• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.11-24
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• 2001

We introduce an assumption about smoothing operator for mixed formulations and show that convergence of Multigrid method for the mixed finite element formulation for the Linear Elasticity. And we show that Richardson and Kaczmarz smoothing satisfy this assumption.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.529-550
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• 2011

In this work, a numerical solution of the incompressible Navier-Stokes equations is proposed. The method suggested is based on an algorithm of discretization by mixed finite elements with a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

• The KIPS Transactions:PartD
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• v.10D no.7
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• pp.1145-1148
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• 2003

We show the mixed finite element method which induces solutions that has the same order of errors for both the gradient of the solution and the solution itself. The technique to construct an efficient reusable matrix is suggested. Two families of mixed finite element methods are introduced with an automatic generating technique for matrix with my order of basis. The generated matrix by this technique has more accurate values and is a sparse matrix. This new technique is applied to solve a minimal surface problem.

• Journal of the Society of Naval Architects of Korea
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• v.34 no.4
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• pp.99-107
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• 1997

A mixed type finite element method is applied to the nonuniform shear warping beam theory which is very useful for the structural analysis of thin-walled sectional beams considering the shear deformation. As known generally, it is shown that the mixed type finite element method, compared with the displacement type one, can give more balanced accuracy of results in calculating the stresses and displacements of the structure. In this paper, one typical example, the flexural-torsional problem of a discontinuously variable sectional beam under coupled end torsional moments, is selected and analyzed to validate the usefulness of the developed beam element.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.267-288
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• 2014

We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order $L^{\infty}((0, T];L^2({\Omega}))$-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.

• Structural Engineering and Mechanics
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• v.13 no.2
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• pp.155-170
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• 2002

In this study, a new functional is obtained for folded plates with geometric (kinematic) and dynamic (natural) boundary conditions. This functional is the combination of two different functionals. Both functionals are obtained for thick plates which carry in-plane and lateral forces. A new mixed finite element is developed with $4{\times}13$ nodal parameters for folded plates (REC52). Forces and moments which are the necessary unknowns in engineering problems are obtained directly using the technique suggested here. The use of the global co-ordinate system causes time consuming operations and therefore the Lagrange multiplier method is used to relate the components of the parameters on the fold line. Numerical results are presented for folded plates and compared with experimental results.

• Structural Engineering and Mechanics
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• v.48 no.1
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• pp.41-56
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• 2013

Initiation and growth of delamination is a great concern of designers of composite structures. Interface elements with de-cohesive constitutive law in the content of continuum damage mechanics can be used to predict initiation and growth of delamination in single and mixed mode conditions. In this paper, an interface element based on the cohesive zone method has been developed to simulate delaminatoin growth of post-buckled laminate under fatigue loading. The model was programmed as the user element and user material by the "User Programmable Features" in ANSYS finite element software. The interface element is a three-dimensional 20 node brick with small thickness. Because of mixed-mode condition of stress field at the delamination-front of post-buckled laminates, a mixed-mode bilinear constitutive law has been used as user material in this model. The constitutive law of interface element has been verified by modelling of a single element. A composite laminate with initial delamination under quasi-static compressive Loading available from literature has been remodeled with the present approach. Moreover, it will be shown that, the closer the delamination to the free surface of laminate, the slower the delamination growth under compressive fatigue loading. The effects of laminate configuration on delamination growth are also investigated.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.427-437
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• 2019

In this study, an alternative solution procedure presented by using variational methods for analysis of shear deformable functionally graded material (FGM) beams with mixed formulation. By using the advantages of $G{\hat{a}}teaux$ differential approaches, a refined complex general functional and boundary conditions which comprises seven independent variables such as displacement, rotation, bending moment and higher-order bending moment, shear force and higher-order shear force, is derived for general thick-thin FGM beams via shear deformation beam theories. The mixed-finite element method (FEM) is employed to obtain a beam element which have a 2-nodes and total fourteen degrees-of-freedoms. A computer program is written to execute the analyses for the present study. The numerical results of analyses obtained for different boundary conditions are presented and compared with results available in the literature.

• Journal of ILASS-Korea
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• v.27 no.1
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• pp.36-41
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• 2022

In this study, the combustion instability characteristics according to the change in the hydrogen ratio in the fuel in the single nozzle system of the hydrogen-natural gas mixed gas turbine for power generation was analyzed using a three-dimensional finite element analysis-based Helmholtz solver. This combustor shows the instability characteristics in which mode transition occurs from a mode having a low amplitude near 70 Hz to a mode having a high amplitude of 250 Hz or higher as the hydrogen fraction in the fuel increases. The current modeling results are found to reasonably predict the main characteristics of the change in measured instability frequency and growth rate with the change in fuel composition.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.56-59
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• 2010

포화된 다공질 매체의 수치해석은 일반적으로 혼합유한요소방법(Mixed Finite Element Method)이 쓰인다. 이 혼합유한요소 방법은 고체변형과 유체의 이동을 동시에 고려하게 되는데 고체의 변형이 거의 없이 유체만 이동할 경우나 고체와 유체의 변형이 없이 간극수압만 존재할 경우에는 요소잠김현상(Element Locking)이 발생하여 혼합유한요소방법으로 해석하기에는 수치적으로 불안정해 진다. 본 논문에서는 이러한 수치적 불안정성을 해결한 스태거드 방법(Park and Tak 2010)을 소개하고 수치적 효율성을 위해 MPI(Message-Passing Interface) 라이브러리를 이용한 병렬해석 기법이 적용된다.