engleski

Meshless approach as an alternative to finite element method in solid mechanics numerical modeling

Meshless approaches enable discretizations of a computational model only by a set of nodes which do not need to be connected into elements. In this paper the meshless local Petrov-Galerkin method is presented, which belongs to truly meshless approaches because it does not require any kind of mesh or background cells for either interpolation or integration. Fully displacement and mixed formulations are presented. The fully displacement approach is used for the solution of a three dimensional elasto-static problem, while the mixed approach is applied for the modeling of deformation responses of shell-like structures. The modeling of material discontinuities is performed by the mixed meshless local Petrov-Galerkin approach employing collocation method. The efficiency and accuracy of all presented methods are tested and compared with finite element formulations in numerical examples. It is demonstrated that the meshless approaches may be considered as an alternative to the well-known finite element method in certain problems.

meshless method ; local Petrov-Galerkin formulation ; mixed meshless approach ; collocation meshless method

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