• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.165-181
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• 2004

Based on Landau-type transformation, a Stefan problem with non-linear free boundary condition is transformed into a system consisting of parabolic equation and the ordinary differential equations. Semidiscrete approximations are constructed. Optimal orders of convergence of semidiscrete approximation in $L_2$, $H^1$ and $H^2$ normed spaces are derived.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.185-199
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• 2003

In this paper, we apply finite element Galerkin method to a single-phase quasi-linear Stefan problem with a forcing term. We consider the existence and uniqueness of a semidiscrete approximation and optimal error estimates in $L_2$, $L_{\infty}$, $H_1$ and $H_2$ norms for semidiscrete Galerkin approximations we derived.

• Earthquakes and Structures
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• v.1 no.4
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• pp.411-425
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• 2010

The effect of dead loads on dynamic responses of uniform elastic beams is examined by means of a governing equation which takes into account initial bending stress due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (Takabatake 1990). In the formulation the effect of dead loads is considered by strain energy produced by conservative initial stresses produced by the dead loads. Second, the effect of dead loads on dynamical responses produced by live loads in simply supported beams and clamped beams is confirmed by the results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. It is shown that the dynamical responses, like dynamic deflections and bending moments produced by dynamic live loads, are decreased in a heavyweight beam when the effect of dead loads is included. Third, an approximate solution for dynamic deflections including the effect of dead loads is presented in closed-form. The proposed solution shows good in agreement with results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. Finally, a method reflecting the effect of dead loads for dynamic responses of beams on the magnitude of live loads is presented by an example.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.386-391
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• 2001

A finite element code based on P2P1 tetra element has been developed for the large eddy simulation (LES) of turbulent flows around a complex geometry. Fractional 4-step algorithm is employed to obtain time accurate solution since it is less expensive than the integrated formulation, in which the velocity and pressure fields are solved at the same time. Crank-Nicolson method is used for second order temporal discretization and Galerkin method is adopted for spatial discretization. For very high Reynolds number flows, which would require a formidable number of nodes to resolve the flow field, SUPG (Streamline Upwind Petrov-Galerkin) method is applied to the quadratic interpolation function for velocity variables, Noting that the calculation of intrinsic time scale is very complicated when using SUPG for quadratic tetra element of velocity variables, the present study uses a unique intrinsic time scale proposed by Codina et al. since it makes the present three-dimensional unstructured code much simpler in terms of implementing SUPG. In order to see the effect of numerical diffusion caused by using an upwind scheme (SUPG), those obtained from P2P1 Galerkin method and P2P1 Petrov-Galerkin approach are compared for the flow around a sphere at some Reynolds number. Smagorinsky model is adopted as subgrid scale models in the context of P2P1 finite element method. As a benchmark problem for code validation, turbulent flows around a sphere and a MIRA model have been studied at various Reynolds numbers.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.237-246
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• 1999

A finite element model is studied to simulate unsteady free surface flow based on dynamic wave equation and collocation method. The collocation method is used in conjunction with Hermite polynomials, and resulting matrix equations are solved by skyline method. The model is verified by applying to hydraulic jump, nonlinear disturbance propagation and dam-break flow in a horizontal frictionless channel. The computed results are compared with those by Bubnov-Galerkin and Petrov-Galerkin methods. It is also applied to the North Han River to simulate the floodwave propagation. The computed results have good agreements with those of DWOPER model in terms of discharge hydrographs. The suggested model has proven to be one of the promising scheme for simulating the gradually and rapidly varied unsteady flow in open channels.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.525-535
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• 2001

In this paper, a new adaptive analysis scheme for element-free Galerkin method(EFGM) is proposed. The novel point of this scheme is that the triangular cell structure based on the Delaunay triangulation is used in the numerical integration and the node adding/removing process. In adaptive analysis with this scheme, there is no need to divide the integration cell and the memory cell structure. For the adaptive analysis of crack propagation, the reconstruction of cell structure by adding and removing the nodes on integration cells based the estimated error should be carried out at every iteration step by the Delaunay triangulation technique. This feature provides more convenient user interface that is closer to the real mesh-free nature of EFGM. The analysis error is obtained basically by calculating the difference between the values of the projected stresses and the original EFG stresses. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples.

• Earthquakes and Structures
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• v.5 no.5
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• pp.589-605
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• 2013

The effect of dead loads on dynamic responses of a uniform elastic beam subjected to moving loads is examined by means of a governing equation which takes into account initial bending stresses due to dead loads. First, the governing equation of beams which includes the effect of dead loads is briefly presented from the author's paper (1990, 1991, 2010). The effect of dead loads is considered by a strain energy produced by conservative initial stresses caused by the dead loads. Second, the effect of dead loads on dynamical responses produced by moving loads in simply supported beams is confirmed by the results of numerical computations using the Galerkin method and Wilson-${\theta}$ method. It is shown that the dynamical responses by moving loads are decreased remarkably on a heavyweight beam when the effect of dead loads is included. Third, an approximate solution of dynamic deflections including the effect of dead loads for a uniform beam subjected to moving loads is presented in a closed-form for the case without the additional mass due to moving loads. The proposed solution shows a good agreement with results of numerical computations with the Galerkin method and Wilson-${\theta}$ method. Finally it is clarified that the effect of dead loads on elastic uniform beams subjected to moving loads acts on the restraint of the transverse vibration for the both cases without and with the additional mass due to moving loads.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1251-1262
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• 1996

In this paper, a mathematical model for a belt driven system is proposed to analyse the vibration characteristics of the driving units with belts and the free and forced vibraiton anlyses are carried out. The mathematical model for a belt-driven system includes belts, pulleys, spindle and bearings. By using Hamilton's principle, four nonlinear governing equations and twelve nonlinear boundary conditions are derived. To linearize and discretize the nonlinear governing equations and boundary conditions, the perturbation method and Galerkin method are used. Also, the free vibration analyses for various parameters of a belt driven system, which are the tension of a belt, the length of a belt, the material properties of belts, the velocity of a velt and the mass of pulley are made. The forced vibration analyses of the system are performed and the dynamic responses for main parameters are anlysed with a belt driven system.

• Nuclear Engineering and Technology
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• v.48 no.1
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• pp.43-54
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• 2016

In the present paper, development of the three-dimensional (3D) computational code based on Galerkin finite element method (GFEM) for solving the multigroup forward/adjoint diffusion equation in both rectangular and hexagonal geometries is reported. Linear approximation of shape functions in the GFEM with unstructured tetrahedron elements is used in the calculation. Both criticality and fixed source calculations may be performed using the developed GFEM-3D computational code. An acceptable level of accuracy at a low computational cost is the main advantage of applying the unstructured tetrahedron elements. The unstructured tetrahedron elements generated with Gambit software are used in the GFEM-3D computational code through a developed interface. The forward/adjoint multiplication factor, forward/adjoint flux distribution, and power distribution in the reactor core are calculated using the power iteration method. Criticality calculations are benchmarked against the valid solution of the neutron diffusion equation for International Atomic Energy Agency (IAEA)-3D and Water-Water Energetic Reactor (VVER)-1000 reactor cores. In addition, validation of the calculations against the $P_1$ approximation of the transport theory is investigated in relation to the liquid metal fast breeder reactor benchmark problem. The neutron fixed source calculations are benchmarked through a comparison with the results obtained from similar computational codes. Finally, an analysis of the sensitivity of calculations to the number of elements is performed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.1
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• pp.85-94
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• 2002

In this study an adaptive node generation procedure in the Element-free Galerkin (EFG) method using bubble-meshing technique is Proposed. Since we construct the initial configuration of nodes by subdivision of background cell, abrupt changes of inter-nodal distance between higher and lower error regions are unavoidable. This unpreferable nodal spacing induces additional errors. To obtain the smooth nodal configuration the nodal configurations are regenerated by bubble-meshing technique. This bubble meshing technique was originally developed to generate a set of well-shaped triangles and tetrahedra. In odder to evaluate the effect of abrupt changes of nodal spacing, one-dimensional problems with various nodal configurations mere investigated. To demonstrate the performance of proposed scheme, the sequences of making optimal nodal configuration with bubble meshing technique are investigated for several problems.