• Proceedings of the KSME Conference
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• 2001.06b
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• pp.482-487
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• 2001

Time responses of a flexible spinning disk of which axis of symmetry is misaligned with the axis of rotation are analyzed in a numerical manner. Equations of motions are derived by Hamilton's principle based on Kirchhoff plate theory and von-Karman strain theory, and the equations are discretized by finite element method. In obtaining the time responses, Generalized-$\alpha$ method is used to solve the equations. Based on the result, the effects of the misalignment are analyzed on the vibration characteristics of a spinning disk.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Advances in concrete construction
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• v.15 no.2
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• pp.115-126
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• 2023

This paper investigates creep analysis of a plate made of Al-SiC functionally graded material using Mendelson's method of successive elastic solution. All mechanical and thermal material properties, except Poisson's ratio, are assumed to be variable along the thickness direction based on the volume fraction of reinforcement and thickness. First, the basic relations of the plate are derived using the Love-Kirchhoff plate theory. The solution of governing equations yields an elastic solution to start creep analysis. The creep behavior is demonstrated through Norton's equation based on Pandey's experimental results extracted for Al-SiC functionally graded material. A linear variation is assumed for temperature distribution along the thickness direction. The creep strain, as well as the thermal strain, are included in the governing equations derived from classical plate theory for mechanical strain. A successive elastic solution based on Mendelson's method is employed to derive the history of stresses, strains, and displacements over a long time. History of stresses and deformations are obtained over a long time to predict damage to the plate because of various loadings, and material composition along the thickness and planar directions.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.4 no.2
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• pp.76-80
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• 2003

In this study, it is presented analysis results of bending problems in the orthotropic thick plates and the orthotropic thin plates. Finite element method in this analysis was used. Both Kirchoffs assumptions and Mindlin assumptions are used as the basic governing equations of bending problems in the orthotropic plates. The analysis results are compared between the orthotropic thick plates and the orthotropic thin plates for the variations of thickness-width ratios.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.24-27
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• 1989

In the case of analyzing electric machinery by finite element method, so far, magnetic current was selected as a driving source. But terminal voltage is a driving source in real systems, and magnetic current is varied according to variation of load conditions. Therfore, in this paper magnetic flux distribution of linear induction motor was analized by using kirchhoff's second law with voltage as a driving source, and magnetic current was calculated.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.50 no.3
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• pp.146-152
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• 2001

This paper describes an accurate fault location algorithm based on sequence current distribution factors for a double-circuit transmission system. The proposed method uses the voltage and current collected at only the local end of a single-circuit. This method is virtually independent of the fault resistance and the mutual coupling effect caused by the zero-sequence current of the adjacent parallel circuit and insensitive to the variation of source impedance. The fault distance is determined by solving the forth-order KVL(Kirchhoff's Voltage Law) based distance equation. The zero-sequence current of adjacent circuit is estimated by using a zero-sequence current distribution factor and the zero-sequence current of the self-circuit. Thousands of fault simulation by EMTP have proved the accuracy and effectiveness of the proposed algorithm.

• Advances in nano research
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• v.10 no.1
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• pp.25-42
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• 2021

In this article, the vibration behavior of embedded Functionally Graded Nanoplate (FGNP) employing nonlocal Kirchhoff's plate theory has been investigated under hygrothermal environment. The FGNP is considered to be supported by Winkler-Pasternak foundation. The Eringen's differential theory is used for size effect on the vibration of the FGNP. Rayleigh-Ritz method with orthogonal polynomials are employed for the governing equations and edge constraints. The advantage of this method is that it overcomes all the drawbacks of edge constraints and can easily handle any combinations of mixed edge constraints. The coefficients viz. moisture expansion, thermal expansion and elastic coefficients are considered to be transversely graded across the FGNP. The similarity of the calculated natural frequencies is examined with the previous research, and a good concurrency is seen. The objective of this article is to analyze the parameters' effect on the nondimensionalized frequency of embedded FGNP under hygrothermal environment subjected to all possible edge constraints. For this, uniform and linear rise of temperature and moisture concentration are considered. The study highlights that the nonlocal effect is pronounced for higher modes. Moreover, the effect of the Pasternak modulus is seen to be prominent compared to the Winkler modulus on non dimensionalized frequencies of FGNP.

• Proceedings of the KIEE Conference
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• 2002.07b
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• pp.867-869
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• 2002

A method for the time step analysis of single phase induction motors is proposed. The unknown variables in differential equations are the currents flowing through rotor bars. They are coupled with the distributed magnetic flux densities in the airgap instead of inductance matrix while applying Kirchhoff's and Faraday's induction laws. Two patterns for magnetic flux densities are necessary. One is given by ideal stator winding distribution. the other is produced by currents flowing a rotor bar with unit magnitude and is calculated by FEM. Formulated set of equations are solved for a simple three phase and single phase example model and the resultant speed torque curve is shown in this paper.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2951-2954
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• 2007

Tumor hemodynamics in vascular state is numerically simulated using pressure node solution. The tumor angiogenesis pattern in our previous study is used for the geometry of vessel networks. For tumor angiogenesis, the equation that governed angiogenesis comprises a tumor angiogenesis factor (TAF) conservation equation in time and space, which is solved numerically using the Galerkin finite element method. A stochastic process model is used to simulate vessel formation and vessel. In this study, we use a two-dimensional model with planar vessel structure. Hemodynamics in vessel is assumed as incompressible steady flow with Newtonian fluid properties. In parent vessel, arterial pressure is assigned as a boundary condition whereas a constant terminal pressure is specified in tumor inside. Kirchhoff's law is applied to each pressure node to simulate the pressure distribution in vessel networks. Transient pressure distribution along with angiogenesis pattern is presented to investigate the effect of tumor growth in tumor hemodynamics.

• 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.