• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.27-43
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• 2002

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

• Wind and Structures
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• v.27 no.4
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• pp.235-245
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• 2018

In this study the stress analysis of orthotropic thin plate with arbitrary shapes for different boundary conditionsis investigated. Meshfreemethod is applied to static analysis of thin plates with various geometries based on the Kirchhoff classical plate theory. According to the meshfree method the domain of the plates are expressed through a set of nodes without using mesh. In this method, a set of nodes are defined in a standard rectangular domain, then via a third order map, these nodes are transferred to the main domain of the original geometry; therefore the analysis of the plates can be done. Herein, Meshless local Petrov-Galerkin (MLPG) as a meshfree numerical method is utilized. The MLS function in MLPG does not satisfy essential boundary conditions using Delta Kronecker. In the MLPG method, direct interpolation of the boundary conditions can be applied due to constructing node by node of the system equations. The detailed parametric study is conducted, focusing on the arbitrary geometries of the thin plates. Results show that the meshfree method provides better accuracy rather than finite element method. Also, it is found that trend of the figures have good agreement with relevant published papers.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1579-1588
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• 2003

In this paper, the finite element equations for the transient linear viscoelastic stress analysis are presented in time domain, whose variational formulation is derived by using the Galerkin's method based on the equations of motion in time integral. Since the inertia terms are not included in the variational formulation, the time integration schemes such as the Newmark's method widely used in the classical dynamic analysis based on the equations of motion in time differential are not required in the development of that formulation, resulting in a computationally simple and stable numerical algorithm. The viscoelastic material is assumed to behave as a standard linear solid in shear and an elastic solid in dilatation. To show the validity of the presented method, two numerical examples are solved nuder plane strain and plane stress conditions and good results are obtained.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.27 no.1
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• pp.46-52
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• 2013

The current distribution passing through grounding electrode is required for calculating an impedance of grounding electrode using the electromagnetic field model. In this paper the numerical calculation for currents passing through a grounding electrode as a function of frequency was given. The proposed approach is based on the wire antenna model(AM) in the frequency domain. The Pocklington's equation driven from the wire antenna theory was numerically calculated by the Galerkin's method. The triangle function was applied to both the basis function and the weighting function. The current distribution of a horizontal ground electrode was simulated in MATLAB. Also these results were compared with the data obtained from the CDEGS HIFREQ calculation.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.427-436
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• 2000

This study presents the nonlinear responses of a hinged-clamped beam under broadband random excitation. By using Galerkin's method the governing equation is reduced to a system or nonautonomous nonlinear ordinary differential equations. The Fokker-Planck equation is used to generate a general first-order differential equation in the joint moments of response coordinates. Gaussian and non-Gaussian closure schemes are used to close the infinite coupled moment equations. The closed equations are then solved for response statistics in terms of system and excitation parameters. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. Monte Carlo simulation is used for numerical verification.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.365-391
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• 2007

The vibration and stability analysis is investigated for composite cylindrical shells that composed of ceramic, FGM, and metal layers subjected to various loads. Material properties of FG layer are varied continuously in thickness direction according to a simple power distribution in terms of the ceramic and metal volume fractions. The modified Donnell type stability and compatibility equations are obtained. Applying Galerkin's method analytic solutions are obtained for the critical parameters. The detailed parametric studies are carried out to study the influences of thickness variations of the FG layer, radius-to-thickness ratio, lengths-to-radius ratio, material composition and material profile index on the critical parameters of three-layered cylindrical shells. Comparing results with those in the literature validates the present analysis.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.7
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• pp.667-678
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• 2002

In this paper, a new radiating structure with a multi-layered two-dimensional metallic disk array was proposed for shaping the flat-topped element pattern. It is an infinite periodic planar array structure with metallic disks finitely stacked above the radiating circular waveguide apertures. The theoretical analysis was in detail performed using rigid full-wave analysis, and was based on modal representations for the fields in the partial regions of the array structure and for the currents on the metallic disks. The final system of linear algebraic equations was derived using the orthogonal property of vector wave functions, mode-matching method, boundary conditions and Galerkin's method, and also their unknown modal coefficients needed for calculation of the array characteristics were determined by Gauss elimination method. The application of the algorithm was demonstrated in an array design for shaping the flat-topped element patterns of $\pm$20$^{\circ}$ beam width in Ka-band. The optimal design parameters normalized by a wavelength for general applications are presented, which are obtained through optimization process on the basis of simulation and design experience. A Ka-band experimental breadboard with symmetric nineteen elements was fabricated to compare simulation results with experimental results. The metallic disks array structure stacked above the radiating circular waveguide apertures was realized using ion-beam deposition method on thin polymer films. It was shown that the calculated and measured element patterns of the breadboard were in very close agreement within the beam scanning range. The result analysis for side lobe and grating lobe was done, and also a blindness phenomenon was discussed, which may cause by multi-layered metallic disk structure at the broadside. Input VSWR of the breadboard was less than 1.14, and its gains measured at 29.0 GHz. 29.5 GHz and 30 GHz were 10.2 dB, 10.0 dB and 10.7 dB, respectively. The experimental and simulation results showed that the proposed multi-layered metallic disk array structure could shape the efficient flat-topped element pattern.