• 대한기계학회논문집
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• 제19권11호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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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.

• 대한기계학회논문집A
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• 제23권6호
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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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• 제38권5호
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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.

• 호남수학학술지
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• 제40권4호
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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.

• 소음진동
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• 제9권1호
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• pp.163-173
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• 1999

Precise and reasonable modelling is necessary and indispensable to the analysis of dynamic characteristics of mechanical structures. Also. the effective prediction of the change of modal properties due to the variation of design parameters is required especially for the application of finite element method to the structural dynamics problems. To meet those necessity and requirement, three model updating algorithms are proposed for finite element methods. Those algorithms are based on sensitivity analysis of the modal data obtained from experimental modal analysis(EMA) and analytical modal analysis(AMA). The adapted sensitivity analysis methods of the algorithms are 1)eigensensitivity(EGNS) method. 2)frequency response function sensitivity(FRFS) method. 3)sensitivity based element-by-element method (SBEEM), Singular value decomposition(SVD) is used for performing eigenanalysis and parameter estimation in the updating process. Those algorithms are applied to finite element of a plate and the updating capability of each algorithm is compared in terms of accuracy. reliability and stability of the updating process. It is shown that the model updating method using frequency response function is superior to the other methods in view of various updating capabilities.

• East Asian mathematical journal
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• 제36권5호
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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].

• 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.

• 한국생산제조학회지
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• 제21권2호
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권1호
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• pp.13-23
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• 2008

In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in $H^2$ is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and Poisson equations with the mixed boundary condition. In this paper, we give NSF method for the Helmholtz equations ${\Delta}u+Ku=f$ with homogeneous Dirichlet boundary condition. Examples with a singular point are given with numerical results.