Izvorni znanstveni članak
Numerical analyses of 2D problems using Fupn(x,y) basis functions
Vedrana Kozulić
; University of Split, Faculty of Civil Engineering, Split, Croatia
Blaž Gotovac
; University of Split, Faculty of Civil Engineering, Split, Croatia
Sažetak
This paper presents a procedure of numerical modeling of two-dimensional engineering problems using functions Fupn(x,y). They are finite, infinitely derivable functions which belong to a class of Rvachev’s basis functions Rbf. The properties of these functions enable hierarchic approach to expansion of the numerical solution base either in the entire domain or its segments.
The approximate solution of the problem is assumed in the form of a linear combination of basis functions Fupn(x,y). Instead of traditional discretization into finite elements, here, the entire domain can be analyzed at once, as one fragment. A system of equations is formed by the collocation method 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, the required accuracy of the approximate solution is obtained simply by increasing the number of basis functions. The values of the main solution function and all the values derived from the main solution are calculated in the same points since numerical integration is avoided. This method is tested on the torsion of prismatic bars, plane states 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 fragment collocation method using basis functions Fupn(x,y) gives excellent results for elaborated problems either with regard to accuracy or continuity of all fields derived from approximate solutions.
Ključne riječi
approximate solution, Rvachev’s basis functions, collocation method, fragment
Hrčak ID:
318822
URI
Datum izdavanja:
15.6.2000.
Posjeta: 0 *