• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.487-492
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• 2007

The enhancement of the service life of damaged or cracked structures is a major issue for researchers and engineers. The hierarchical void element with the integrals of Legend polynomials is used to characterize the fracture behavior of unpatched crack as well as repaired crack with bonded composite patches by computing the stress intensity factors and stress contours at the crack tip. The numerical approach is based on the v-version degenerate shell element including the theory of anisotropic laminated composites. Since the equivalent single layer approach is adopted in this study, the proposed element is necessary to represent a discontinuous crack part as a continuum body with zero stiffness of materials. Thus the aspect ratio of this element to represent the crack should be extremely slender. The sensitivity of numerical solution with respect to energy release rate, displacement and stress has been tested to show the robustness of hierarchical void element as the aspect ratio is increased up to 2000. The stiffness derivative method and displacement extrapolation method have been applied to calculate the stress intensity factors of Mode I problem.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.481-486
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• 2007

The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.375-382
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• 2008

The particular integral formulation for two(2D) and three(3D) dimensional inelastic transient dynamic stress analysis is presented. The elastostatic equation is used for the complementary solution. Using the concept of global shape function, the particular integrals for displacement and traction rates are obtained to approximate acceleration of the inhomogeneous equation. The Houbolt time integration scheme is used for the time-marching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. Numerical results of four example problems are given to demonstrate the validity and accuracy of the present formulation.

• Journal of the Institute of Convergence Signal Processing
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• v.5 no.4
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• pp.317-324
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• 2004

Electromagnetically coupled coaxial dipole (ECCD) array antenna with and without short-ended termination is investigated theoretically. The integral equations are derived for the structure by use of the Fourier transform and mode expansion of radial waveguide. The integrals appearing in the integral equations are evaluated along the branch cut instead of real axis for a faster convergent integral. The effects of slots and dipoles, short-ended termination length, and dielectric coating on the radiation characteristics are presented. Radiation pattern of the structure is also investigated. The results of the present method are compared with those of the commercial EM simulator and good agreement is found.

• Geophysics and Geophysical Exploration
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• v.3 no.1
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• pp.13-18
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• 2000

We describe the concept of the singularity in the integral equation of electromagnetic (EM) modeling in comparison with that in the integral representation of electric fields in EM theory, which would clarify the singular integral problems of the Green's tensor. We have also derived and classified the singular integrals of the Green's tensors in 3-D, 2.5-D and 2-D as well as in the thin sheet integral equations of the EM scattering problem, which have the most important effect on the accuracy of the numerical solution of the problems.

• Journal of the Korean Chemical Society
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• v.17 no.6
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• pp.395-405
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• 1973

By use of an Integral Hellmann-Feynman formula, the cubic crystal field splitting 1O Dq in $KNiF_3$ is calculated from first principles. Numerical values of covalency parameters and necessary integrals are quoted from Sugano and Shulman. The result, 7100$cm^{-1}$, is in excellent agreement with the observed value, 7250$cm^{-1}$. It is found that higher order perturbation energy correction is of the same order of magnitude as 10 Dq itself and is, therefore, essential tin calculating 10 Dq from first principles. It is also found that the point charge potential is the dominant part of the crystal field potential.

• Korean Chemical Engineering Research
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• v.46 no.5
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• pp.949-957
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• 2008

Estimating the first order plus time delay model on the basis of the step responses has been widely used in industry for the tuning of PID controllers. Even though various model identification methods from simple graphical approaches to complicated approaches based on least squares method have been proposed, simple approaches to incorporate noisy step responses are rarely available. In this research, we will compare and analyze recent approaches using the integrals of the step responses and develop an improved identification method to incorporate real situations more effectively.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1055-1071
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• 2010

Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1347-1355
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• 1996

The purpose of this paper is to evaluate the delamination and fracture integrity of the IC plastic package under hygrothermal loading by stress analysis and fracture mechanics approaches. The plastic SOJ package with a dimpled diepad under the reflow slodering process of IR heating type is considered. On the package without a crack, the stress variation according to the change of the design variables such as the material and shape of the package is calculated and the possibility of delamination is considered. For the model fully delaminated between the chip and diepad, J-integrals are calculated for the various design variables and the fracture integrity is discussed. From the results, optimal design values of variables to prevent the delamination and fracture of IC package are obtained. In this study, FDM program to obtain the vapor pressure from the content of moisture absorbed into the package is developed.

• Journal of the Optical Society of Korea
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• v.20 no.6
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• pp.653-662
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• 2016

An optimized multilayer superlens is designed, using a rigorous and efficient approach based on the method of moments (MoM) in conjunction with a simulated annealing (SA) algorithm. For the MoM solution, fast evaluation of closed-form Green's functions (GFs) in the spatial domain is performed by applying the complex-image (CI) technique, which obviates the time-consuming numerical evaluation of Sommerfeld integrals. The imaging capability of the superlens is examined with the correlation coefficient; results show that using circular polarization for the incident wave can improve this coefficient. To validate the proposed method, finite-element-based simulations are exploited, which reveal the method's accuracy and computational efficiency. Simulation results indicate that the designed structure is capable of producing two-dimensional sub-diffraction-limited images in the visible range, which may make it more versatile for practical applications. Finally, as a considerable finding, it is demonstrated for the proposed design that using circularly polarized illumination provides improved super-resolving performance, compared to linearly polarized illumination.