• Steel and Composite Structures
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• v.10 no.3
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• pp.207-222
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• 2010

Fire incident in buildings is common, so the fire safety design of the framed structure is imperative, especially for the unprotected or partly protected bare steel frames. However, software for structural fire analysis is not widely available. As a result, the performance-based structural fire design is urged on the basis of using user-friendly and conventional nonlinear computer analysis programs so that engineers do not need to acquire new structural analysis software for structural fire analysis and design. The tool is desired to have the capacity of simulating the different fire scenarios and associated detrimental effects efficiently, which includes second-order P-D and P-d effects and material yielding. Also the nonlinear behaviour of large-scale structure becomes complicated when under fire, and thus its simulation relies on an efficient and effective numerical analysis to cope with intricate nonlinear effects due to fire. To this end, the present fire study utilizes a second-order elastic/plastic analysis software NIDA to predict structural behaviour of bare steel framed structures at elevated temperatures. This fire study considers thermal expansion and material degradation due to heating. Degradation of material strength with increasing temperature is included by a set of temperature-stress-strain curves according to BS5950 Part 8 mainly, which implicitly allows for creep deformation. This finite element stiffness formulation of beam-column elements is derived from the fifth-order PEP element which facilitates the computer modeling by one member per element. The Newton-Raphson method is used in the nonlinear solution procedure in order to trace the nonlinear equilibrium path at specified elevated temperatures. Several numerical and experimental verifications of framed structures are presented and compared against solutions in literature. The proposed method permits engineers to adopt the performance-based structural fire analysis and design using typical second-order nonlinear structural analysis software.

• Ocean Systems Engineering
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• v.10 no.1
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• pp.67-86
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• 2020

The main goal of this study is to investigate the free vibration analysis of a large sag catenary with application to the jumper in hybrid riser system. The equation of motion is derived by using the variational method based on the virtual work principle. The finite element method is applied to evaluate the numerical solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.8
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• pp.598-604
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• 2003

In this paper a general solution method is presented to obtain the unbalance response orbit from the finite element based equations of motion of a gear-coupled two-shaft rotor-bearing system, whose shafts rotate at their different speeds from each other. Particularly, are proposed analytical solutions of the maximum and minimum radii of the orbit. The method has been applied to analyze the unbalance response of a 800 refrigeration-ton turbo-chiller rotor-bearing system having a bull-pinion speed increasing gear. Bumps in the unbalance response of the driven high speed compressor rotor system have been observed at the first torsional natural frequency due to the coupling effect of lateral and torsional dynamics. Further, the proposed analytical solutions have agreed well with those obtained by a full numerical approach. The proposed analytical solutions can be generally applied to obtain the maximum and minimum radii of the unbalance response orbits of dual-shaft rotor-bearing systems coupled by bearings as well.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.836-839
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• 2005

The in-plane vibration response of a clamped circular plate should be predicted in many applications. Up to now, papers on the in-plane vibration of rectangular plate are published. However, analytical derivation on the in-plane vibration of the clamped circular plate is not carried out. Therefore, the in-plane vibration of the clamped circular plate is the concern of this paper. In order to derive the equations of motion for the clamped circular plate in the cylindrical coordinate, the kinetic energy and potential energy for the in-plane behavior are obtained by us ing the stress-strain-displacement expressions. Application of Hamilton's principle leads to two sets of differential equations. These displacement equations were highly coupled. It is possible to obtain a simpler set of equations by introducing Helmholtz decomposition. Substituting them into the coupled differential equations, we obtain the uncoupled equations of motion. In order to solve them, we assume that the solutions are harmonic. Then, they lead to the wave equations. Using the separation of variable, we obtain the general solutions for the equations. Based on the solutions, the displacements for r and $\theta$ direction are assumed. Finally we obtain the frequency equation for the clamped circular plate by the application of boundary conditions. The derived equation is compared with the finite element analysis for validation by using the some numerical examples.

• Journal of the Korean Society for Heat Treatment
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• v.5 no.4
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• pp.224-232
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• 1992

Coolingability of coolants is important factor in cooling processor heat treatment of steel. Using standard apparatus and method defined in the Korean Industrial Standard three different shapes of probe were designed, ie, cylinderical, spherical and square on shape with same volume of standard probe. Distilled water and sodium aquious solutions with different concentration of NaOH, NaCl and $Na_2CO_3$ were examined. Estimation of coolingability of each quenchants for the probes of cylinderical, spherical or square shape, the cooling rate is greater square, cylinder and sphere in order. Coolingability of sodium aquious solution of NaCl, $Na_2CO_3$ and NaOH is found generally greater then that of distilled water. Effectiveness of ingredients is in the order of $Na_2CO_3$, NaOH and NaCl. In both solutions coolingability increases in 20%, 5%, and 10%in order. Analytical results obtained from Finite Element Method were compared with experimental ones and found as practically satisfactional.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.1
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• pp.131-138
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• 2002

This paper provides the fully plastic J solutions for circumferential cracked pipes with inner, semi- elliptical surface cracks, subject to internal pressure and global bending. Solutions are given in the form of two different approaches, the GEF/EPRl approach and the reference stress approach. For the GE/EPRl approach, the plastic influence functions for fully plastic J are tabulated based on extensive 3-D FE calculations using the Ramberg-Osgood (R-O) materials, covering a wide range of pipe and crack geometries. The developed GEf/EPRl-type fully plastic J estimation equations are then re-formulated using the concept of the reference stress approach for wider applications. Based on the FE results, optimized reference load solutions for the definition of the reference stress are found for internal pressure and for global bending. Advantages of the reference stress based approach over the GE/EPRl-type approach are fully discussed. Validation of the proposed reference stress based J estimation equations will be given in Part II, based on 3-D elastic-plastic or elastic creep FE results using typical tensile properties of stainless steels and generalized creep- deformation behaviours.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.4
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• pp.545-551
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• 2015

This paper deals with torque analysis of magnetic spur gear with radial magnetized permanent magnets based on analytical method. The analysis is implemented in three parts: First, on the basis of magnetic vector potential and a two-dimensional (2D) polar-coordinate system, the magnetic field solution due to permanent magnet of source gear are obtained. And by using derived magnetic field solutions, the analytical solutions for external magnetic field distribution which affects load gear are obtained. Second, by using coordinate conversion, external magnetic field which is on the primary coordinate system is converted to the secondary coordinate system. Finally, the load gear is reduced to equivalent current densities, and the torque is computed on these currents in the external field of the source magnet. These analytical results are validated by comparing with the 2-D finite element analysis (FEA).

• Steel and Composite Structures
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• v.46 no.5
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• pp.709-718
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• 2023

The absence of an important portion of the web plate in steel beams with multiple circular perforations, cellular beams, causes the web plate to undergo distortions prior to and during lateral torsional buckling (LTB). The conventional LTB equations in the codes and literature underestimate the buckling moments of cellular beams due to web distortions. The present study is an attempt to develop analytical methods for estimating the elastic buckling moments of cellular beams. The proposed methods rely on the reductions in the torsional and warping rigidities of the beams due to web distortions and the reductions in the weak-axis bending and torsional rigidities due to the presence of web openings. To test the accuracy of the analytical estimates from proposed solutions, a total of 114 finite element analyses were conducted for six different standard IPEO sections and varying unbraced lengths within the elastic limits. These analyses clearly indicated that the LTB solutions in the AISC 360-16 and AS4100:2020 codes overestimate the buckling loads of cellular beams within elastic limits, particularly at shorter span lengths. The LDB solutions in the literature and the Eurocode 3 LTB solution, on the other hand, provided conservative buckling moment estimates along the entire range of elastic buckling.

• Geophysics and Geophysical Exploration
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• v.19 no.3
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• pp.136-144
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• 2016

Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.2A
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• pp.145-153
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• 2009

The lateral-torsional buckling strengths of the parabolic arches are investigated in this study. The curvatures of a parabolic arch vary along the center line of the arch. Thus, the problem is much more complicated comparing that of arches with constant curvature such as circular arches. Moreover, most of previous studies are limited to the circular arches. In this study, lateral-torsional buckling equations are derived for the arches with varying curvatures considering the warping effects. To obtain the buckling strength of parabolic arches, numerical solutions based on the finite difference technique are provided. The numerical solutions are compared with the those of previous researchers and finite element analyses. Then, the lateral-torsional strengths of parabolic arches are successfully verified. Finally, comparison study of critical buckling loads of parabolic arches with those of circular arches for the various rise to span ratios are discussed.