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## Computational Modeling of Structural Problems using Atomic Basis Functions

Kozulić, Vedrana; Gotovac, Blaž
Computational Modeling of Structural Problems using Atomic Basis Functions // Abstract Book - ACEX2014 - Paris, France / Oechsner, Andreas (ur.).
Pariz: ICC - International Conferences and Courses Limited - ACEX Conference, 2014. (predavanje, međunarodna recenzija, sažetak, znanstveni)

Naslov
Computational Modeling of Structural Problems using Atomic Basis Functions

Autori
Kozulić, Vedrana ; Gotovac, Blaž

Sažeci sa skupova, sažetak, znanstveni

Izvornik
Abstract Book - ACEX2014 - Paris, France / Oechsner, Andreas - Pariz : ICC - International Conferences and Courses Limited - ACEX Conference, 2014

Skup
8th International Conference on Advanced Computational Engineering and Experimenting - ACEX-2014

Mjesto i datum
Pariz, Francuska, 30.06.-03.07.2014.

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Numerical modeling; mesh free method; atomic basis functions; collocation

Sažetak
This paper presents application of the Fupn(x) basis functions in numerical modeling of different engineering problems. Fupn(x) basis functions belong to a class of atomic functions which are infinitely-differentiable functions with compact support. The collocation method has been applied in development of numerical models. A system of algebraic equations is formed in which differential equation of the problem is satisfied in collocation points of a closed domain while boundary conditions are satisfied exactly at the domain boundary. In such a way, required accuracy of approximate solution is obtained simply by increase in the number of basis functions. So, this concept represents a fully mesh free method. Properties of atomic basis functions enable hierarchic expansion of approximate solution base either in the entire domain or in its segments. Presented numerical models are illustrated by examples of the torsion of prismatic bars, elasto-plastic analyses of beam bending and thin plate bending problems. The results of the analyses are compared with the existing exact and relevant numerical solutions. It can be concluded that the possibility of hierarchically expanding the number of basis functions in the domain significantly accelerates the convergence of a numerical procedure in a simple way. Values of the main solution function, e.g. displacements, and all the values derived from the main solution of the problem such as stresses, bending moments and transversal forces, are calculated in the same points and with the same degree of accuracy since numerical integration is avoided.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Temeljne tehničke znanosti