• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.207-212
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• 2001

This paper considers a pipeline conveying one-dimensional unsteady flow inside. The dynamics of the fluid-pipe system is represented by two coupled equations of motion for the transverse and axial displacements, which are linearized from a set of partial differential equations which consists of the axial and transverse equations of motion of the pipeline and the equations of momentum and continuity of the internal flow. Because of the complex nature of fluid-pipe interactive mechanism, a very accurate solution method is required to get sufficiently accurate dynamic characteristics of the pipeline. In the literatures, the finite element models have been popularly used for the problems. However, it has been well recognized that finite element method (FEM) may provide poor solutions especially at high frequency. Thus, in this paper, a spectral element model is developed for the pipeline and its accuracy is evaluated by comparing with the solutions by FEM.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.7
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• pp.1408-1415
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• 2002

In this paper, we investigate the effect and the importance of the accuracy of finite element analysis in the shape optimization based on the finite element method and improve the existing finite element which has inaccuracy in some cases. And then, the shape optimization is performed by using the improved finite element. One of the main stream to improve finite element is the prevention of locking phenomenon. In case of bending dominant problems, finite element solutions cannot be reliable because of shear locking phenomenon. In the process of shape optimization, the mesh distortion is large due to the change of the structure outline. So, we have to raise the accuracy of finite element analysis for the large mesh distortion. We cannot guarantee the accurate result unless the finite element itself is accurate or the finite elements are remeshed. So, we approach to more accurate shape optimization to diminish these inaccuracies by improving the existing finite element. The shape optimization using the modified finite element is applied to a two and three dimensional simple beam. Results show that the modified finite element has improved the optimization results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.293-302
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• 2005

In this paper, the thick-walled laminated, orthotropic as well as bimaterial, composite hollow spheres under impact pressure are analyzed in detail by using the semi-discrete finite element method with the Houbolt time-integration scheme which results in unconditionally stable transient numerical results. Numerical results are obtained by using the self-constructed spherically symmetric (one-dimensional) and axially symmetric (two-dimensional) finite element programs, and compared with the previous solutions by other researchers, being shown some of which are incorrect. The finite element package Nastran is also adopted for numerical comparison.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• Structural Engineering and Mechanics
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• v.83 no.2
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• pp.273-282
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• 2022

In this paper, we propose a new concept for error estimation in finite element solutions, which we call mode-based error estimation. The proposed error estimation predicts a posteriori error calculated by the difference between the direct finite element (FE) approximation and the recovered FE approximation. The mode-based FE formulation for the recently developed self-updated finite element is employed to calculate the recovered solution. The formulation is constructed by searching for optimal bending directions for each element, and deep learning is adopted to help find the optimal bending directions. Through various numerical examples using four-node quadrilateral finite elements, we demonstrate the improved predictive capability of the proposed error estimator compared with other competitive methods.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.6 s.237
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• pp.703-710
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• 2005

A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.4
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• pp.252-258
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• 1987

Time periodic finite element solutions for sinusoidally excited electromagnetic field problems in moving media are presented. Solutions by the Galerkin method contain spurious oscillations when grid Peclet number is more than one. To suppress these oscillations an upwind finite element method using two different time periodic test functions is introduced. One is multiplied to second and first-order space derivative terma and the other to the time derivative term. Test functions are obtained from trial functions by adding or subtracting quadratic bias functions with appropriate scaling factors. Phase differences are considered between trial functions and bias functions. For simple interpretations of the phase differences, complex scaling factors are used. The proposed method is developed to give nodally exact solutions for uniform grid spacing in one dimensional problems. Based on the one dimensional results, a two dimensional upwinding scheme is also derived.

• Coupled systems mechanics
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• v.10 no.1
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• pp.79-102
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• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• 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.