• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.391-399
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• 2008

In this paper, we further generalize the work of Lin and Abel to the case of the first and the second order derivatives of energy release rates for two-dimensional, multiply cracked systems. The direct integral expressions are presented for the energy release rates and their first and second order derivatives. The salient feature of this numerical method is that the energy release rates and their first and second order derivatives can be computed in a single analysis. It is demonstrated through a set of examples that the proposed method gives expectedly decreasing, but acceptably accurate results for the energy release rates and their first and second order derivatives. The computed errors were approximately 0.5% for the energy release rates, $3\sim5%$ for their first order derivatives and $10\sim20%$ for their second order derivatives for the mesh densities used in the examples. Potential applications of the present method include a universal size effect model and a probabilistic fracture analysis of cracked structures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.993-1000
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• 2006

Practical stability design method of main members of cable-stayed bridges is proposed and discussed through a design example. For this purpose, initial tensions of stay cables and axial forces of main members are firstly determined using initial shaping analysis of bridges under dead loads. And then the effective buckling length using system elastic/inelastic buckling analysis and bending moments considering $P-{\delta}-{\Delta}$ effect by second-order elastic analysis are calculated for main girder and pylon members subjected to both axial forces and moments, respectively. Particularly, load combinations of dead and live loads, in which maximum load effects due to live loads are obtained, are taken into account and effects of live loads on effective buckling lengths are investigated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.246-252
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• 2000

The nonlinearity of a cable-stayed bridge results in the large displacement of main girder due to a long span, the large axial forces reduce the catenary action of cables and the flexural stiffness. Therefore, the static and dynamic behavior of pylon for a cable-stayed bridge plays an important role in determining its safety. This study was performed to find the behavior of pylon of cable-stayed bridge for the first-order analysis considering of axial load only and for the second-order analysis considering of lateral deflection due to axial load. The axial force and moment values of pylon were different from the results of the first-order analysis and second-order analysis according to pylon shape and cross beam stiffness when the pylon was subjected to earthquake and wind loads. In the second-order analysis, comparing the numerical values of the member forces for the dynamic analysis, types 3 and 4 (A type) were relatively more advantageons types than types 1 and 2 (H type). Considering the stability for pylon of cable-stayed bridge (whole structural system), types 3 and 4 (A type) with pre-buckling of girder were proper types than types 1 and 2 (H type) with buckling of pylon.

• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.585-595
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• 2001

A second-order response surface model is often used to approximate the relationship between a response factor and a set of explanatory factors. In this article, we deal with canonical analysis in response surface models. For the interpretation of the geometry of second-order response surface model, standard errors and confidence intervals for the eigenvalues of the second-order coefficient matrix play an important role. If the confidence interval for some eigenvalue includes 0 or the estimate of some eigenvalue is very small (near to 0) with respect to other eigenvalues, then we are able to delete the corresponding canonical factor. We propose a formulation of criterion which can be used to select canonical factors. This criterion is based on the IMSE(=Integrated Mean Squared Error). As a result of this method, we may approximately write the canonical factors as a set of some important explanatory factors.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.977-984
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• 2006

Generally main girders and steel piers of temporary bridges form the steel rahmen structure. In this study, the rational stability design procedure for main members of temporary bridges is presented using 3D system buckling analysis and second-order elastic analysis. 2 types of temporary bridges, which are possible to be designed and fabricated in reality, are chosen and the buckling design for them is performed considering load combinations of dead and live loads, thermal load, and wind load. Effective buckling length of steel piers, effects of live loads on effective length of main members, transition of ~id buckling modes, and effects of second-order analysis are investigated through case study of 2 temporary bridges.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.9 no.2
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• pp.239-248
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• 1997

Steady components and unsteady components of second-order velocity and temperature within pulse tube refrigerators were obtained. Second-order solutions were obtained from the first-order solutions of continuity, momentum and energy equations, assuming that the amplitude of the piston motion is small. The axial temperature gradient was considered in the analysis. The flow direction of the streaming was consistent with previous experimental observations. Effects of axial temperature gradient on secondary flow and second-order temperature were shown.

• International Journal of Ocean System Engineering
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• v.1 no.3
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• pp.155-164
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• 2011

The second-order motion characteristics of a semi-submersible are investigated in regular waves. A higher-order boundary element method in a frequency domain and a finite element method in a time-domain were applied to the numerical analysis of the nonlinear hydrodynamic force and motion characteristics of semi-submersibles in view point of potential flow. Various aspects of nonlinear effects on the heave and roll of a semi-submersible were numerically investigated and some selected cases were compared with the model test data.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.37 no.4
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• pp.313-320
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• 2001

In the presence of incident waves with different frequencies, there are second order sum and difference frequency wane exciting forces due to the nonlinearty of the incident waves. Although the magnitudes of these nonlinear forces are small, they act at sum and difference frequencies away from those of the incident waves. So, the second order sum and difference frequency wane loads occurring close to the natural frequencies of TLPs often give greater contributions to high and low frequency resonant responses. The components of the second order forces which depend on first order quantities have been evaluated using the three dimensional source distribution method. The numerical results of time domain motion analysis for the nonlinear wave exciting forces in regular waves are compared with the numerical ones of frequency domain analysis. The results of comparison confirmed the validity of the proposed approach.

• Journal of Korean Society of Steel Construction
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• v.22 no.1
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• pp.87-97
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• 2010

The purpose of this study was to evaluate the validity of the second-order analysis for asymmetric unbraced frame using the load amplification factor suggested by design codes. For this purpose, the first-order analysis with the B1 and B2 factors suggested by KBC 2005 and the direct analysis with the load amplification factors suggested by KBC 2009 were performed for five story - two bay and five story - four bay asymmetric unbraced steel frames. The results of the analyses were compared with the results of the second-order inelastic analysis to evaluate the validity of the suggested methods. The main parameters of the analysis were the shape of the frame, the axial load ratio of the column, the methods of analysis and the location of column. The research results show that the asymmetric shape of the frame deteriorates the validity of the factor B2 and the suggested methods. The range of error is increased in case of irregular or inclined column.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.8 no.2
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• pp.208-218
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• 1996

Performance of a VM heat pump is considerably affected by various losses, such as enthalpy dump, reheat loss, pumping loss, conduction loss and shuttle loss. A second-order analysis model of VM heat pumps, which allows consideration of the major losses, was presented. Actual heat transfer rates for heat exchangers were calculated from the heat transfer rates obtained by the adiabatic analysis and various losses. New effective temperatures of heat exchangers were calculated from the actual heat transfer rates and the mean heat transfer coefficients until there was no appreciable change in the effective temperatures. Effects of design parameters, such as phase angle, swept volume ratio, regenerator length and speed on heating capacity, cooling capacity and COP were shown.