• 연구논문집
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• s.28
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• pp.123-135
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• 1998

A shape function for element free Galerkin method is carved from Shepard interpolant of singular weight and consistency condition. Thus present shape function is an interpolation and has no singularities. The shape function is applied to cantilever bending problems and gives good results in comparison with beam theory. Finally it is shown that the coupling with finite element method is made easily without any additional treaties.

• Computational Structural Engineering
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• v.11 no.1
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• pp.261-274
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• 1998

In this paper, local and global error estimates for the element-free Galerkin (EFG) method are proposed. The essence of proposed error estimates is to use the difference between the values of the projected stress and these given directly by the EFG solution. The stress projection can be obtained simply by taking product of shape function based on a different domain of influence with the stresses at nodes. In this study, it was found that the effectivity index is optimized if the domain of influence in stress projection procedure is the smallest that retains regularity of the matrices in EFG. Numerical tests are shown for various 1D and 2D examples illustrating the good effectiveness of the proposed error estimator in the global energy norm and in the local error estimates.

• Advances in nano research
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• v.7 no.2
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• pp.99-108
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• 2019

Higher-order theories are very important to investigate the mechanical properties and behaviors of nanoscale structures. In this study, a free vibration behavior of SiNW resting on elastic foundation is investigated via Eringen's nonlocal elasticity theory. Silicon Nanowire (SiNW) is modeled as simply supported both ends and clamped-free Euler-Bernoulli beam. Pasternak two-parameter elastic foundation model is used as foundation. Finite element formulation is obtained nonlocal Euler-Bernoulli beam theory. First, shape function of the Euler-Bernoulli beam is gained and then Galerkin weighted residual method is applied to the governing equations to obtain the stiffness and mass matrices including the foundation parameters and small scale parameter. Frequency values of SiNW is examined according to foundation and small scale parameters and the results are given by tables and graphs. The effects of small scale parameter, boundary conditions, foundation parameters on frequencies are investigated.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.88-97
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• 1996

This paper treats an adaptive finite-element method for the viscous compressible flow governed by Navier-Stokes equations in two dimensions. The numerical algorithm is the two-step Taylor-Galerkin mettled using unstructured triangular grids. To increase accuracy and stability, combined moving node method and grid refinement method have been used for grid adaption. Validation of the present algorithm has been made by comparing the present computational results with the existing experimental data and other numerical solutions. Four benchmark problems are solved for demonstration of the present numerical approach. They include a subsonic flow over a flat plate, the Carter flat plate problem, a laminar shock-boundary layer interaction. and finally a laminar flow around NACA0012 airfoil at zero angle of attack and free stream Mach number of 0.85. The results indicates that the present adaptive triangular grid method is accurate and useful for laminar viscous flow calculations.

• Computers and Concrete
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• v.16 no.5
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• pp.669-682
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• 2015

Degradation of reinforced concrete (RC) structures due to chloride penetration followed by reinforcement corrosion has been a serious problem in civil engineering for many years. The numerical simulation methods at present are mainly finite element method (FEM) and finite difference method (FDM), which are based on mesh. Mesh generation in engineering takes a long time. In the present article, the numerical solution of chloride transport in concrete is analyzed using radial point interpolation method (RPIM) and element-free Galerkin (EFG). They are all meshless methods. RPIM utilizes radial polynomial basis, whereas EFG uses the moving least-square approximation. A Galerkin weak form on global is used to attain the discrete equation, and four different numerical examples are presented. MQ function and appropriate parameters have been proposed in RPIM. Numerical simulation results are compared with those obtained from the finite element method (FEM) and analytical solutions. Two case of chloride transport in full saturated and unsaturated concrete are analyzed to test the practical applicability and performance of the RPIM and EFG. A good agreement is obtained among RPIM, EFG, and the experimental data. It indicates that RPIM and EFG are reliable meshless methods for prediction of chloride concentration in concrete structures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.17-26
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• 2014

This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.237-246
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• 1999

A finite element model is studied to simulate unsteady free surface flow based on dynamic wave equation and collocation method. The collocation method is used in conjunction with Hermite polynomials, and resulting matrix equations are solved by skyline method. The model is verified by applying to hydraulic jump, nonlinear disturbance propagation and dam-break flow in a horizontal frictionless channel. The computed results are compared with those by Bubnov-Galerkin and Petrov-Galerkin methods. It is also applied to the North Han River to simulate the floodwave propagation. The computed results have good agreements with those of DWOPER model in terms of discharge hydrographs. The suggested model has proven to be one of the promising scheme for simulating the gradually and rapidly varied unsteady flow in open channels.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.10
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• pp.3152-3159
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• 1996

Previous works about the cylindrical shape elastic body which is under longitudinal temperature distribution mostly show the results of free expansion, therefore exact thermo-elastic analysis is needed. The object of this work is to analyze the thermo-elastic problem of the hollow cylinder when the cylinder is under longitudinal temperature distribution. In this paper, the analytical solution is found by using Galerkin vector, and it is compared by the results of FEM. For displacements of cylinder, analytical values are almost same as the results of FEM, but free expansion is not fit for analytical solution and the results of FEM. stresses from analytical solution and the results of FEM show good agreement also. but the results are different near the end boundary, since St. Venant principle is applied.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.61-74
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• 1995

A linearly tapered, doubly symmetric thin-walled closed member, such as power-transmission towers and tourist towers, are often characterized by local variation in mass and/or rigidity, due to additional mass and rigidity. On the preliminary stage of design the closed-form solution is more effective than the finite element method. In order to propose approximate solutions, the discontinuous and local variation in mass and/or rigidity is treated continuously by means of a usable function proposed by Takabatake(1988, 1991, 1993). Thus, a simplified analytical method and approximate solutions for the free and forced transverse vibrations in linear elasticity are demonstrated in general by means of the Galerkin method. The solutions proposed here are examined from the results obtained using the Galerkin method and Wilson-${\theta}$ method and from the results obtained using NASTRAN.

• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.257-270
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• 2013

The use of lightweight materials has been steadily increasing in the automotive industry, and presents new challenges to material joining. Among many joining processes, self-piercing riveting (SPR) is particularly promising for joining lightweight materials (such as aluminum alloys) and dissimilar materials (such as steel to Al, and metal to polymer). However, to establish a process window for optimal joint performance, it often requires a long trial-and-error testing of the SPR process. This is because current state of the art in numerical analysis still cannot effectively resolve the problems of severe material distortion and separation in the SPR simulation. This paper presents a coupled meshfree/finite element with a moving boundary algorithm to overcome these numerical difficulties. The simulation results are compared with physical measurements to demonstrate the effectiveness of the present method.