• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.2971-2980
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• 1995

A numerical study of fluid flow in driven cavity was carried out using singular finite element method. The driven cavity problem is known to have infinite velocity gradients as well as dual velocity conditions at the singular points. To overcome such difficulties, a finite element method with singular shape functions was used and a special technique was employed to allow multiple values of velocities at the singular points. Application of singular elements in the driven cavity problem has a significant influence on the stability of solution. It was found the singular elements gave a stable solution, especially, for the pressure distribution of the entire flow field by keeping up a large pressure at the singular points. In the existing solutions of driven cavity problem, most efforts were focused on the study of streamlines and vorticities, and pressure were seldom mentioned. In this study, however, more attention was given to the pressure distribution. Computations showed that pressure decreased very rapidly as the distance from the singular point increased. Also, the pressure distribution along the vertical walls showed a smoother transition with singular elements compared to those of conventional method. At the singular point toward the flow direction showed more pressure increase compared with the other side as Reynolds number increased.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.464-469
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• 2000

In order to analyze effectively the discontinuous parts such as holes or notches included in mechanical structures by the finite element method, a singular finite element for orthotropic materials. is proposed. This singular element is formulated by the Trefftz method and the hybrid variational principles, which the displacements and stresses are simultaneously assumed using the Trefftz functions. Through several numerical tests, it is shown that the proposed singular element is very efficient for the accurate stress analysis of the various types of discontinuous parts.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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• pp.1018-1025
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• 1999

For the effective analysis of two dimensional plane problems with geometrical discontinuities, singular finite element has been proposed. The element matrix equation was formulated on the basis of hybrid variational principle and Trefftz function sets derived consistently from the complex theory of plane elasticity by introducing a conformal mapping function. In order to suggest the accuracy characteristics of the proposed singular finite element, typical plane problems were analyzed and these results were compared with exact solutions. The singular finite element gives the comparatively exact values of stress concentration factors or stress intensity factors and can be effectively used for the analysis of mechanical structures containing various geometrical discontinuities.

• East Asian mathematical journal
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• v.38 no.5
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• pp.603-610
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• 2022

In [6, 7] 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. They considered a partial differential equation with the input function f ∈ L²(Ω). In this paper we consider a PDE with the input function f ∈ H¹(Ω) and find the corresponding singular and dual singular functions. We also induce the corresponding extraction formula which are the basic element for the approach.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1143-1156
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• 2018

In this paper, we define right singular clean rings as rings in which every element can be written as a sum of a right singular element and an idempotent. Several properties of these rings are investigated. It is shown that for a ring R, being singular clean is not left-right symmetric. Also the relations between (nil) clean rings and right singular clean rings are considered. Some examples of right singular clean rings have been constructed by a given one. Finally, uniquely right singular clean rings and weakly right singular clean rings are also studied.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.04a
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• pp.573-577
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• 1995

An integration method for the hypersingular kernels, in the boundary integralequations used for the solution of crack-like problems in elasticity, has been developed. To isolate the stronger singularities, the actual boundaries are replaced by the smoothly curved auxiliary boundaries which provide the detoured, non-singular integration paths. The auxiliary boundary can be interpreted as a contracted form of the actual boundaries except for the singular element where the collocating point is located. For an optimal integration path for every singular collocation point, the auxiliary boundary may have different shape depending on the position of the collocation point on the singular element.

• 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.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.2
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• pp.232-240
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• 2012

This study proposed efficient method of singular value for inverse problem, linear approximation of contact position and loading in single and double meshing of transmission contact element, using 2-dimension model considered near the tooth by root stress. Determination of root stress is carried out for the gear tooth by finite element method and boundary element method. Boundary element discretization near contact point is carefully performed to keep high computational accuracy. The predicted results of boundary element method are good accordance with that of finite element method.

• East Asian mathematical journal
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• v.36 no.5
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• pp.583-591
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• 2020

In [8, 9] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods 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. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].

• The Journal of the Acoustical Society of Korea
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• v.22 no.1E
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• pp.11-18
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• 2003

Non-singular boundary element method (BEM) codes are developed in acoustics application. The BEM code is then used to calculate unknown boundary surface normal displacements and surface pressures from known exterior near field pressures. And then the calculated surface normal displacements and surface pressures are again applied to the BEM in forward in order to calculate reconstructed field pressures. The initial exterior near field pressures are very well agreed with the later reconstructed field pressures. Only the same number of boundary surface nodes (1178) are used for the initial exterior pressures which are at first calculated by Finite Element Method (FEM) and BEM. Pseudo-inverse technique is, used for the calculation of the unknown boundary surface normal displacements. The structural object is a tuning fork with 128.4 ㎐ resonant. The boundary element is a quadratic hexahedral element (eight nodes per element).