• Structural Engineering and Mechanics
• /
• v.17 no.1
• /
• pp.1-14
• /
• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.7
• /
• pp.1147-1154
• /
• 2001

One of major problems in analyzing failure mechanism of real components is the accurate measurement of crack size and shape. The DCPD(Direct Current Potential Drop) method has been widely used for the crack measurement of a structure and finite element analysis has been used for the derivation of calibration equations, which relates the potential drop with the crack depth. In this paper, finite element analyses were performed for semi-elliptical surface cracks with various crack shapes(a/c) and crack depths(a/t). As a result, a calibration equation has been derived for the measurement of a semi-elliptical surface crack in wide plates. Analytical results are compared with experimental results to evaluate the validity and the applicability of the derived equation. The proposed method is expected to provide efficient and accurate measurement of a surface crack during crack growth.

• Journal of the Korean Society for Precision Engineering
• /
• v.23 no.11 s.188
• /
• pp.34-41
• /
• 2006

Nanoimprint lithography is an emerging technology which has an ability to make patterns under 100nm width. Recently many researches have been focused to develop multilayer patterning function in nanoimprint lithography and aligning method is attracting attention as a key technology. $Moir\'{e}$ has been used widely to measure dislocation or deformation of objects and considered one of the best solutions to detect aligning error in nanoimprint lithography. Concentric circular patterns are used to generate a $moir\'{e}$ fringe in this paper and aligning offset and direction are extracted from it. Especially this paper shows the difference of fringe equation of $moir\'{e}$ which can be obtained in nanoimprint process atmosphere from normal one.

• Journal of Korean Society for Atmospheric Environment
• /
• v.12 no.5
• /
• pp.577-585
• /
• 1996

A screening study was performed in order to resolve the flow, combustion and emission characteristics of the gas furmace with co-axial diffusion flane burner. A control-valume based finite-difference method with the power-law scheme was employed for discretization. Numerical procedure for the differential equation was used by SIMPLEST to enclosute rapid converge. A k-.varepsilon. model was incorporated for the closure of turbulence. The mass fraction and mixture fraction were calculated by cinserved scalar method. An equilibrium analysis was employed to determine the concentration of radicals in the product stream and conserbation equations were them solved for N amd NO by Zelovich reaction scheme. The method was exercised in a simple one-dimensional case first, to determine the effects of air ratio, temperature and residence time on NO formation and applied to a furnace with co-axial diffusion flame burner.

• Journal of the Korea Concrete Institute
• /
• v.12 no.5
• /
• pp.101-110
• /
• 2000

A practical approach of calculating the ultimate strength of composite beams with unreinforced web opning is proposed through shear behavioral tests. In this method, the slab shear contribution at the opening is calculated as the smaller value of the pullout capacity of shear connector at the high moment end and the one way shear capacity of slab. A simple interaction equation is used to predict the ultimate strength under simultaneous bending moment and shear force. Strength prediction by the proposed method is compared with previous test results and the predictions by other analytical methods. The comparison shows that the proposed method predicts the ultimate capacity with resonable accuracy.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.29 no.6
• /
• pp.583-590
• /
• 2016

This paper presents a dynamic crack propagation algorithm with Rayleigh damping effect based on the MLS(Moving Least Squares) Difference Method. Dynamic equilibrium equation and constitutive equation are derived by considering Rayliegh damping and governing equations are discretized by the MLS derivative approximation; the proportional damping, which has not been properly treated in the conventional strong formulations, was implemented in both the equilibrium equation and constitutive equation. Dynamic equilibrium equation including time relevant terms is integrated by the Central Difference Method and the discrete equations are simplified by lagging the velocity one step behind. A geometrical feature of crack is modeled by imposing the traction-free condition onto the nodes placed at crack surfaces and the effect of movement and addition of the nodes at every time step due to crack growth is appropriately reflected on the construction of total system. The robustness of the proposed numerical algorithm was proved by simulating single and multiple crack growth problems and the effect of proportional damping on the dynamic crack propagation analysis was effectively demonstrated.

• Korean journal of applied entomology
• /
• v.61 no.4
• /
• pp.549-554
• /
• 2022

Life table-related studies in insect ecology have been an interesting topic for insect researchers. Two calculation methods are commonly applied to estimate the intrinsic rate of natural increase (r_m) in the life table statistics. The first method is to estimate an approximate r_m by dividing the natural logarithm of the net reproductive rate (R₀) by mean generation time (T) (namely mean generation time-based method). Another approach is to apply the Lotka-Euler equation derived from the population growth equation of Lotka-Volterra to estimate accurate r_m using the maximum likelihood method (Lotka-Euler equation-based method). In the latter case, there is a difference in the estimated r_m value when the initial age class of the target cohort was set to "0" or "1", which confused the application. In this short review, a brief history of the calculation process of the life table was reviewed. It was again confirmed in the Lotka-Euler equation-based method that the form of $\sum\limits_{x=1}^{w}e^{-rx}l_xm_x=1$ should be applied to estimate r_m when the first age class was set to zero, while the form of $\sum\limits_{x=0}^{w}e^{-r(x+1)}l_xm_x=1$ when set to one.

• Journal of Korea Water Resources Association
• /
• v.34 no.5
• /
• pp.439-448
• /
• 2001

A two-dimensional finite difference numerical model was developed in order to simulate two-phase fluid flow in a single fracture. In the model, variation of viscosity with pressure and that of relative permeability with water saturation can be treated. For the numerical solution, IMPES method was used, from which the pressure and the saturation of water and gas were computed one by one. Seven cases of model test using parallel plates for a single fracture were performed in order to obtain the characteristic equation of relative permeability which would be used in the numerical model. it was difficult to match the characteristic curves of relative permeability from the model tests with the existing emperical equations, consequently a logistic equation was proposed. As the equation is composed of the parameters involving aperture size, it can be applied to any fracture.

• Geophysics and Geophysical Exploration
• /
• v.5 no.1
• /
• pp.18-22
• /
• 2002

As a single arrival traveltime, maximum energy arrival traveltime has been known as the most proper operator for Kirchhoff migration. In case of the model having the simple structure, both the first arrival traveltime and the maximum energy arrival traveltime can be used as the correct operators for Kirchhoff migration. However for some model having the complex and high velocity contrast structure, the migration using the first arrival traveltime can't give the correct depth section. That is, traveltime to be required in Kirchhoff migration is the maximum energy traveltime, but, needs considerably more calculation time than that of first arrival. In this paper, we propose the method for calculating the traveltime approximated to the maximum energy arrival using one-way wave equation. After defining the WAS(Wrap Around Suppression) factor to be used for calculating the first arrival traveltime using one-way wave equation as the function of lateral grid interval and depth and considering the delay time of source wavelet. we calculate the traveltime approximated to the maximum energy arrival. to verify the validity of this traveltime, we applied this to the migraion for simple structure and complex structure and compared the depth section with that obtained by using the first arrival traveltime.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.13 no.1
• /
• pp.17-23
• /
• 1976

Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.