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The use of the mesh free methods (radial basis functions) in the modeling of radionuclide migration and moving boundery value problems
Leopold Vrankar, Franc Runovc, Goran Turk, 2007, original scientific article

Abstract: Recently, the mesh free methods (radial basis functions-RBFs) have emerged as a novel computing method in the scientific and engineering computing community. The numerical solution of partial differential equations (PDEs) has been usually obtained by finite difference methods (FDM), finite element methods (FEM) and boundary elements methods (BEM). These conventional numerical methods still have some drawbacks. For example, the construction of the mesh in two or more dimensions is a nontrivial problem. Solving PDEs using radial basis function (RBF) collocations is an attractive alternative to these traditional methods because no tedious mesh generation is required. We compare the mesh free method, which uses radial basis functions, with the traditional finite difference scheme and analytical solutions. We will present some examples of using RBFs in geostatistical analysis of radionuclide migration modeling. The advection-dispersion equation will be used in the Eulerian and Lagrangian forms. Stefan's or moving boundary value problems will also be presented. The position of the moving boundary will be simulated by the moving data centers method and level set method.
Keywords: mesh free methods, radial basis functions, finite difference methods, finite elemnt methods, boundary elements methods, geostatistics, Eulerian method, Lagrangian method, level set method
Published: 18.05.2018; Views: 510; Downloads: 44
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Determination of stresses and forces on the orthodontic system by using numerical simulation of the finite elements method
Janko Ferčec, Branislav Glišić, I. Šćepan, Evgenija Marković, Dragoslav Stamenković, Ivan Anžel, Jože Flašker, Rebeka Rudolf, 2012, original scientific article

Abstract: This study was addressed to use knowledge about the orthodontic system with numerical simulation of the nite elements method. For the rst time we simulated the stresses on the orthodontic system and, in this manner, calculated the orthodontic force on the tooth. A 3D orthodontic model or orthodontic system was designed resembling moderate crowding in the dental arch with all supporting structures. CATIA V5 computer software was used to set up a model for the orthodontic system and ABAQUS was used for simulation of the stresses on the orthodontic system. Our attention was focused on the stresses on the tooth lateral incisor and its periodontal ligament. The results of the numerical simulation showed complex stresses on the tooth lateral incisor and its periodontal ligament. In this paper is presented a calculation of the orthodontic force acting on the tooth lateral incisor due to the orthodontic wire. This orthodontic force was calculated from the stresses on the bracket. The calculated orthodontic force was in the area which is considered as the optimal orthodontic force for movement of the tooth.
Keywords: okluzija, ortodontski sistem, metoda končnih elementov, ortodonske sile, zobje, malocclusion, orthodontic system, finite elements method, orthodontic force, tooth
Published: 10.07.2015; Views: 665; Downloads: 86
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Symmetry preserving algorithm for large displacement frictionless contact by the pre-discretization penalty method
Dušan Gabriel, Jiři Plešek, Miran Ulbin, 2004, original scientific article

Abstract: A three-dimensional contact algorithm based on the pre-discretization penalty method is presented. Using the pre-discretization formulation gives rise to contact searching performed at the surface Gaussian integration points. It is shown that the proposed method is consistent with the continuum formulation ofthe problem and allows an easy incorporation of higher-order elements with midside nodes to the analysis. Moreover, a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments. Theproposed algorithm utilizes the BFGS method modified for constrained non-linear systems. The effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements. The symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders.
Keywords: mechanics, numerical methods, contacting surfaces, contact problems, 3D contact algorithm, discretization, higher order elements, finite element method, Gauss point search, pre-discretization penalty method
Published: 01.06.2012; Views: 1808; Downloads: 68
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Application of numerical simulations in the deep-drawing process and the holding system with segments' inserts
Mihael Volk, Blaž Nardin, Bojan Dolšak, 2011, original scientific article

Abstract: The demands for complicated products have increased dramatically over the last few years taking into consideration the utilisation of sheet metal, product quality and process conditions. For reliable product development and stable production process, the use of FEM is necessary. One of the most significant parameters in the sheet metal forming process is the blank holding force. In the research work, the optimisation of the blank holding force was performed with the help of FEM analysis. For the optimisation the geometry and the structure of the blank holder was optimised. The best results were obtained with flexible, segmented blank holders, which enables wider technological window for good parts.
Keywords: sheet metal forming, deep drawing, segmented holding system, finite elements method, optimization
Published: 01.06.2012; Views: 1417; Downloads: 67
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