• Steel and Composite Structures
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• v.13 no.1
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• pp.71-89
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• 2012

The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of pre-buckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.

• Structural Engineering and Mechanics
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• v.35 no.1
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• pp.67-82
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• 2010

The beam string structure (BSS) has been widely applied in large span roof structures, while no analytical solutions of BSS were derived for it in the existing literature. In the first part of this paper, calculation formulas of displacement and internal forces were obtained by the Ritz-method for the most commonly used arc-shaped BSS under the vertical uniformly distributed load and the prestressing force. Then, the failure mode of BSS was proposed based on the static equilibrium. On condition the structural stability was reliable, BSS under the uniformly distributed load would fail by tensile strength failure of the string, and the beam remained in the elastic or semi-plastic range. On this basis, the limit load of BSS was given in virtue of the elastic solutions. In order to verify the linear elastic and limit state solutions proposed in this paper, three BSS modal were tested and the corresponding elastoplastic large deformation analysis was performed by the ANSYS program. The proposed failure mode of BSS was proved to be correct, and the analytical results for the linear elastic and limit state were in good agreement with the experimental and FEM results.

• Journal of Advanced Marine Engineering and Technology
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• v.13 no.2
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• pp.43-63
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• 1989

Various kinds of corrosion prevention methods have been developed. It is known that the method of electrochemical protection is more effective and economical than any other method on the large scale metal structures in corrosive solutions. Strong acid solutions such as nitric and sulfuric acid solutions are often used in industries, and the expensive stainless steel is almost exclusively used for the equipment that comes in contact with such acid solutions. However, it is more reasonable that carbon steel is used rather than stainless steel depending upon concentration of those acid solutions from the economical viewpoint. In this study, the typical strong acid solution such as nitric and sulfuric acid solutions are chosen for the experiment and the selected materials of specimen are the stainless steels of SUS 304L and SUS 316L, the carbon steels of SS 41, SM 50 and RA 32, and highly pure lead. Electrochemical protection diagrams can be drawn with data from the external cathodic and anodic polarization curves of SUS 304L, SUS 316L and SM 50 steels in 5-60% nitric acid solutions and from those polarization curves of SS 41, RA 32, SM 50 and SUS 316L steels, and highly pure lead in 2.5-98% sulfuric acid solutions at the slow scanning rate. The data obtained with using the determination method of the optimum cathodic protection potential, the Tafel extrapolation method and the characteristics of anodic polarization curves. The main results obtained from the diagrams are as follows: 1) In nitric acid solution : (1) Corrosion potentials exist in each of those corrosion zones on the stainless steels in the lower concentration than about 12% solutions and on the high tensile strength steels in the lower concentration than about 30% solutions, but the corrosion current (density) in each zone is small on the above mentioned former steels and large on the latter ones. (2) The stainless steels can be self-passivated in the higher concentration than 15% solutions, and the high tensile strength steels gives rise to the same phenomenon in the higher concentration than 35% solutions. (3) The stainless steels in the lower concentration than 60% solutions and the high tensile strength steels in the higher concentration than 35% solutions can be used without protection, but the latter steels must ve protected anodically in the lower conccentration than about 30% solutions. 2) In sufuric acid solution : (1) The carbon steels can be self-passivated in the higher concentration than 45% solutions, and the SUS 316L steel in higher concentration than 75% solutions and the lead in all concentration solutions also gives rise to the same phenomenon. (2) The lead in the lower concentration than 80% solutions and the SUS 316L steel in the higher concentration than 80% solutions can be used without protection. (3) The carbon steels in the higher concentration than 50% solutions also can be used without protecting economically, but the SUS 316L steel in the 20-70% solutions are considerably corrosive without protecting anodically.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Structural Engineering and Mechanics
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• v.40 no.1
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• pp.121-148
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• 2011

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using Integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.721-736
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• 2014

We consider the equation ${\Delta}_mu=p(x)u^{\alpha}+q(x)u^{\beta}$ on $R^N(N{\geq}2)$, where p, q are nonnegative continuous functions and 0 < ${\alpha}{\leq}{\beta}$. Under several hypotheses on p(x) and q(x), we obtain existence and nonexistence of blow-up solutions both for the superlinear and sublinear cases. Existence and nonexistence of entire bounded solutions are established as well.

• Journal of Korean Institute of Industrial Engineers
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• v.12 no.2
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• pp.33-44
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• 1986

This research is concerned with group scheduling problems in multi-stage manufacturing system with dependent setup time. The objective of the research is to develop and evaluate a heuristic algorithm for determining group sequence and job sequence within each group to minimize total tardiness in multi-stage manufacturing systems with sequence dependent group setup time. The group scheduling heuristic algorithm is developed and evaluated by comparisons with twenty-seven problems with the known optimum solutions and 144,000 random schedules of a large variety problems. The results indicate that the proposed heuristic algorithm gets the same optimum solutions for the problems and also provides the good solutions in comparison with the random schedules of the large variety problems. A numerical example is given to illustrate the heuristic algorithm.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.1-14
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• 2016

In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.10 no.2
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• pp.83-92
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• 1998

To evaluate the hydraulic resistance behind bodies in a large scale grid numerical model, a drag stress term which is formulated by the drag force is introduced in the depth-integrated Reynolds equations. And also, the applicability and problems of this model are discussed through various numerical experiments where the analytical solutions exist. In the case of a single body, the error range of velocity difference between analytical and numerical solutions is within $\pm$10% and the wake width behind the body shows a good agreement with the analytical solution. When the drag coefficient and the eddy viscosity are precisely decided, the numerical solutions behind a row of bodies will be efficiently used in real situations.

• Journal of the Korean earth science society
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• v.34 no.1
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• pp.51-58
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• 2013

An appropriate determination of time step is one of the important problems in atmospheric modeling. In this study, we investigate the sensitivity of numerical solutions to time step in a nonlinear atmospheric model. For this purpose, a simple nondimensional dynamical model is employed, and numerical experiments are performed with various time steps and nonlinearity factors. Results show that numerical solutions are not sensitive to time step when the nonlinearity factor is not influentially large and truncation error is negligible. On the other hand, when the nonlinearity factor is large (i.e., in a highly nonlinear regime), numerical solutions are found to be sensitive to time step. In this situation, smaller time step increases the intensity of the spatial filter, which makes small-scale phenomena weaken. This conflicts with the fact that smaller time step generally results in more accurate numerical solutions owing to reduced truncation error. This conflict is inevitable because the spatial filter is necessary to stabilize the numerical solutions of the nonlinear model.