• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.281-292
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• 2009

The solution of the interface problem or Poisson problem with concave corner has singular perturbation at the interface corners or singular corners. The decoupled dual singular function method (DDSFM) which exploits the singular representations of the solutions was suggested in [3, 9] and estimated optimal accuracy in [10]. The convergence rates consist with theoretical results even for the problems with very strong singularity, with the efficiency depending on parameters used in the methods. Furthermore the errors in $L^2$ and $L^\infty$-spaces display some oscillation, in the cases with meshsize not small enough. In this paper, we present an answer to remove the oscillation via numerical experiments. We observe the effects of parameters in DDSFM, and show the consisting efficiency of the method over the strong singularity.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.9
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• pp.823-829
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• 2012

An excitation table is commonly used for vibration and ride tests for parts or assemblies of automobiles, aircrafts, or other heavy systems. The authors have analyzed several kinematic properties of an excitation table that is under development for heavy transport vehicles. It consists of one table and 7 linear hydraulic actuators. The authors have performed mobility analysis, inverse kinematics, forward kinematics, and singularity analysis. Especially, we have proposed a fast forward kinematic solution considering the limited motion of the excitation table. On the assumption that the motion variables such as rotation angles and displacements are small, the forward kinematic problem is converted to the observer problem of a linear system. This provides a fast solution. Also we have verified that there are no singularity points in the working range by numerical analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.182-189
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.12
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• pp.2040-2047
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• 2001

In this paper, a singularity problem of the state transition matrix is investigated in the spatial propagation when the spatial matrix differential equation is constructed via time finite element analysis. A parametric study shows that the degree of singularity of the state transition matrix depends on the degree of flexibility of the structures. As an alternative to avoid the numerical problems due to the singularity, an analytic solution fur spatial propagation of the flexible structures is proposed. In the proposed method, the spatial properties of the structure are analytically expressed by a combination of transcendental functions. The analytic solution serves fast and accurate results by eliminating the possibility of the error accumulation caused by the boundary condition. Several numerical examples are shown to validate the effectiveness of the proposed methods.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.22-32
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• 2002

V-notched crack problems can be formulated as eigenvalue problems. The problem ova v-notched crack in anisotropic and/or pseudo-isotropic dissimilar materials was formulated as an eigenvalue problem to discuss stress singularities. The eigenvalue problem was served by the commercial numerical program; MATHEMATICA. The specific data of eigenvalues possessing the stress singularity were obtained. Stress singularities fur v-notched cracks in anisotropic and/or pseudo-isotropic dissimilar materials were discussed according to the relation between wedge angle and material property. It was shown that there are three cases of eigenvalues possessing the stress singularity; one real, two real and one complex.

• Proceedings of the KIEE Conference
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• 1999.07a
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• pp.217-219
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• 1999

This paper presents a study of 2-dimensional(2-D) eddy current problem using boundary element method(BEM). When compared with finite element method(FEM), there are only a few unknown variables in BEM because it implements numerical analysis only for the surface or boundary of a model. As a result, a lot of computational memory and time can be saved. In order to analyze 2-D eddy current problem, potentials and its derivatives(flux) in a boundary are used as variables. The Mantel function of the second kind of the zero order is used here as a fundamental solution. In order to remove singularity and to solve the integral equations in a boundary, Subtracting Singularity Method and Gauss Quadrature Formula are adopted in this paper.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1311-1322
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• 2005

We consider the several plane sector domains which are bonded together along common edges with vertex at the origin. Such domains appear in electric conducting problem with multi-layered heterogeneous media. Our aim is to give a structure theorem of the singularities of the electric field at the corner. Also, we provide a regularity theorem for the electric field.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.95.4-95
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• 2001

In this paper, we proposed and analyze an robust adaptive control scheme for uncertain nonlinear systems using Universal function approximators. The proposed scheme completely overcomes the singularity problem which occurs in the indirect adaptive feedback linearizing control. No projection in the estimated parameters and no switching in the control input are needed. The stability of the closed-loop systems is guaranteed in the Lyapunov standpoint.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.356-356
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• 2000

For irregular nonlinear systems, switching controlk form is proposed recently. This control law is designed to overcome the singularities through the scheme that switches between an approximate tracking law close to the singularities, and an exact tracking law away from the singularities. But, that form has problems which may break the system's stability through unstable control input value at switching procedure. In this paper, We propose new switching control law which supervises approximate tracking control law and exact tracking control law by fuzzy rules to overcome unstability problem in switching procedure.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.1
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• pp.48-56
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• 2008

Nowadays, CMG(Control Moment Gyros) becomes one of the essential actuators for satellite attitude control. The method to define the key requirements of CMG is suggested to avoid CMG's singularity problem for the limited envelope of angular momentum of 2H. Furthermore, the analysis and simulation are carried out to provide a necessary guideline when three CMGs are used for spacecraft control purpose. An improved configuration of redundant four CMG cluster, slightly different from the conventional configuration, is proposed not only to avoid the CMG singularity problem, but to improve agility about roll or pitch-axis.