• Steel and Composite Structures
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• v.52 no.3
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• pp.343-356
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• 2024

This paper presents an analytical solution for correctly predicting the Lateral-Torsional Buckling critical moment of simply supported castellated beams, the solution covers uniformly distributed loads combined with compressive loads. For this purpose, the castellated beam section with hexagonal-type perforation is treated as an arrangement of double "T" sections, composed of an upper T section and a lower T section. The castellated beam with regular openings is considered as a periodic repeating structure of unit cells. According to the kinematic model, the energy principle is applied in the context of geometric nonlinearity and the linear elastic behavior of materials. The differential equilibrium equations are established using Galerkin's method and the tangential stiffness matrix is calculated to determine the critical lateral torsional buckling loads. A Finite Element simulation using ABAQUS software is performed to verify the accuracy of the suggested analytical solution, each castellated beam is modelled with appropriate sizes meshes by thin shell elements S8R, the chosen element has 8 nodes and six degrees of freedom per node, including five integration points through the thickness, the Lanczos eigen-solver of ABAQUS was used to conduct elastic buckling analysis. It has been demonstrated that the proposed analytical solution results are in good agreement with those of the finite element method. A parametric study involving geometric and mechanical parameters is carried out, the intensity of the compressive load is also included. In comparison with the linear solution, it has been found that the linear stability underestimates the lateral buckling resistance. It has been confirmed that when high axial loads are applied, an impressive reduction in critical loads has been observed. It can be concluded that the obtained analytical solution is efficient and simple, and offers a rapid and direct method for estimating the lateral torsional buckling critical moment of simply supported castellated beams.

• 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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.6 s.97
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• pp.571-579
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• 2005

This paper presents the classical site attenuation characteristics of a forced resonant electromagnetic interference (EMI) dipole antenna for frequencies below 80 MHz. The coupled integral equations for unknown current distribution are solved by the Galerkin's method of moments with piecewise sinusoidal functions. The results show that the forced resonant type EMI dipole antenna for frequencies below 80 MHz can be used effectively for measuring the classical site attenuation of horizontal polarization. The theoretical site attenuation curves presented can be used as reference curves for evaluating the performance of an open area test site.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.6
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• pp.939-947
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• 2001

This paper presents the penetrated electric fields and resonant frequencies inside a metallic enclosure with aperture excited by an external dipole source. In the theoretical analysis, integral equations for the current distribution and electric field distributions on the aperture are solved by applying Galerkin\`s method of moments. The results show that the electric fields inside metallic enclosure is maximum at the near the aperture and resonant frequencies are the same as calculated of the enclosure without aperture. To verify the theoretical analysis the electric field inside enclosure and resonant frequencies are compared with the experimental results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.1
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• pp.65-73
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• 1987

An efficient plate bending finite element has been developed using higher-order inplane displacement profiles of the plate. The 6-noded, 21-d.o.f. triangular element including shear deformation effect has been derived from the plate-like continuum by the Galerkin's weighted residual method. Square plate examples were tested with selected element meshes and several aspect ratios for their static behavior under uniformly distributed load. The result of the example tests indicated consistently good performance of the present higher-order plate bending element in comparison with the thin and thick plate solution and other existing finite element solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.923-934
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• 1987

A flexible one-link robotic manipulator is modelled as a rotating cantilever beam with a hub and tip mass. An active control law is developed with consideration of the distributed flexibility of the arm. Equation of motion is derived by Hamilton's principle and, for modal control, represented as state variable form using Galerkin's mode summation method. Feedback coefficients are chosen to minimize the linear quadratic performance index(PI). To reconstruct the complete state vector from the measurements, an observer is proposed. In order to suppress vibration of the manipulator arm to desirable extent and to obtain accuracy of the positioning, weighting factor of input in PI is adjusted. Spillover effect due to the controller which controls several important modes is examined. Experiment is also performed to validate the theoretical analysis.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.3
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• pp.253-259
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• 2003

This paper presents the basic characteristics of a 5 element dipole array antenna which has a four parastic element and one driving element at the center of the circular array. The coupled integral equations for the unknown current distributions on dipole elements are derived and solved by applying Galerkin's method of moments. The numerical results show that the highest power gain of 7.8 dBi is obtained at radius of d = 0.3lλ when two short circuited parastic element neighbors. In order to verify the theoretical analysis, the radiation pattern is compared with Preston's results.

• Water for future
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• v.26 no.3
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• pp.87-101
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• 1993

A finite element model RIV-FEM2 for the hydrodynamic study in a river is developed based on two-dimensional shallow water wave equation and dissipative Galerkin's method. RIV-FEM2 consists of pre-processing, analysis processing and post-processing. Pre- and analysis processing is programmed with Fortran-77 and post-processing with turbo-Pascal respectively. The model is tested with two dimensional problems, including flow through bends, bridges, and symmetric contraction. The two dimensional tests shows stable and efficient results for various situations. Applicability of the model is verified by applying to natural river. The model will provide a basic contribution to the hydrodynamic analysis in a river.

• Tribology and Lubricants
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• v.21 no.1
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• pp.8-15
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• 2005

In this study a general Galerkin FE lubrication analysis method is utilized to analyze the complex lubrication performance of a spiral groove seal, which is being designed and developed for a high-speed flying object application operating at a high-speed of over 50,000 rpm. As at the equilibrium seal clearance the axial stiffness of the seal is predicted to have almost such a constant high value of $1.04\times10^8\;N/m$ regardless of a rotating speed, the seal is expected to maintain a stable thickness of lubrication film under a certain external excitation acting. Also, as even at an ultra high-speed of 80,000 rpm the axial damping of the seal is shown to have a rotatively high value of 5,775 N-s/m, the dynamic stability of the seal system at the axial degree of freedom is assured well enough.

• Tribology and Lubricants
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• v.20 no.2
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• pp.68-76
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• 2004

Applying a general Galerkin FE lubrication analysis method to spiral groove dry gas seals, this study intends to analyze in detail the effects of groove design parameters, such as a spiral angle, groove width ratio, groove radius ratio, groove depth ratio, and groove taper ratio, on the lubrication performances of an opening force, leakage, axial stiffness and damping, and angular stiffness and damping at low and high rotating speeds: 3,600 and 15,000 nm. Results show that, for the primary design consideration performances such as the opening force and axial and angular stiffnesses, a spiral angle of $25^{\circ}$, a groove width ratio of 0.46, a groove radius ratio of 1.1, a groove depth ratio of 1.0, and a groove taper ratio of 0.0 are preferred. Where the recommended relatively low values of groove depth and taper ratios are to keep the axial and angular dampings positive or higher than 0 particularly at the high rotating speed.