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## Atomic basis functions in computational modelling of engineering problems by solution structure method

Kozulić, Vedrana; Gotovac, Blaž
Atomic basis functions in computational modelling of engineering problems by solution structure method // 10th European Solid Mechanics Conference ESMC2018
Bolonja, Italija, 2018. (predavanje, međunarodna recenzija, neobjavljeni rad, znanstveni)

Naslov
Atomic basis functions in computational modelling of engineering problems by solution structure method

Autori
Kozulić, Vedrana ; Gotovac, Blaž

Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
10th European Solid Mechanics Conference ESMC2018

Mjesto i datum
Bolonja, Italija, 2-6.07.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Collocation, solution structure, boundary conditions

Sažetak
This paper describes a numerical procedure called solution structure method that enables exact treatment of all prescribed boundary conditions at all boundary points. Solution structure method is based on the theory of R-functions , . The solution of a boundary value problem is expressed by the formula called solution structure in which the geometry of the domain is described exactly in analytical form, all boundary conditions are described exactly, and only one component is unknown that is usually represented by a linear combination of some basis functions. This unknown component contains information about the differential equation of the problem. Here, we present the use of atomic basis functions (ABFs) to approximate unknown differential component of the solution structure. These functions are infinitely differentiable functions with compact support . All derivatives of atomic basis functions required by differential operators in the solution structure can be used directly in the numerical procedure. This fact allows us to use procedures based on strong formulation. To determine the coefficients of linear combination in the solution structure, a collocation technique is used. The combination of atomic basis functions and the solution structure method gives numerical solutions that have characteristics of analytical solutions because the solution structure method enables exact treatment of boundary conditions while ABFs ensure numerical solutions with the desired level of accuracy. Application of the proposed method to solution of heat transfer problems is illustrated on a number of benchmark problems. The proposed method is also applied to solve the torsion problem. Numerical examples have shown that properly constructed solution structures are complete in the sense that they converge to the exact solution of a problem.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Temeljne tehničke znanosti