Naslov
Meshless Numerical Method for Modeling of Heterogeneous Materials

Autori
Jalušić, Boris

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Fakultet strojarstva i brodogradnje

Mjesto
Zagreb

Datum
05.10

Godina
2016

Stranica
195

Mentor
Sorić, Jurica

Ključne riječi
heterogeneous material; MLPG concept; collocation method; mixed approach; gradient elasticity; operator-split procedures

Sažetak
In recent decades, an increasing interest in using meshless methods has existed due to their beneficial properties in comparison to more commonly used numerical methods such as the Finite Element Method (FEM). In this class of numerical approaches, the discretization of geometry and the approximation of unknown field variables have been done by using only points that are not connected into elements. Hence, there is no need for a time-consuming mesh creation process and the problems associated with the distorsion of elements are avoided. Despite these attractive properties of meshless methods, high numerical costs and low accuracy associated with the calculation of high-order derivatives of approximation functions, which are particularly needed for solving problems involving the gradient elasticity, still represent a severe setback. The use of meshless methods based on the mixed approach can alleviate the aforementioned drawbacks since they require a lower continuity degree of the approximation functions. The research conducted in the frame of this Thesis is related to the improvement of numerical modeling of heteroge- neous materials using newly developed meshless collocation methods based on the mixed approach. The heterogeneous materials are defined by partitioning the total material domain into subdomains with different linear-elastic isotropic properties. These subdomains define the homogeneous constituents. The discretization and approximation of unknown field variables is done for each homogeneous material independently, therein the interface of the homogeneous materials is discretized with overlapping nodes. The solution for the entire heterogeneous structure is obtained by enforcing appropriate boundary conditions at the nodes representing the interface boundary depending on the utilized formulation. The methods are applied to the linear elastic and the strain gradient formulation of the boundary value problem. For the approximation, the Moving Least Squares method with the imposed interpolation condition and Radial Point Interpolation method with polynomial reproduction are utilized. The numerical efficiency of the presented methods is demonstrated by suitable numerical examples. The obtained results are compared with a standard fully displacement meshless approach as well as with available analytical and numerical solutions. Excellent agreement of the solutions is obtained and a more robust and superior modeling of material discontinuity is achieved. Furthermore, the use of the mixed approach reduces the required degree of continuity of the approximation function, which increases the accuracy and stability in comparison to the same class of meshless methods based only on the approximation of the displacements used up to now.

Izvorni jezik
Engleski

Znanstvena područja
Strojarstvo

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