• East Asian mathematical journal
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• 제34권5호
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• pp.623-632
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• 2018

In [7, 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 boundary conditions, compute the finite element solutions using standard FEM and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.

• 대한전자공학회논문지
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• 제26권8호
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• pp.1137-1144
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• 1989

In this paper, for eliminating the spurious solutions which have been necessarily included in the solutions of earlier vectorial finite-element method, we have proposed the improved finite-element method for the analysis of dielectric waveguides in the three-component magnetic field.

• 소음진동
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• 제8권1호
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• pp.122-131
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• 1998

Internal and external acoustic fields of the engine inlet are calculated by using a finite element method. The far fields non reflecting boundary condition is enforced by using a wave envelope element, which is a kind of infinite element. The geometry is assumed an axisymetric duct. Sources of the fan are modeled by the Tyler and Sofrin's theory. Effects of uniformly moving medium are considered. A pulsating sphere and an oscillating piston problem are calculated to verify the external problems, and compared with exact solutions. When the wave envelope element is applied at the far boundary, the calculated finite element solutions show good agreements with the exact solutions. The engine inlet is solved with the combined internal and external grid. The cut-off phenomena on engine inlet duct are observed.

• 한국광학회:학술대회논문집
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• 한국광학회 1989년도 제4회 파동 및 레이저 학술발표회 4th Conference on Waves and lasers 논문집 - 한국광학회
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• pp.157-160
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• 1989

The most serious difficulty in using the finite element method is the appearance of the so-called spurious, nonphysical modes. We have proposed the finite element formulation of the variational expression in the three-component magnetic field based on Galerkin's method. In this approach, the divergence relation H is satisfied and spurious modes does not appear and finite-element solutions agree with the exact solutions.

• 소음진동
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• 제3권2호
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• pp.169-178
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• 1993

Internal & External duct acoustic fields are calculated by using a finite element method. The geometry is assumed as an axisymmetric duct. External acoustic field; outside the duct, and combined internal & external acoustic fields are solved. For both cases a far field's nonreflecting boundary condition is enforced by using a wave envelope element, which is a kind of finite element. First, a pulsating sphere and an oscillating sphere problem are calculated to verify the external problems, and the results are compared with exact solutions. When the wave envelope element is applied at the far boundary, the calculated finite element solutions show good agreements with the exact solutions. Secondly, the combined internal & external duct acoustic fields are calculated and visualized when monopole sources are distributed inside the duct. It is observed that the directivity of sound intensity outside the duct is beaming toward the axis for high frequency sources.

• Nuclear Engineering and Technology
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• 제41권5호
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• pp.649-654
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• 2009

The finite element based lattice Boltzmann method (FELBM) has been developed to model complex fluid domain shapes, which is essential for studying fluid-structure interaction problems in commercial nuclear power systems, for example. The present study addresses a new finite element formulation of the lattice Boltzmann equation using a general weighted residual technique. Among the weighted residual formulations, the collocation method, Galerkin method, and method of moments are used for finite element based Lattice Boltzmann solutions. Different finite element geometries, such as triangular, quadrilateral, and general six-sided solids, were used in this work. Some examples using the FELBM are studied. The results were compared with both analytical and computational fluid dynamics solutions.

• Structural Engineering and Mechanics
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• 제28권5호
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• pp.603-633
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• 2008

A four-node plate finite element for the analysis of laminated composites which is developed using strain gradient notation is presented. The element is based on a first-order shear deformation theory and on the equivalent lamina assumption. Strains and stresses can be calculated at different points through the thickness of the plate. They are averaged values due to the equivalent lamina assumption. A shear correction factor is used as the transverse shear strain is taken to be constant over the plate thickness while its actual variation is parabolic. Strain gradient notation, which is physically interpretable, allows for the detailed a-priori analysis of the finite element model. The polynomial expansions are inspected and spurious terms responsible for modeling errors are identified in the shear strains polynomial expansions. The element is corrected by simply removing the spurious terms from the shear strains expansions. The element is implemented into a FORTRAN finite element code in two versions; namely, with and without spurious terms. Results are compared to show the effects of the spurious terms on the solutions. It is also shown that a refined mesh composed of corrected elements provides solutions which approximate very well the analytical solutions, validating the procedure.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 추계학술대회논문집
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• pp.819-822
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• 2006

This paper has the objects of deciding dynamic instability regions of thick plates on inhomogeneous Pasternak foundation by finite element method and providing kinematic design data for mats and slabs of building structures. In this paper, dynamic stability analysis of tapered opening thick plate is done by use of Serendipity finite element with 8 nodes considering shearing strain of plate. To verify this finite element method, buckling stress and natural frequencies of thick pate with or without in-plane stress are compared with existing solutions. The results are as follow that this finite element solutions with $4{\times}4$ meshes are shown the error of maximum 0.56% about existing solutions, and the larger foundation parameters, the farther dynamic instability regions are from vertical axis of graph presented relation of ${\beta}\;and\;\overline{\omega}/\omega$.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 춘계학술대회논문집
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• pp.1177-1180
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• 2007

This paper has the objects of deciding dynamic instability regions of thick plates by finite element method and providing kinematic design data for mats and slabs of building structures. In this paper, dynamic stability analysis of tapered opening thick plate is done by use of Serendipity finite element with 8 nodes considering shearing strain of plate. To verify this finite element method, buckling stress and natural frequencies of thick pate with or without in-plane stress are compared with existing solutions. The results are as follow that this finite element solutions with $4{\times}4$ meshes are shown the error of maximum 0.56% about existing solutions, and obtained dynamic instability graph according with variation of opening positions.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.955-962
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• 2006

This paper has the objects of deciding dynamic instability regions of thick plates on Pasternak foundation by finite element method and providing kinematic design data for mats and slabs of building structures. In this paper, dynamic stability analysis of tapered opening thick plate is done by use of Serendipity finite element with 8 nodes considering shearing strain of plate. To verify this finite element method, buckling stress and natural frequencies of thick pate with or without in-plane stress are compared with existing solutions. The results are as follow that this finite element solutions with 4x4 meshes are shown the error of maximum 0.56% about existing solutions, and obtained dynamic instability graph according with variation of opening positions.