• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.10
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• pp.115-121
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• 2008

This paper presents bisymmetric dual iron core lineal motor stage for heavy-duty high precision applications such as large area micro-grooving machines or high precision roll die machines. In this stage, two iron core linear motors are installed in laterally symmetric way to cancel out the attractive forces. Main focus was given to analyzing the effect of cogging force and moment for two different layouts, which are symmetric and half-pitch shifted ones. Experimental results showed that the symmetric layout is more adequate for high precision applications because of its clear moment cancellation effect. It was also verified that the effect of the residual cogging moment can be suppressed further by increasing the bearing stiffness. One problem of the symmetric layout is added cogging force which hinders smooth motion, but its effect was relatively small compared with that of moment cancellation.

• Steel and Composite Structures
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• v.15 no.2
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• pp.175-202
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• 2013

The super convergent laminated composite beam element is newly derived for the lateral stability analysis. For this, a theoretical model of the laminated composite beams is developed based on the first-order shear deformation beam theory. The present laminated beam takes into account the transverse shear and the restrained warping induced shear deformation. The second-order coupling torque resulting from the geometric nonlinearity is rigorously derived. From the principle of minimum total potential energy, the stability equations and force-displacement relationships are derived and the explicit expressions for the displacement parameters are presented by applying the power series expansions of displacement components to simultaneous ordinary differential equations. Finally, the member stiffness matrix is determined using the force-displacement relationships. In order to show accuracy and superiority of the beam element developed by this study, the critical lateral buckling moments for bisymmetric and monosymmetric I-beams are presented and compared with other results available in the literature, the isoparametric beam elements, and shell elements from ABAQUS.

• Steel and Composite Structures
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• v.18 no.3
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• pp.603-621
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• 2015

In this study, theoretical models and design procedures of the behavior of thin-walled simply supported steel beams with an open cross section under a large torsional effect are presented. I-sections were chosen as the cross section types. Firstly, the widely used differential equations for the lateral buckling for the pure bending moment effect in a beam element were adopted for the various moment distributions along the span of the beam. This solution was obtained for both mono-symmetric and bisymmetric sections. The buckling loads were then obtained by using the energy method. When using the energy method to solve the problem, it is possible to locate the load not only on the shear center but also at several points of the section depth. Buckling loads were obtained for six different load types. Results obtained for different load and cross section types were checked with ABAQUS software and compared with several standard rules.

• Journal of the Society of Naval Architects of Korea
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• v.46 no.5
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• pp.460-470
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• 2009

In recent practice a half round prismatic bar has fillet welded or formed through foundry work along the centerline on rear concave surface of the horn to mitigate gap flow between fixed and movable part of the rudder system. When the gap clearance has been blocked with this practice, numerical simulations indicate that the practices are not only effective in reducing the gap flow but also in mitigating the cavitation. The blocking effects are remarkably improved when a pair of blocking bar is bisymmetrically attached with respect to centerline on the opposite convex surface of the movable part. The blocking bar could be placed on the exposed surface under maximum rudder angle. This implies that the blocking bar could be easily adopted not only in a design stage but also in a maintenance stage for mitigating rudder cavitation. In addition, the numerical simulations imply that more improvements could be anticipated through the selection of section shape of prismatic bar for gap flow blocking.

• Geotechnical Engineering
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• v.12 no.4
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• pp.131-144
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• 1996

In order to accelerate the rate of consolidation settlement and to gain a required shear strength for a given soft clay deposit, the preloadina technique combined with a vertical drainage system has been widely applied. Even if a sophisticated numerical analysis technique is applied to solve the consolidation behavior of drainage-installed soft deposits, the actual field behavior is often different from the behavior predicted in the design state due to several uncertainties involved in soil properties, numerical modelling, and measuring system. In this paper, two back-analysis schemes such hs simplex and BFGS methods have been implemented in an a Bisymmetric consolidation program, AXICON which considers the variation of compressibility and permeability during the consolidation process. Utilizing the program, one might be able to appropriately predict the subsequent consolidation behavior from the measured data in an early stage of consolidation of drainage-installed soft deposits.