• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.04a
• /
• pp.608-608
• /
• 2008

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.2
• /
• pp.65-92
• /
• 2019

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface. The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven. For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid. Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.24 no.2
• /
• pp.143-159
• /
• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• Computational Structural Engineering
• /
• v.26 no.2
• /
• pp.43-47
• /
• 2013

• Nuclear Engineering and Technology
• /
• v.49 no.1
• /
• pp.234-244
• /
• 2017

Natural frequencies of immersed square sections decrease due to a contribution of added mass to the movement of square sections. In this study, natural frequencies of square sections are obtained as a function of gap size between the square section and a rigid square wall using the finite element method. Additionally, they are used to extract the added mass effect on translational and rotation motions. Published information and studies on the translational and torsional vibration of square beams are also examined for practical use. D coupling of a square section is also investigated for multiple square sections. The suggested added mass estimation can be applicable to the spent fuel storage design of a pressurized light water modulated nuclear power plant.

• Journal of the Korean Society of Visualization
• /
• v.18 no.3
• /
• pp.35-41
• /
• 2020

We conduct numerical simulations of the interaction of a deformable structure with two-phase compressible flow. The finite volume method (FVM) is used to simulate fluid phenomena including a shock wave, a gas bubble, and the deformation of free surface. The deformation of a floating structure is computed with the finite element method (FEM). The compressible two-phase volume of fluid (VOF) method is used for the generation and development of a cavitation bubble, and the immersed boundary method (IBM) is used to impose the effect of the structure on the fluid domain. The result of the simulation shows the generation of a shock wave, and the expansion of the bubble. Also, the deformation of the structure due to the hydrodynamic loading by the explosion is identified.

• Journal of Biomedical Engineering Research
• /
• v.25 no.3
• /
• pp.183-188
• /
• 2004

Magnetic resonance current density imaging (MRCDI) is a useful method for measuring electrical current density distribution inside an object. To avoid object rotations during the conventional MRCDI scans, we have reconstructed current density component images by applying a spatial filter to the magnetic field data measured both inside and outside the object. To measure the magnetic field outside the object with MRI, we immersed the object in a water tank. To evaluate accuracy of the current density imaging, we have made a conductivity phantom with a corresponding finite element method model. We have compared the experimentally obtained current density images with the ones calculated by the finite element method. The average errors of the reconstructed current density images were 6.6 ∼ 45.4 ％ when the injected currents were 1 ∼ 24 mA. We expect that the current density component imaging technique can be used in diverse biomedical applications such as electrical therapy system developments and biological electrical safety analysis.

• Journal of the Korean Society for Precision Engineering
• /
• v.21 no.1
• /
• pp.181-188
• /
• 2004

Structural analysis for materials containing regularly spaced in-homogeneities is usually executed by using averaged material properties. For the homogenization process, a unit cell is defined and loaded somehow, and its response is investigated to evaluate the properties. The imposed loading conditions should accord to the behavior of unit cell immersed in the macroscopic structure in order to guarantee the accuracy of the effective properties. Each unit cell shows periodic variation of strain if the material is loaded uniformly, and in this study, direct implementation of this characteristic behavior is attempted on FE models of unit cell. Conventional finite element analysis tool can be used without any modification, and the boundary of unit cell is constrained in a way that the periodicity is satisfied. The proposed method is applicable to skew arrayed in-homogeneity problems. The flexibility matrix relating tonsorial stress and strain components in skewed rectilinear coordinate system is transformed so that the required engineering constants can be evaluated. Effective properties are computed for the materials with square and skew arrayed circular holes, and its accuracy is examined.

• Steel and Composite Structures
• /
• v.16 no.1
• /
• pp.77-96
• /
• 2014

In this paper, magneto-thermo-elastic problem of a thick truncated conical shell immersed in a uniform magnetic field and subjected to internal pressure is investigated. Material properties of the shell including the elastic modulus, magnetic permeability, coefficients of thermal expansion and conduction are assumed to be isotropic and graded through the thickness obeying the simple power law distribution, while the poison's ratio is assumed to be constant. The temperature distribution is assumed to be a function of the thickness direction. Governing equations of the truncated conical shell are derived in terms of components of displacement and thermal fields and discretised with the help of differential quadrature (DQ) method. Results are obtained for different values of power law index of material properties and effects of thermal load on displacement, stress, temperature and magnetic fields are studied. Results of the present method are compared with those of the finite element method.

• Journal of the Society of Naval Architects of Korea
• /
• v.45 no.2
• /
• pp.168-174
• /
• 2008

To calculate the fluid-structure interaction(FSI) problem rationally, it should be the basic technology to analyse each domain of fluid and structure accurately. In this paper, a new FSI analysis algorithm was introduced using the 3D solid finite element for structural analysis and CFD code based on the HCIB method for viscous flow analysis. The fluid and structural domain were analysed successively and alternatively in time domain. The structural domain was analysed by the Newmark-b direct time integration scheme using the pressure field calculated by the CFD code. The results for example calculation were compared with other research and it was shown that those coincided each other. So we can conclude that the developed algorithm can be applied to the general FSI problems.