• Steel and Composite Structures
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• 제39권5호
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• pp.493-509
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• 2021

There is not enough mixed finite element method (MFEM) model developed for static and dynamic analysis of functionally graded material (FGM) beams in the literature. The main purpose of this study is to develop a reliable and efficient computational modeling using an efficient functional in MFEM for free vibration and static analysis of FGM composite beams subject to high order shear deformation effects. The modeling of material properties was performed using mixture rule and Mori-Tanaka scheme which are more realistic determination techniques. This method based on the assumption that a two phase composite material consisting of matrix reinforced by spherical particles, randomly distributed in the beam. To explain the displacement components of the shear deformation effects, it was accepted that the shear deformation effects change sinusoidal. Partial differential field equations were obtained with the help of variational methods and then these equations were transformed into a novel functional for FGM beams with the help of Gateaux differential derivative operator. Thanks to the Gateaux differential method, the compatibility of the field equations was checked, and the field equations and boundary conditions were reflected to the function. A MFEM model was developed with a total of 10 degrees of freedom to apply the obtained functional. In the numerical applications section, free vibration and flexure problems solutions of FGM composite beams were compared with those predicted by other theories to show the effects of shear deformation, thickness changing and boundary conditions.

• 대한수학회지
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• 제59권3호
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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 Mechanical Science and Technology
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• 제18권9호
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• pp.1529-1536
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• 2004

A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed-free and free-free elements. The flexibility and stiffness matrices of the free-free elements are the Moore-Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of the complete structure composed of two mixed types of substructures. This study provides the general form of equilibrium equation of the entire structure through the process of assembling the equilibrium equations of substructures with end conditions of mixed types. Applications demonstrate that the proposed method is effective in the structural analysis of geometrically complicated structures.

• 한국CDE학회논문집
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• 제1권1호
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• pp.56-64
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• 1996

A quadrilateral-triangular mixed grid method for the solution of incompressible viscous flow is presented. The solution domain near the body surface is meshed using elliptic grid geneator to acculately simulate the viscous flow. On the other hand, we used unstructured triangular grid system generated by advancing front technique of a simple automatic grid generation algorithm in the rest of the computational domain. The present method thus is capable of not only handling complex geometries but providing accurate solutions near body surface. The numerical technique adopted here is PISO type finite element method which was developed by the present author. Investigations have been made of two-dimensional unsteady flow of Re=550 past a circular cylinder. In the case of use of the unstructured grid only, there exists a considerable amount of difference with the existing results in drag coefficient and vorticity at the cylinder surface; this may be because of the lack of the grid clustering to the surface that is a inevitable requirement to resolve the viscous flow. However, numerical results on the mixed grid show good agreements with the earlier computations and experimental data.

• Steel and Composite Structures
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• 제27권1호
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• pp.27-33
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• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.585-598
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• 2014

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ normed spaces.

• 한국항공우주학회지
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• 제30권4호
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• pp.1-9
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• 2002

항공기 동체에 널리 사용되고 있는 기계적 체결은 응력집중 및 접촉압력 등으로 인해 체결부로부터의 균열발생 가능성이 상대적으로 높다. 본 연구에서는 가중함수법을 적용하여 기계적 체결부에 존재하는 경사진 타원형 모서리균열의 표면점과 최심점에서의 혼합모드 응력확대계수 해석을 수행하였다. 가중함수에 포함된 미정계수들은 기준하중에 대한 유한 요소해석으로부터 구하였다. 경사각에 따른 응력확대계수의 변화를 해석하여 모드 I 응력 확대계수가 최대가 되는 임계 경사각을 결정하였고, 간극의 크기와 균열깊이가 임계 경사각에 미치는 영향을 조사하였다.

• 한국전산구조공학회논문집
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• 제15권3호
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• pp.389-398
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• 2002

동전모양의 균열이 이상복합 실린더 계면에 존재하는 혼합모드 조건(I, II)에 대해 유한요소법을 사용하여 에너지해방율을 구하였다. 두재료의 탄성비와 노치율을 변화시켜 상업용 FEM 프로그램인 ABAQUS로부터 얻은 결과를 가상 균열법과 J 적분법에 적용하였으며 에너지해방율을 구하여 무차원함수로 표현하였다. 모드 II의 무차원 에너지해방율($\sqrt{G_{II}E^*}/\sqrt[p]{\pi a}$)은 균열길이와 탄성비가 증가되면서 그 값이 증가됨을 알수 있었다. 반면, 모드 I의 무차원 에너지해방율($\sqrt{G_{I}E^*}/\sqrt[p]{\pi a}$)은 탄성비가 증가하면서 그 값이 감소하며, 두재료의 탄성비가 3 이상인 경우에 균열길이가 증가되면서 무차원 에너지해방율이 감소하다가 다시 증가하게 나타났다. 또한 수치해석된 결과치를 무한판 실린더의 응력확대계수에 대한 정해와 비교하여 본 해석의 신뢰성을 확보하였다.

• 한국생산제조학회지
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• 제7권3호
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• pp.79-84
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• 1998

It is very difficult to analyze the transient temperature distribution during quenching of the steel because of coupled effects among temperature, structures and stresses. In this paper, using Inoue's equation of evolution and mixture rule, transient temperature distribution is calculated by the finite element method considering latent heat of transformation structure and temperature dependence of physical and mechanical prperties for the 0.45% carbon cylindrical steel bar with 40mm diameter and 20mm height during end-quenching.

• 대한기계학회논문집B
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• 제25권7호
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• pp.989-996
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• 2001

High-speed and low-speed flows are simulated numerically by flowfield-dependent mixed explicit-implicit (FDMEI) method. This algorithm depends on implicitness parameters of convection, diffusion, diffusion gradients, and source terms which are calculated from the changes of local Mach, Reynolds, Peclet, and Damkohler numbers between adjacent nodes. Convection phenomena or shock waves are resolved from Mach number-dependent implicitness parameters whereas diffusion or viscous actions are simulated by Reynolds number or Peclet number-dependent implicitness parameters. Fluctuation components of all variables are properly accommodated spatially and temporally in the FDMEI procedure. To illustrate, some benchmark example problems are presented for comparisons of the FDMEI results with other available data. These results appear to be encouraging and point toward the need for further investigations of the FDMEI theory.