TECHICAL Series MATHEMATICS • INFORMATICS • PHYSICS Series PHILOLOGY Series ECONOMIC SCIENCES Sereies EDUCATIONAL SCIENCES Series LAW AND SOCIAL SCIENCES Series
Modeling and Calculation of Cracks in Solids with Fractal Interpolation Method
(Modelarea şi calculul fisurilor în materiale solide prin metoda interpolării fractale)
Vol LXV • No. 4/2013
Marius Suciu
ASTRA National Museum Complex, Sibiu
e-mail: suciu_mariusd22@yahoo.com

 Keywords   modeling cracks, fractal interpolation, crack geometry, solid materials, computer generated.

 Abstract
The object of this study is the modeling and the computational calculations for various geometries of cracks in different solid materials, that are were generated within the rules of calculation of fractal geometry. The premises of the paper are using forms similar to those from reality, i.e. fractal forms that, unlike the continuous forms from classical models, manage to better replicate the shapes in the real world. Cracks as found in solid materials, and fractals as computer generated abstract forms have the same common properties of self-similarity. Research tools are discrete mathematical functions obtained by fractal interpolation; for their implementation and delivery in an application, a mathematical programming method involving matrix computation and recursive was used. In order to model the crack geometry, one begins with various arrangements of points in the plane, to obtain in the end result through fractal interpolation to similar forms present in reality. The subject of this paper is the modelling and calculation of cracks found in various materials with particular aspects of interest.

 Rezumat
Obiectul prezentului studiu constă în modelarea şi calculul computaţional pentru diverse geometrii de fisuri care se găsesc la diferite materiale solide, generarea lor respectând regulile de calcul ale geometriei fractale. Premisele lucrării sunt utilizarea formelor similare cu cele din realitate, adică a formelor fractale care spre deosebire de formele continue din modelele clasice, reuşesc să copieze mai bine formele din lumea reală. Fisurile ca aspect, întâlnit la materialele solide, şi fractalii ca formă abstractă generată de calculator, au aceleaşi proprietăţi comune de auto-asemănare. Instrumentele de cercetare sunt funcţiile matematice discrete obţinute prin interpolare fractală, iar pentru implementarea şi concretizarea lor într-o aplicaţie, s-a folosit metoda programării matematice ce implică calcul matriceal şi recursiv. Pentru modelarea geometriei fisurilor se porneşte de la diverse dispuneri ale punctelor în plan, pentru a se ajunge apoi prin interpolare fractală, la forme similare prezente în realitate. Lucrarea urmăreşte modelarea şi calculul unor fisuri din diverse materiale ce prezintă anumite aspecte particulare şi de interes.



Journal INFO (ISSN 1224-8495)
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