• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.230-237
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• 2004

In this study, equation of finite element is formulated to analyze relations of large deformation-small deformation considering geometrical nonlinear for membrane structure. Total Lagrangian Formulation(TLF) is introduced to formulate theory and equation of motion considering Triangular Constant Strain(TCS) element in finite, element analysis is formulated. Finite element program is made by equation of motion considering TLF. This study analyzed a variety of examples, so compared with the past results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.1-19
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• 1998

A Chebyshev pseudospectral-finite element method is proposed for two-dimensional unsteady Navier-Stokes equation. The generalized stability and the convergence are proved strictly. The numerical results show the advantages of this method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1129-1141
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• 2011

In this paper, a class of large time-stepping method based on the finite element discretization for the Cahn-Hilliard equation with the Neumann boundary conditions is developed. The equation is discretized by finite element method in space and semi-implicit schemes in time. For the first order fully discrete scheme, convergence property is investigated by using finite element analysis. Numerical experiment is presented, which demonstrates the effectiveness of the large time-stepping approaches.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.349-352
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• 2006

The conventional segregated finite element formulation produces a small and simple matrix at each step than in an integrated formulation. And the memory and cost requirements of computations are significantly reduced because the pressure equation for the mass conservation of the Navier-Stokes equations is constructed only once if the mesh is fixed. However, segregated finite element formulation solves Poisson equation of elliptic type so that it always needs a pressure boundary condition along a boundary even when physical information on pressure is not provided. On the other hand, the conventional integrated finite element formulation in which the governing equations are simultaneously treated has an advantage over a segregated formulation in the sense that it can give a more robust convergence behavior because all variables are implicitly combined. Further it needs a very small number of iterations to achieve convergence. However, the saddle-paint-type matrix (SPTM) in the integrated formulation is assembled and preconditioned every time step, so that it needs a large memory and computing time. Therefore, we newly proposed the P2PI semi-segregation formulation. In order to utilize the fact that the pressure equation is assembled and preconditioned only once in the segregated finite element formulation, a fixed symmetric SPTM has been obtained for the continuity constraint of the present semi-segregation finite element formulation. The momentum equation in the semi-segregation finite element formulation will be separated from the continuity equation so that the saddle-point-type matrix is assembled and preconditioned only once during the whole computation as long as the mesh does not change. For a comparison of the CPU time, accuracy and condition number between the two methods, they have been applied to the well-known benchmark problem. It is shown that the newly proposed semi-segregation finite element formulation performs better than the conventional integrated finite element formulation in terms of the computation time.

• Nuclear Engineering and Technology
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• v.49 no.1
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• pp.29-42
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• 2017

The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

• Journal of Advanced Marine Engineering and Technology
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• v.2 no.1
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• pp.3-14
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• 1978

The authors have developed a calculating method of propeller shaft alignment by the finite element method. The propeller shaft is divided into finite elements which can be treated as uniform section bars. For each element, the nodal point equation is derived from the stiffness matrix, the external force vector and the section force vector. Then the overall nodal point equation is derived from the element nodal point equation. The deflection, offset, bending moment and shearing force of each nodal point are calculated from the overall nodal point equation by the digital computer. Reactions and deflections of supporting points of straight shaft are calculated and also the reaction influence number is derived. With the reaction influence number the optimum alignment condition that satisfies all conditions is calculated by the simplex method of linear programming. All results of calculation are compared with those of Det norske Veritas, which has developed a computor program based on the three-moment theorem of the strength of materials. The authors finite element method has shown good results and will be used effectively to design the propeller shaft alignment.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.2
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• pp.183-188
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• 1996

The compressive stress-strain response of Low Density Polyurethane foam material is modeled using the finite element method. A constitutive equation which include experimental constants based on quasi-static and dynamic uniaxial compression test is proposed. Impact test with different impactor masses and velocities are performed to verify the proposed model. The comparison between impact test and finite element analysis shows good agreements.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1409-1419
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• 2017

We introduce an extrapolated Crank-Nicolson characteristic finite element method to approximate solutions of a convection dominated Sobolev equation. We obtain the higher order of convergence in both the spatial direction and the temporal direction in $L^2$ normed space for the extrapolated Crank-Nicolson characteristic finite element method.

• East Asian mathematical journal
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• v.33 no.3
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• pp.295-308
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• 2017

We introduce a Crank-Nicolson characteristic finite element method to construct approximate solutions of a nonlinear Sobolev equation with a convection term. And for the Crank-Nicolson characteristic finite element method, we obtain the higher order of convergence in the temporal direction and in the spatial direction in $L^2$ normed space.