• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.7 s.94
• /
• pp.1710-1718
• /
• 1993

This paper investigates the problem of a crack approaching two circular holes in an orthotropic infinite plate. The stress intensity factors were obtained by using the modified mapping-collocation method. The present results show excellent agreement with existing solutions for a crack approaching two circular holes in an isotropic infinite plate. In the numerical examples, various types of cross-ply laminated composites were considered. To investigate the effect of orthotropy and geometry(d/R and a/(d-R)) on crack tip singularity, stress intensity factors were considered as functions of the normalized crack length. It is expected that the modified mapping-collocation method can be applied to the analysis of various kinds of cracks existing around the stress-concentration region of composite laminate.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.611-624
• /
• 2010

A Numerical scheme based on collocation method using quartic B-spline functions is designed for the numerical solution of one-dimensional modified equal width wave (MEW) wave equation. Using Von-Neumann approach the scheme is shown to be unconditionally stable. Performance of the method is validated through test problems including single wave, interaction of two waves and use of Maxwellian initial condition. Using error norms $L_2$ and $L_{\infty}$ and conservative properties of mass, momentum and energy, accuracy and efficiency of the suggested method is established through comparison with the existing numerical techniques.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.11a
• /
• pp.778-783
• /
• 2003

The problem considered in this paper is about the collocation of sensor and actuator for the active control of sound and vibration. It is well-known that a point collocated sensor-actuator pair offers an unconditional stability with very high performance when it is used with a direct velocity feedback (DVFB) control, because the pair has strictly positive real (SPR) property. In order to utilize this SPR characteristics, a matched piezoelectric sensor and actuator pair is considered, but this pair suffers from the in-plane motion coupling problem with the out-of$.$plane motion due to the piezo sensor and actuator interaction. This coupling phnomenon limits the stability and performance of the matched pair with DVFB control. As a new alternative, a point sensor and piezoelectric actuator pair is also considered, which provides SPR property in all frequency range except at the first resonance in very low frequency. This non-SPR resonance could be minimized by applying a phase lag compensator.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.2
• /
• pp.123-135
• /
• 2015

In this paper, a reduced-order modeling(ROM) of Burgers equations is studied based on pseudo-spectral collocation method. A ROM basis is obtained by the proper orthogonal decomposition(POD). Crank-Nicolson scheme is applied in time discretization and the pseudo-spectral element collocation method is adopted to solve linearlized equation based on the Newton method in spatial discretization. We deliver POD-based algorithm and present some numerical experiments to show the efficiency of our proposed method.

• Journal of the korean Society of Automotive Engineers
• /
• v.4 no.1
• /
• pp.31-39
• /
• 1982

In this paper, the stress intensity factors at the crack tips in a finite plate having a straight crack with arbitrary lengths and directions are analyzed by means of Boundary Collocation Method in Cartesian coordinates under the following two cases. A) Case of only considering stress components at the boundary collocation points B) Case of considering stress resultant at the boundary, in addition to case of )A) and analyzed by means of F.E.M. To certify the Boundary Collocation Method the solutions of B.C.M. are compared with the solutions of F.E.M. demonstrates the simplicity of input data preparation and the reduction of cpu time against F.E.M.

• Journal of Power System Engineering
• /
• v.8 no.1
• /
• pp.69-74
• /
• 2004

A structure-control combined optimal design problem is discussed taking a 3-D truss structure as a design object. We use descriptor forms for a controlled object and a generalized plant because the structural parameters appear naturally in these forms. We consider not only minimum weight design problem for structure system, but also suppression problem of the effect of disturbances for control system as the purpose of the design. A numerical example shows the validity of combined optimal design of structure and control systems. We also consider the validity of sensor-actuator collocation for control system design in this paper.

• Solar Energy
• /
• v.8 no.1
• /
• pp.82-94
• /
• 1988

The hydrodynamic stability equations for natural convection flows adjacent to a vertical isothermal surface in cold or warm water (Boussinesq or non-Boussinesq situation for density relation), constitute a two-point-boundary-value (eigenvalue) problem, which was solved numerically using the simple shooting and the orthogonal collocation method. This is the first instance in which these stability equations have been solved using a computer code COLSYS, that is based on the orthogonal collocation method, designed to solve accurately two-point-boundary-value problem. Use of the orthogonal collocation method significantly reduces the error propagation which occurs in solving the initial value problem and avoids the inaccuracy of superposition of asymptotic solutions using the conventional technique of simple shooting.

• Structural Engineering and Mechanics
• /
• v.17 no.5
• /
• pp.671-690
• /
• 2004

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

• Journal of Korea Society of Industrial Information Systems
• /
• v.5 no.2
• /
• pp.56-61
• /
• 2000

The quality of English to Korean Machine Translation depends on how well it deals with target word selection of verbs containing enormous ambiguity. Verb sense disambiguation can be done by using collocation, but the construction of verb collocations costs a lot of efforts and expenses. So, existing methods should be examined in the practical view points. This paper describes the practical method of target word selection using existing collocation and semantic distance computed from minimum semantic features of nouns.

• Bulletin of the Korean Mathematical Society
• /
• v.30 no.1
• /
• pp.35-51
• /
• 1993

This paper concerns collocation methods for integro-differential equations in which memory kernels have a singularity at t = 0. There has been extensive research in recent years on Volterra integral and integro-differential equations for physical systems with memory effects in which the stabilty and asymtotic stability of solutionsl have been the main interest. We will study a class of hereditary equations with singular kernels which interpolate between well known model equations as the order of singularity varies. We are also concerned with the smoothing effect of singular kernels, but we use energy methods and our results involve fractional time in fixed spatial norms. Galerkin methods for our models was studied and existence, uniqueness and stability results was obtained in [4]. Our major goal is to study collocation methods.