• Journal of the Korean Society for Precision Engineering
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• v.12 no.3
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• pp.32-41
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• 1995

In the analysis of metal forming processes by the finite element method, there are many numerical instabilities such as element locking, hourglass mode and shear locking. These instabilities may have a bad effect upon accuracy and convergence. The present work is concerned with improvement of stability and efficiency in two-dimensional rigid-plastic finite element method using various type of elemenmts and numerical intergration schemes. As metal forming examples, upsetting and backward extrusion are taken for comparison among the methods: various element types and numerical integration schemes. Comparison is made in terms of stability and efficiency in element behavior and computational efficiency and a new scheme of adaptive directional reduced integration is introduced. As a result, the finite element computation has been stabilized from the viewpoint of computational time, convergency, and numerical instability.

• Journal of Biomedical Engineering Research
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• v.28 no.1
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• pp.108-116
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• 2007

Recently, it has been reported that the posterior stabilized implant, which is clinically used for the total knee replacement (TKR), may have failure risk such as wear or fracture by the contact pressure and stress on the tibial post. The purpose of this study is to investigate the influence of the mal alignment of the posterior stabilized implant on the tibial post by estimating the distributions of contact pressure and von-Mises stress on a tibial post and to analyze the failure risk of the tibial post. Finite element models of a knee joint and an implant were developed from 1mm slices of CT images and 3D CAD software, respectively. The contact pressure and the von-Mises stress applying on the implant were analyzed by the finite element analysis in the neutral alignment as well as the 8 malalignment cases (3 and 5 degrees of valgus and varus angulations, and 2 and 4 degrees of anterior and posterior tilts). Loading condition at the 40% of one whole gait cycle such as 2000N of compressive load, 25N of anterior-posterior load, and 6.5Nm of torque was applied to the TKR models. Both the maximum contact pressure and the maximum von-Mises stress were concentrated on the anterior-medial region of the tibial post regardless of the malalignment, and their magnitudes increased as the degree of the malalignment increased. From present result, it is shown that the malalignment of the implant can influence on the failure risk of the tibial post.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.65-67
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• 2011

The moment-of-fluid (MOF) method is a new volume-tracking method that accurately treats evolving material interfaces. The MOF method uses moment data, namely the material volume fraction, as well as the centroid, for a more accurate representation of the material configuration, interfaces and concomitant volume advection. In this paper, unstructured mesh extension of the MOF method is to be presented. The MOF method is coupled with a stabilized finite element incompressible Navier-Stokes solver for two materials. The effectiveness of the MOF method is demonstrated with a free-surface dam-break problem.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.195-199
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• 1993

In the analysis of metal forming processes by the finite element method, there are many numerical instabilities such as element locking, hourglass mode, shear locking. These instabilities may have a bad effect upon accuracy and convergence. The present work is concerned with improvement of stability and efficiency in two dimensional rigid-plastic finite element method using various type of elements and numerical integration schemes. AS metal forming examples, upsetting and backward extrusion are taken for comparison among the methods : various element types and numerical integration schemes. comparison is made in terms of stability and efficiency. As a result, it has been shown that the finite element computation is stabilized from the viewpoint of computational time, convergency, and numerical instability.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.1-13
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• 2012

In this paper we present an a posteriori error estimator for the stabilized P1 nonconforming finite element method of the linear elasticity problem based on a nonsymmetric H(div)-conforming approximation of the stress tensor in the first-order Raviart-Thomas space. By combining the equilibrated residual method and the hypercircle method, it is shown that the error estimator gives a fully computable upper bound on the actual error. Numerical results are provided to confirm the theory and illustrate the effectiveness of our error estimator.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.519-548
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• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Journal of Ocean Engineering and Technology
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• v.23 no.5
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• pp.1-8
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• 2009

This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.172-176
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• 2008

In this paper, three dimensional linear conforming variable-finite elements are presented with the aid of a smoothed integration (a class of stabilized conforming nodal integration), for mnltiscale mechanics problems. These elements meet the desirable properties of an interpolation such as the Kronecker delta condition, the partition of unity condition and the positiveness of interpolation function. The necessary condition of linear exactness is fully relaxed by employing the smoothed integration, which renders us to meet the linear exactness in a straightforward manner. This novel element description extend the category of the conventional finite elements space to ration type function space and give the flexibility on the number of nodes of element which are fixed in the conventional finite elements. Several examples are provided to show the convergence and the accuracy of the proposed elements, and to demonstrate their potential with emphasis on the multiscale mechanics problems such as global/local analysis, nonmatching contact problems, and modeling of composite material with defects.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.10a
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• pp.445-446
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• 2006

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.311-325
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• 2020

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.