaniky

Bézier entities, especially curves areas and bodies are often used in CAD systems by graphics processing currently. Their application in mechanics is relative not common. In this contribution is presented the general description of entities order 3, including their derivations. For Bézier entities description are used the Bernstein multinominals. It is necessary to use derivations for solution the partial differential equations. For geometrical configuration definition or for the approximation of unknown function values it is possible to use real or rational Bézier entities. In approximation functions are unknown values in control points according to application of control volumes method. For geometrical configuration description was chosen the Bézier curve, because in this paper the one-dimensional motion is considered currently. Whole volume is divided into the segments; each one is subdivided into finite volumes (finite elements), which can be identical with control volumes (control element). There are two differences in solid and fluid mechanics applications. Control volumes method application does not require computational mesh configuration change in hydromechanics (Euler approach). Contrary in mechanics of rigid body, especially in the Finite Element Method (FEM) application with large displacement or strain causes the change of mesh configuration (Lagrange approach). We have choose the method of control volumes in our approach, where the shaft position change causes the change of mesh configuration. This method is called Arbitrary Lagrange-Eulerian (ALE) method. The Bézier entities applications are very suitable for solution of these problems. The application of the Bézier curve is used in continuum mechanics thermomechanics and hydromechanics analysis. The one-dimensional body is used in all applications and the results are compared with exact solutions. Eigen value problem, steady state and transient response was solved in continuum mechanics. Nonstationary thermal convection was solved in thermomechanics. Eigen values problem, stationary and transient response of liquid flow in compliance pipe was solved in hydraulics.

Bézier curves, areas, bodies, Bernstein multinominals, continuum mechanics, thermomechanics, hydromechanics, longitudinal vibrations, steady-state vibrations, transient vibrations, nonstationary thermal convection, nonstationary liquid flow

MALENOVSKÝ, E.

2003

1. 1. 2000

brno

1210-2717

Inženýrská mechanika - Engineering Mechanics

7

6

Czech Republic

401

425

25