• 한국전산유체공학회지
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• 제9권3호
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• pp.57-65
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• 2004

The incompressible Navier-Stokes equations in two dimensions are stabilized by a modified residual method, and then discretized by hierarchical elements. The stabilization is necessary to escape from the Ladyzhenskaya-Babuska-Brezzi(LBB) constraint and hence to achieve an equal order formulation. To expedite a standard iterative method such as the conjugate gradient squared(CGS) method, a preconditioning technique called the Hierarchical Iterative Procedure(HIP) has been applied. In this paper, we increased the order of interpolation within an element up to cubic. The hierarchical elements have been used to achieve a higher order accuracy in fluid flow analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far The numerical results by the present HIP for the lid driven cavity flow and others showed the present procedure to be stable, very efficient and useful in flow analyses in conjunction with hierarchical elements.

• Steel and Composite Structures
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• 제47권3호
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• pp.365-374
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• 2023

This paper presents a new scheme for constructing locking-free finite elements in thick and thin plates, called Discrete Shear Gap element (DSG), using multiphase material topology optimization for triangular elements of Reissner-Mindlin plates. Besides, common methods are also presented in this article, such as quadrilateral element (Q4) and reduced integration method. Moreover, when the plate gets too thin, the transverse shear-locking problem arises. To avoid that phenomenon, the stabilized discrete shear gap technique is utilized in the DSG3 system stiffness matrix formulation. The accuracy and efficiency of DSG are demonstrated by the numerical examples, and many superior properties are presented, such as being a strong competitor to the common kind of Q4 elements in the static topology optimization and its computed results are confirmed against those derived from the three-node triangular element, and other existing solutions.

• Geomechanics and Engineering
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• 제10권6호
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• pp.757-774
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• 2016

Soils are usually weak in tension therefore different materials such as geosynthetics are used to address this inadequacy. Worldwide annual consumption of geosynthetics is close to $1000million\;m^2$, and the value of these materials is probably close to US$1500 million. Since the total cost of the construction is at least four or five times the cost of the geosynthetic itself, the impact of these materials on civil engineering construction is very large indeed. Nevertheless, there are several significant problems associated with geosynthetics, such as creep, low modulus of elasticity, and susceptibility to aggressive environment. Carbon fiber reinforced polymer (CFRP) was introduced over two decades ago in the field of structural engineering that can also be used in geotechnical engineering. CFRP has all the benefits associated with geosynthetics and it boasts higher strength, higher modulus, no significant creep and reliability in aggressive environments. In this paper, the performance of a CFRP reinforced retaining wall is investigated using the finite element method. Since the characterization of behavior of soils and interfaces are vital for reliable prediction from the numerical model, soil and interface properties are obtained from comprehensive laboratory tests. Based on the laboratory results for CFRP, backfill soil, and interface data, the finite element model is used to study the behavior of a CFRP reinforced wall. The finite element model was verified based on the results of filed measurements for a reference wall. Then the reference wall simulated by CFRP reinforcements and the results. The results of this investigations showed that the safety factor of CFRP reinforced wall is more and its deformations is less than those for a retaining wall reinforced with ordinary geosynthetics while their construction costs are in similar range.

• 한국전산유체공학회지
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• 제10권2호
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• pp.38-47
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• 2005

Substructuring methods are often used in finite element structural analyses. In this study a multi-level substructuring(MLSS) algorithm is developed and proposed as a possible candidate for finite element fluid solvers. The present algorithm consists of four stages such as a gathering, a condensing, a solving and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At the highest level, each sub-domain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each sub-domain has been replaced by a sequential static condensation of gathered element matrices. The global algebraic system arising from the assembly of each sub-domain matrices is solved using a well-known iterative solver such as the conjugare gradient(CG) or the conjugate gradient squared(CGS) method. A time comparison with CG has been performed on a 2-D Poisson problem. With one domain the computing time by MLSS is comparable with that by CG up to about 260,000 d.o.f. For 263,169 d.o.f using 8 x 8 sub-domains, the time by MLSS is reduced to a value less than $30\%$ of that by CG. The lid-driven cavity problem has been solved for Re = 3200 using the element interpolation degree(Deg.) up to cubic. in this case, preconditioning techniques usually accompanied by iterative solvers are not needed. Finite element formulation for the incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et al.[9].

• Geomechanics and Engineering
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• 제36권3호
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• pp.277-293
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• 2024

Shored Mechanically Stabilized Earth (SMSE) walls are types of soil retaining structures that increase soil stability under static and dynamic loads. The damage caused by an earthquake can be determined by evaluating the probabilistic seismic response of SMSE walls. This study aimed to assess the seismic performance of SMSE walls and provide fragility curves for evaluating failure levels. The generated fragility curves can help to improve the seismic performance of these walls through assessing and controlling variables like backfill surface settlement, lateral deformation of facing, and permanent relocation of the wall. A parametric study was performed based on a non-linear elastoplastic constitutive model known as the hardening soil model with small-strain stiffness, HSsmall. The analyses were conducted using PLAXIS 2D, a Finite Element Method (FEM) program, under plane-strain conditions to study the effect of the number of geogrid layers and the axial stiffness of geogrids on the performance of SMSE walls. In this study, three areas of damage (minor, moderate, and severe) were observed and, in all cases, the wall has not completely entered the stage of destruction. For the base model (Model A), at the highest ground acceleration coefficient (1 g), in the moderate damage state, the fragility probability was 76%. These values were 62%, and 54%, respectively, by increasing the number of geogrids (Model B) and increasing the geogrid stiffness (Model C). Meanwhile, the fragility values were 99%, 98%, and 97%, respectively in the case of minor damage. Notably, the probability of complete destruction was zero percent in all models.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2002년도 추계학술대회 논문집
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• pp.381-386
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• 2002

Recently, The machine tools have been needed for high speed and accuracy to increase productivity. The most important thing to get a more stabilized machine is to know the frequncy response which has an effect on manufacture a lot. This problem should be considered seriously by many researchers. There are many programs about FEM. but just using FEM program to get information of the object is not enough to put our confidence in the stability of the structure design. Therefore, the purpose of this research is to make a study for proving one of the ways to design to produce stabilized a machine more efficiently by comparing FRT with Simulation through FEM. At this two tests, we can learn about the frequency response area causing resonance and we can reconfirm the result to trust.

• 대한수학회지
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• 제50권5호
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• 대한수학회보
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• 제53권2호
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• pp.423-440
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• 2016

The bubble stabilization technique of Chebyshev-Legendre high-order element methods for one dimensional advection-diffusion equation is analyzed for the proposed scheme by Canuto and Puppo in [8]. We also analyze the finite element lower-order preconditioner for the proposed stabilized linear system. Further, the numerical results are provided to support the developed theories for the convergence and preconditioning.

• 한국전산유체공학회지
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• 제12권1호
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• pp.35-42
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• 2007

This paper describes a recent development on the divergence free basis function based on a hermite stream function and verifies its validity by comparing results with those from a modified residual method known as one of stabilized finite element methods. It can be shown that a proper choice of degrees of freedom at a node with a proper arrangement of the hermite interpolation functions can yield solenoidal or divergent free interpolation functions for the velocities. The well-known cavity problem has been chosen for validity of the present algorithm. The comparisons from numerical results between the present and the modified residual showed the present method yields better results in both the velocity and the pressure within modest Reynolds numbers(Re = 1,000).

• Geomechanics and Engineering
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• 제9권4호
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• pp.415-426
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• 2015

Researches have been done to discover ways to strengthen peat soil deposits. In this model study, fibrous peat that is the most compressible types of peat has been reinforced with precast peat columns stabilized with ordinary Portland cement and polypropylene fibres. Rowe cell consolidation tests as well as plate load tests (PLTs) were conducted on various types of test samples to evaluate the strength and deformation of untreated peat and peat reinforced by various types of columns. PLTs were conducted in a specially designed and fabricated circular steel test tank. The compression index ($C_c$) and recompression index ($C_r$) of fibrous peat samples reduced considerably upon use of precast columns. Also, PLT results confirmed the results obtained from Rowe cell tests. Use of polypropylene fibres added to cement further decreased ($C_c$) and ($C_r$) and increased load bearing capacity of untreated peat. Finite element method (FEM) using Plaxis 3D was carried out to evaluate the stress distributions along various types of tested samples and also, to compare the deformations obtained from FEM analysis with the actual maximum deformations found from PLTs. FEM results indicate that most of the induced stresses are taken on the upper portion of tested samples and reach their maximum values below the loading plate. Also, a close agreement was found between actual deformation values obtained from PLTs and values resulted from FEM analysis for various types of tested samples.