• Journal of Mechanical Science and Technology
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• v.17 no.7
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• pp.986-998
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• 2003

In this paper, an adaptive numerical integration scheme, which does not need non-overlapping and contiguous integration meshes, is proposed for the MLPG (Meshless Local Petrov-Galerkin) method. In the proposed algorithm, the integration points are located between the neighboring nodes to properly consider the irregular nodal distribution, and the nodal points are also included as integration points. For numerical integration without well-defined meshes, the Shepard shape function is adopted to approximate the integrand in the local symmetric weak form, by the values of the integrand at the integration points. This procedure makes it possible to integrate the local symmetric weak form without any integration meshes (non-overlapping and contiguous integration domains). The convergence tests are performed, to investigate the present scheme and several numerical examples are analyzed by using the proposed scheme.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.279-287
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• 2003

This paper deals with a comparative study on coupling of Element-free Galerkin(EFG) method and Infinite Element(IE) by IE's shape function. In this study, mapped infinite elements(mapped IE) and decay function infinite elements(decay IE) are coupled with the EFG method. A coupling procedure of EFG-Mapped IE is much easier to be integrated than a coupled EFG-Decay IE. A coupled EFG-IE method used well-defined functions to preserve the continuity and linear consistency on the interface of the EFG region and IE region. Several benchmark problems are solved to verify the effectiveness and accuracy of the coupling algorithms by IE's shape function. The numerical results show that the developed algorithms work well for the elastic problems with infinite boundaries.

• Steel and Composite Structures
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• v.44 no.1
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• pp.91-104
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• 2022

The purpose of the present work is to study the parametric nonlinear vibration behavior of three layered symmetric laminated plate. In the analytical formulation; both normal and shear deformations are considered in the core layer by means of the refined higher-order zig-zag theory. Harmonic balance method in conjunction with Galerkin procedure is adopted for simply supported laminate plate, to obtain its natural and damping properties. For these aims, a set of complex amplitude equations governed by complex parameters are written accounting for the geometric nonlinearity and viscoelastic damping factor. The frequency response curves are presented and discussed by varying the material and geometric properties of the core layer.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.1
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• pp.85-94
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• 2002

In this study an adaptive node generation procedure in the Element-free Galerkin (EFG) method using bubble-meshing technique is Proposed. Since we construct the initial configuration of nodes by subdivision of background cell, abrupt changes of inter-nodal distance between higher and lower error regions are unavoidable. This unpreferable nodal spacing induces additional errors. To obtain the smooth nodal configuration the nodal configurations are regenerated by bubble-meshing technique. This bubble meshing technique was originally developed to generate a set of well-shaped triangles and tetrahedra. In odder to evaluate the effect of abrupt changes of nodal spacing, one-dimensional problems with various nodal configurations mere investigated. To demonstrate the performance of proposed scheme, the sequences of making optimal nodal configuration with bubble meshing technique are investigated for several problems.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.149-154
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• 1997

Based on the full Navier-Stokes solutions, the thermohydrodynamic performance of a long journal bearing is investigated. A numerical method based on Galerkin's procedure and B-spline test functions has been presented for solving two-dimensional problems involving fluid flow and heat transfer. For numerical stability the artificial compressibility is employed to the conservation of mass. The discretized algebraic equations are solved by Newton's method. Effects of varying the speed of an inner cylinder to load carrying capacity are investigated. The results indicated that the increase of the speed of an inner cylinder has a significant effect on the temperature profile and ultimately on the performance.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.504-514
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• 2003

We investigate global bifurcation in the subharmonic motion of a circular plate with one-to-one internal resonance. A system of autonomous equations are obtained from the partial differential equations governing the system by using Galerkin's procedure and the method of multiple scales. A perturbation method developed by Kovacic and Wiggins is used to find Silnikov type homoclinic orbits. The conditions under which the orbits occur are obtained.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.324-331
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• 2000

In this study, a new algorithm analyzing dynamic crack propagation problem by the coupling technique of Meshfree Method and Finite Element Method is proposed. The coupling procedure of two methods is presented with a short description of Meshfree Method especially, Element-free Galerkin (EFG) method. The elastodynamic fracture theory is presented, and a numerical implementation procedure for dynamic fracture analysis by Meshfree Method is also discussed. A couple of dynamic crack propagation problems illustrate the performance of the propsed technique. The accuracy of numerical solutions by the developed algorithm are compared with those of analytical solutions and experimental ones.

• Transactions of the Korean Society of Mechanical Engineers
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• v.1 no.3
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• pp.141-145
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• 1977

In this paper, approximate solutions of the von Karman equations for the free flexural vibration of a transversely isotropic thin rectangular plate with two simply supported edges and two clamped edges are obtained. Applying one term Ritz-Galerkin procedure, the spatial dependent part of the equation is separated and time dependent function is found to be the Duffing's equation. Then the relation between nonlinear period and amplitude of the vibration is obtained by using averaging method which is a method of the perturbation procedure. It can be seen that averaging method is easy and agrees well with prior results.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.61-68
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• 1991

The system such as railway bridge can be modelled as the restrained beam with intermediate supports. This kind of structures are subject to the moving load, which has a great effect on dynamic stresses and can cause sever motions, especially at high velocities. Therefore, to analyze the dynamic characteristics of the system due to the moving load is very important. In this paper, the governing equation of motion of a restrained beam subjected to the moving load is derived by using the Hamilton's principle. The orthogonal polynomial functions, which are trial functions and satisfying the geometric and dynamic boundary conditions, are obtained through simple procedure. The dynamic response of the system subjected to the moving loads is obtained by using the Galerkin's method and the numerical time integration technique. The numerical tests for various constraint, velocity and boundary conditions were preformed. Furthermore, the effects of mass of the moving load are studied in detail.

• Journal of Advanced Navigation Technology
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• v.11 no.2
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• pp.196-202
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• 2007

In this paper, The TE(transverse electric) scattering problems by a resistive strip grating over a grounded dielectric plane with edge boundary condition are analyzed by applying the FGMM(Fourier-Galerkin Moment Method) known as a numerical procedure. For a TE scattering problem, the induced surface current density is expected to the zero value at both edges of the resistive strip, then the induced surface current density on the resistive strip is expanded in a series of the multiplication of Gegenbauer(Ultraspherical) polynomials with the first order and functions of appropriate edge boundary condition. To verify the validity of the proposed method, the numerical results of normalized reflected power for the uniform resistivity R = 100 ohms/square and R = 0 as a conductive strip case show in good agreement with those in the existing papers.