• The KIPS Transactions:PartA
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• v.11A no.5
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• pp.401-406
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• 2004

Among many algorithms for the integration problems in which one wants to compute the approximation to the definite integral in the average case setting, we study the average case errors of numerical integration rules using interpolation. In particular, we choose the composite Newton-Cotes quadratures and the function values at equally spaced sample points on the given interval as information. We compute the average case error of composite Newton-Cotes quadratures and show that it is minimal(modulo a multiplicative constant).

• Economic and Environmental Geology
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• v.25 no.1
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• pp.73-77
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• 1992

This paper compares numerical quadrature techniques for computing an inverse Fourier transform integral in two-dimensional resistivity modeling. The quadrature techniques using exponential and cubic spline interpolations are examined for the case of a homogeneous earth model. In both methods the integral over the interval from 0 to ${\lambda}_{min}$, where ${\lambda}_{min}$, is the minimum sampling spatial wavenumber, is calculated by approximating Fourier transformed potentials to a logarithmic function. This scheme greatly reduces the inverse Fourier transform error associated with the logarithmic discontinuity at ${\lambda}=0$. Numrical results show that, if the sampling intervals are adequate, the cubic spline interpolation method is more accurate than the exponential interpolation method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.5
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• pp.453-462
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• 2009

The differential quadrature method(DQM) is applied to the free in-plane vibration analysis of circular curved beams with varying cross-section neglecting transverse shearing deformation. Natural frequencies are calculated for the beams with various opening angles and end conditions. Results obtained by the DQM are compared with available results by other methods in the literature. It is found that the DQM gives good accuracy even with a small number of grid points. In addition, the corrected results are given for the beams not previously presented for this problem.

• Journal of the Korean Society of Safety
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• v.16 no.4
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• pp.208-212
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• 2001

DQM(differential quadrature method) is applied to computation of two dimensional elasticity problems in helical spring. Elastic shear stresses in an axially loaded helical spring having rectangular and square cross sections are calculated. The results are compared with those obtained using the method of successive approximations. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.629-638
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• 2002

This paper deals with the free vibration analysis of compressive tapered members resting on elastic foundation using the Differential Quadrature Method. Based on the differential equation subjected to the boundary conditions, adopted from the open literature, which governs the free vibrations of such member, this equation is applied to the Differential Quadrature Method. For computing natural frequencies, the numerical procedures are developed by QR Algorithm, in which the Chebyshev-Gauss-Lobatto method is used for choosing the grid points. The numerical methods developed herein for computing natural frequencies are programmed in FORTRAN code, and all solutions obtained in this study are quite agreed with those in the open literature.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.417-425
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• 2007

The differential quadrature method(DQM) is applied to computation of eigenvalues of the equations of motion governing the free out-of-plane vibration for circular curved beams including the effects of rotatory inertia and transverse shearing deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with exact solutions or numerical solutions by other methods for cases in which they are available. The DQM provides good accuracy even when only a limited number of grid points is used.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.11
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• pp.8064-8073
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• 2015

One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. This method has been applied to a large number of cases to circumvent the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In-plane vibrations of curved beams with inextensibility and extensibility of the arch axis are analyzed by the differential quadrature method (DQM). Fundamental frequencies are calculated for the member with various end conditions and opening angles. The results are compared with exact experimental and numerical results by other methods for cases in which they are available. The DQM gives good accuracy even when only a limited number of grid points is used, and new results according to diverse variation are also suggested.

• Journal of the Korean Society of Safety
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• v.17 no.1
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• pp.99-104
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• 2002

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration for circular curved beams including mid-surface extension and the effects of rotatory inertia. Fundamental frequencies are calculated for the members with various end conditions and opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.8
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• pp.2734-2740
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• 2010

The free in-plane vibration of asymmetric circular curved beams with varying cross-section is analyzed by the differential quadrature method (DQM) neglecting transverse shearing deformation. Natural frequencies are calculated for the beams with various opening angles and boundary conditions. Results obtained by the DQM are compared with available results by other methods in the literature. It is found that the DQM gives the good accuracy even with a small number of grid points.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.5
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• pp.284-293
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• 2016

One of the most efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method (DQM) has been applied to a large number of cases to overcome the difficulties of complex algorithms of computer programming, as well as the excessive use of storage due to the conditions of complex geometry and loading. The in-plane vibrations of curved beams with extensibility of the arch axis, including the effects of rotatory inertial and shear deformation, are analyzed by the DQM. The fundamental frequencies are calculated for members with various slenderness ratios, shearing flexibilities, boundary conditions, and opening angles. The results are compared with the numerical results obtained by other methods for cases in which they are available. The DQM gives good mathematical precision even when only a limited number of grid points is used, and new results according to diverse variations are also suggested.