• Structural Engineering and Mechanics
• /
• v.5 no.3
• /
• pp.329-338
• /
• 1997

In this paper a general analytical approach is proposed to analyse the nonlinear response of elastic cable under complex loads. The effect of temperature change on the cable is also considered. From the vertical equilibrium equations of cable, the general analytical formula of vertical displacement is derived. Based on the vertical displacement formula and on the compatibility condition of the cable, the dimensionless equation with respect to cable tension is established. By means of such analytical procedures, the exact solutions of various cable problems can be obtained quickly. The example given in this paper shows that the new procedure is efficient for practical analysis and can be easily implemented by a general computer program without the superposition problem which there has always been in traditional analytical methods.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.63 no.10
• /
• pp.1377-1383
• /
• 2014

This paper deals with eddy current loss of magnetic coupling with radial permanent magnet (PM) using analytical method such as a space harmonic method. Superposition of two kinds analysis model is used to analyze eddy current loss induced in inner PM and outer PM of magnetic coupling. When the eddy current is induced, the environmental temperature increases, and the permanent magnet(PM) characteristics are degraded because the performance of PM is greatly influenced by temperature rise. Hence, the calculation of eddy current loss becomes an important factor in the magnetic coupling. In order to analyze eddy current loss, first, on the basis of the magnetic vector potential and two-dimensional(2-D) polar-coordinate system, the magnetic field solutions of the radial magnetized PM are obtained. And we obtain the analytical solutions for the eddy current density produced by permanent magnet. Lastly, analytical solutions for eddy current loss are derived by using equivalent, electrical resistance calculated from magnet volume and analytical solution for eddy current density. This analytical results are validated by comparing with the 2-D finite element analysis (FEA).

• Bulletin of the Society of Naval Architects of Korea
• /
• v.13 no.1
• /
• pp.25-34
• /
• 1976

Analytical solutions for the transient temperature and quasi-static thermal stresses which arise in thin plates subjected to an instantaneous point source of heat have been investigated. And the solutions have been extended to the case of a moving source of heat with the aid of the Duhamel's superposition integral. For finite disk an experiment was conducted, the measured temperature histories show a good agreement with the theoretical temperature histories, And the histories of thermal stresses show a good qualitative agreement with the physical phenomena. And also we can find out that the maximum temperature and thermal stresses and their location can be estimated by using the solutions for infinite plates instead of the solutions for a finite plate. The solutions can be used for the problems such as a welding or line heating in a hull construction.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.12 no.2
• /
• pp.13-34
• /
• 1975

Analytical solutions for the transient temperature distribution and quasi-static thermal stresses which arise in a thin circular disk of finite radius subjected to an instantaneous point source acting in its interior have been obtained. And the solutions have been extended to the case of a moving heat source with the aid of the Duhamel's superposition integral. The solutions given are in the form of double infinite serieses, and their numerical results have been compared with the experimental temperature histories. It can be found out that the theoretical histories of thermal stresses show a good agreement with the experimental results and the theoretical histories of thermal stresses show a good qualitative agreement with a physical phenomena. The solutions can be applied to the problems such as a flame hardening of the cylindrical machine elements and a circular patch welding or a circular cutting of the structural member.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.17 no.4
• /
• pp.232-242
• /
• 2005

In this study, we get an analytical solution for the diffraction and multi-reflection around a semi-infinite breakwater and breakwaters with a gap by using the solution of Penney and Price (1952). We find analytical solutions for single- and multi-reflections around the breakwaters by assuming that the reflected waves are regarded to be those diffracting through a breakwater gap. On the basis of these solutions, it is possible to understand the wave diffraction with different cases of incident wave direction and breakwater layout. These solutions may help harbor engineers to understand the phenomena of diffraction and multi-reflections around the breakwaters. These solutions may also be used to evaluate the applicability of wave transformation models which are used in designing coastal structures.

• Journal of Mechanical Science and Technology
• /
• v.20 no.6
• /
• pp.882-895
• /
• 2006

Surface and interfacial waves in two superposed horizontal inviscid fluids of finite depths are studied. The flow is induced by translating a vertical rigid plate with a prescribed velocity. Analytical solutions that accurately predict the motion of the free surface and the interface are obtained by using a small-Froude-number approximation. Three different velocities of the plate are considered, while flows induced by any arbitrary motion of the plate can be easily analyzed by a linear superposition of the solutions obtained. It is shown that pinching of the upper layer can occur for a sufficiently thin upper layer, which leads to its rupture into small segments. Other interesting phenomena, such as primary and secondary wiggles generated on the interface near the wavemaker, are discussed.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.9 no.1
• /
• pp.43-54
• /
• 1997

This paper presents an approximate analytical solution to a two-region one-dimensional model for the charging process of stratified thermal storage tanks with variable inlet temperature in the presence of momentum-induced mixing. Based on the superposition principle, an arbitrary-varying inlet temperature is decomposed into inherent discontinuous steps and continuous intervals approximated as a finite number of piecewise linear functions. This approximation allows the temperature of the upper perfectly-mixed layer to be expressed in terms of constant, linear and exponential functions with respect to time. Applying the Laplace transform technique to the model equation for the lower thermocline layer subject to each of three representative interfacial conditions yields compact-form solutions, a linear combination of which constitutes the final temperature profile. A systematic method for deriving solutions to the plug-flow problem having polynomial-type boundary conditions is also established. The effect of adiabatic exit boundary on solution behaviors proves to be negligible under the actual working conditions, which justifies the assumption of semi-infinite domain introduced in the solution procedure. Finally, the approximate solution is validated by comparing it with an exact solution obtained for a specific variation of inlet temperature. Excellent agreements between them suffice to show the necessity and utility of this work.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.9 no.1
• /
• pp.10-17
• /
• 1985

A new method is suggested for the solution of plane elasticity problems. With use of the dislocation model in the crack problems, the basic scheme of this method is to find equilibrium Burgers vectors of dislocations which are distributed along the boundary of the first fundamental boundary value problems. The stress distribution in the region can be found by superposition of the contributions of each dislocation. The method is applied to three cases with known analytical solutions, and to a V-notched specimen under uniaxial tension. The numerical results are compared with other available solutions. This method is effective and simple in its use, compared with other numerical methods. The method also provides very accurate solutions in the region except near the boundary where the discretization error is significant. The extrapolation method is suggested for the stresses in the boundary region. Extensive application are also suggested for a general estimate of the computational efficiency of the method.