• 제어로봇시스템학회:학술대회논문집
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• 1988.10b
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• pp.749-752
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• 1988

In this paper, the delay margins of the LQ and the LQG regulators are obtained in the time domain. These margins are represented in terms of the singular values of system matrices and the solutions of a Riccati equation and a Lyapunov one. And their asymptotical properties when gains tend to infinity are investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.1
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• pp.206-214
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• 1998

When a crack meets bimaterial interface stress singularity depends on the elastic constants of the adjacent materials. In the present study we are going to describe the finite element formulation for problems with a crack to be embedded in the stiffer material$({\mu}_2/{\mu}_1)$. The cubic isoparametric singular element, represented by adequately shifting the mid-side nodes adjacent to the crack tip is constructed to enclose the crack tip. An alternative method to obtain the optimal position of the mid-side nodes of cubic isoparametric elements is presented. In addition, a proper definition for the stress intensity factors of a crack normal to bimaterial interface is provided. It is based upon near a tip displacement solutions. Models for numerical analysis are two dimensional elastic bodies with a through crack under plain strain. The results obtained are compared with the previous solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.179-189
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• 1991

Composite materials are generally treated as anisotropic or an orthotropic materials. Unlike isotropic materials, the orthotropic materials can divided three groups depending upon the relationship of the four material constants or depending upon the characteristic roots of orthotropic materials. In particular, the fundamental solutions of two dimensional BEM for composite materials (orthotropic or anisotropic material) generally have a singularity in the conventional method when the characteristic roots are equal. In consideration of this singularity in the conventional method when the characteristic roots are equal. In consideration of this singular problems, in this paper, the fundamental solutions of BEM are systematically analysed for orthotropic materials. And the stress and displacement fields for a crack in an orthotropic materials are singular when the characteristic roots of orthotropic materials are equal. Therefore, these fields for a crack in an orthotropic materials are analysed by the analogous method to isotropic materials when the characteristic roots are equal.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.23-27
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• 1990

Adaptive mesh refinement scheme is incorporated with the Boundary Element Method (BEM) in order to get accurate solution with relatively fewer unknowns for the case of magnetostatic field analysis and A new and simple posteriori local error estimation method is presented. The local error is defined as integration over the element of the difference between solutions acquired us ing second order and first order interpolation function and is used as the criterion for mesh refinement at given grid. Case study for two dimensional problems with singular point reveals that meshes are concentrated on the neighbor of singular point and the error is decreased gradually and the solutions calculated on the domain are converged to the analytic solution as the number of unknowns increases. The adaptive mesh gives much better rate of convergence in global errors than the uniform mesh.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.121-130
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• 2017

This study is concerned with the existence of positive solution for the following nonlinear elliptic system $$\{-M_1(\int_{\Omega}{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^pdx)div({\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)\\{\hfill{120}}={\mid}x{\mid}^{-(a+1)p+c_1}\({\alpha}_1A_1(x)f(v)+{\beta}_1B_1(x)h(u)\),\;x{\in}{\Omega},\\-M_2(\int_{\Omega}{\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^qdx)div({\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^{q-2}{\nabla}v)\\{\hfill{120}}={\mid}x{\mid}^{-(b+1)q+c_2}\({\alpha}_2A_2(x)g(u)+{\beta}_2B_2(x)k(v)\),\;x{\in}{\Omega},\\{u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}$ is a bounded smooth domain of ${\mathbb{R}}^N$ with $0{\in}{\Omega}$, 1 < p, q < N, $0{\leq}a$ < $\frac{N-p}{p}$, $0{\leq}b$ < $\frac{N-q}{q}$ and ${\alpha}_i,{\beta}_i,c_i$ are positive parameters. Here $M_i,A_i,B_i,f,g,h,k$ are continuous functions and we discuss the existence of positive solution when they satisfy certain additional conditions. Our approach is based on the sub and super solutions method.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.3
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• pp.99-108
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• 2003

This paper is concerned with the problem of designing a guaranteed cost state feedback controller for singular systems with time-varying delays. The sufficient condition for the existence of guaranteed cost controller, the controller design method, and the optimization problem to get the upper bound of guaranteed cost function are proposed by LMI(linear matrix inequality), singular value decomposition, Schur complements, and change of variables. Since the obtained sufficient conditions can be changed to LMI form, all solutions including controller gain and the upper bound of guaranteed cost function can be obtained simultaneously. Moreover, the proposed controller design method can be extended to the problem of robust guaranteed cost controller design method for singular systems with parameter uncertainties and time-varying delays. The validity of the proposed design algorithm is investigated through a numerical example.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.5
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• pp.904-913
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• 2002

In this paper, the dynamic stress intensity factors of fracture mechanics are numerically computed in time domain using the FEM. For which the finite element formulations are derived applying the Galerkin method to the equations of motion in convolution integral as has been presented in the previous paper. To assure the strain fields of r$^{-1}$ 2/ singularity near the crack tip, the triangular quarter-point singular elements are imbedded in the finite element mesh discretized by the isoparametric quadratic quadrilateral elements. Two-dimensional problems of the elastodynamic fracture mechanics under the impact load are solved and compared with the existing numerical and analytical solutions, being shown that numerical results of good accuracy are obtained by the presented method.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.661-674
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• 2016

In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.635-648
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• 2015

We consider a weakly coupled system of singularly perturbed convection-diffusion equations with discontinuous source term. The diffusion term of each equation is associated with a small positive parameter of different magnitude. Presence of discontinuity and different parameters creates boundary and weak interior layers that overlap and interact. A numerical method is constructed for this problem which involves an appropriate piecewise uniform Shishkin mesh. The numerical approximations are proved to converge to the continuous solutions uniformly with respect to the singular perturbation parameters. Numerical results are presented which illustrates the theoretical results.