• Nuclear Engineering and Technology
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• v.22 no.2
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• pp.151-158
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• 1990

The new discrete elements method (DEM) is applied to the one-group neutron transport equation in one-dimensional slab geometry. The fixed source and the criticality problems are treated and three spatial differencing schemes (the DD, the SC, -and the LC schemes) are tested to determine the most computationally efficient in the DEM. In all cases, the accuracy of the results obtained from the DEM shows an improvement over that obtained from the standard discrete ordinates calculations. And the LC scheme gives the most accurate results in the DEM.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.411-418
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• 2018

In this paper, we prove the discrete compactness property for Kim-Kwak finite element spaces of any order under a weak quasi-uniformity assumption.

• Structural Engineering and Mechanics
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• v.26 no.6
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• pp.725-739
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• 2007

In recent years there are many plate bending elements that emerged for solving both thin and thick plates. The main features of these elements are that they are based on mix formulation interpolation with discrete collocation constraints. These elements passed the patch test for mix formulation and performed well for linear analysis of thin and thick plates. In this paper a member of this family of elements, namely, the Discrete Reissner-Mindlin (DRM) is further extended and developed to analyze both thin and thick plates with geometric nonlinearity. The Von K$\acute{a}$rm$\acute{a}$n's large displacement plate theory based on Lagrangian coordinate system is used. The Hu-Washizu variational principle is employed to formulate the stiffness matrix of the geometrically Nonlinear Discrete Reissner-Mindlin (NDRM). An iterative-incremental procedure is implemented to solve the nonlinear equations. The element is then tested for plates with simply supported and clamped edges under uniformly distributed transverse loads. The results obtained using the geometrically NDRM element is then compared with the results of available analytical solutions. It has been observed that the NDRM results agreed well with the analytical solutions results. Therefore, it is concluded that the NDRM element is both reliable and efficient in analyzing thin and thick plates with geometric non-linearity.

• Steel and Composite Structures
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• v.47 no.3
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• pp.365-374
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• 2023

This paper presents a new scheme for constructing locking-free finite elements in thick and thin plates, called Discrete Shear Gap element (DSG), using multiphase material topology optimization for triangular elements of Reissner-Mindlin plates. Besides, common methods are also presented in this article, such as quadrilateral element (Q4) and reduced integration method. Moreover, when the plate gets too thin, the transverse shear-locking problem arises. To avoid that phenomenon, the stabilized discrete shear gap technique is utilized in the DSG3 system stiffness matrix formulation. The accuracy and efficiency of DSG are demonstrated by the numerical examples, and many superior properties are presented, such as being a strong competitor to the common kind of Q4 elements in the static topology optimization and its computed results are confirmed against those derived from the three-node triangular element, and other existing solutions.

• Journal of the Korean Society for Railway
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• v.6 no.3
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• pp.174-178
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• 2003

This paper presents the development of 2-dimensional discrete element algorithm to generate circle and line elements for the simulation of the ballast and sleeper in railway. An example of randomly distributed circle elements show a good applicability of this algorithm for the modeling of the behaviors of ballast. The output about unbalaned force, particle velocity, and total energy conservation from the code is evaluated to check if the calculation is conducted properly.

• Journal of Multimedia Information System
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• v.2 no.3
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• pp.263-274
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• 2015

The subject of this work is the complex discrete systems simulation special features with the aid of dynamic graph models. The proposed simulation technique allows to determine the ways for tasks solutions in terms of discrete systems analysis and synthesis of various complication: one-dimensional and multidimensional, steady and unstable, with the pulse elements abnormal operating mode and others. Often complex control systems analysis and synthesis task solutions, via classical approach comes out to be insolvent, because of the computational problems. The application of graph models allows to perform clear and strict characterization and computer procedures automation. The optimal controls synthesis algorithm presented in this paper, transferring the discrete system from target initial state to target final state within the minimum time, allows to consider the zero initial conditions systems, with the initial potential energy, with the control actions limitations and complex pulse elements operating mode.

• Computational Structural Engineering
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• v.5 no.2
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• pp.105-118
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• 1992

Static performance was compared for the triangular plate elements through some numerical experiments. Four Kirchhoff elements and six Mindlin elements were selected for the comparison. Numerical tests were executed for the problems of rectangular plates with regular and distorted meshes, rhombic plates, circular plates and cantilever plates. Among the Kirchhoff 9 DOF elements, the discrete Kirchhoff theory element was the best. Element distortion and the aspect ratio were shown to have negligible effects on the displacement behaviour. The Specht's element resulted in better results than the Bergan's but it was sensitive to the aspect ratio. The element based on the hybrid stress method also resulted in good results but it assumed to be less reliable. Among the linear Mindlin elements, the discrete shear triangle was the best in view of reliability, accuracy and convergence. Since the thin plate behaviour of it was as good as the DKT element, it can be used effectively in the finite element code regardless of the thickness. As a quadratic Mindlin element, the MITC7 element resulted in best results in almost all cases considered. The results were at least as good as those of doubly refined meshes of linear elements.

• Computers and Concrete
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• v.27 no.4
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• pp.297-304
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• 2021

The hybrid Finite-Discrete Element (FDEM) approach combines aspects of both finite elements and discrete elements with fracture mechanics principles, and therefore it is well suited for realistic simulation of quasi-brittle materials. Notwithstanding, in the literature its application for the analysis of concrete is rather limited. In this paper, the proprietary FDEM code ELFEN is used to model concrete specimens under uniaxial compression and indirect tension (Brazilian tests) of different sizes. The results show that phenomena such as size effect and influence of strain-rate are captured using this modeling technique. In addition, a preliminary model of a slab subjected to dynamic shear punching due to progressive collapse is presented. The resulting fracturing pattern of the impacted slab is similar to observations from actual collapse.

• Earthquakes and Structures
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• v.4 no.2
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• pp.133-155
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• 2013

The earthquake responses are studied for the tall flexible structures such as TV towers when the vertical eccentricities between the discrete nodes and the corresponding centroids of investigated lumps are considered. In practical analyses, the tall flexible structures can be made into a spatial-discrete system of some certain length of beam elements with different lengths and cross-sectional areas. These elements are used to construct the investigated lumps in this paper. The different cross-sectional areas and the different lengths of two adjacent elements lead to the appearance of vertical eccentricity between the discrete node and the centroid of investigated lump within the same investigated lump. Firstly, the governing equations are established for a typical investigated lump. Secondly, the calculating formulae of the forces and moments acting on the investigated lump are derived and provided. Finally the new dynamic equilibrium equations with modified mass matrix and assemblage of stiffness matrix have been derived for the stick MDOF model based on beam theory when the existing vertical eccentricities are considered. Numerical results demonstrate that these vertical eccentricities should be considered in order to obtain the accurate earthquake responses for the tall flexible structures.

• Coupled systems mechanics
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• v.9 no.2
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• pp.125-145
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• 2020

In this paper, we present a 3D thermo-hydro-mechanical coupled discrete beam lattice model of structure built of the nonisothermal saturated poro-plastic medium subjected to mechanical loads and nonstationary heat transfer conditions. The proposed model is based on Voronoi cell representation of the domain with cohesive links represented as inelastic Timoshenko beam finite elements enhanced with additional kinematics in terms of embedded strong discontinuities in axial and both transverse directions. The enhanced Timoshenko beam finite element is capable of modeling crack formation in mode I, mode II and mode III. Mode I relates to crack opening, mode II relates to in-plane crack sliding, and mode III relates to the out-of-plane shear sliding. The pore fluid flow and heat flow in the proposed model are governed by Darcy's law and Fourier's law for heat conduction, respectively. The pore pressure field and temperature field are approximated with linear tetrahedral finite elements. By exploiting nodal point quadrature rule for numerical integration on tetrahedral finite elements and duality property between Voronoi diagram and Delaunay tetrahedralization, the numerical implementation of the coupling results with additional pore pressure and temperature degrees of freedom placed at each node of a Timoshenko beam finite element. The results of several numerical simulations are presented and discussed.