• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.221-238
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• 2008

Numerical solution to buckling analysis of beams and columns are obtained by the method of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for various support conditions considering the variation of flexural rigidity. The solution technique is applied to find the buckling load of fully or partially embedded columns such as piles. A simple semi- inverse method of DQ or HDQ is proposed for determining the flexural rigidities at various sections of non-prismatic column ( pile) partially and fully embedded given the buckling load, buckled shape and sub-grade reaction of the soil. The obtained results are compared with the existing solutions available from other numerical methods and analytical results. In addition, this paper also uses a recently developed technique, known as the differential transformation (DT) to determine the critical buckling load of fully or partially supported heavy prismatic piles as well as fully supported non-prismatic piles. In solving the problem, governing differential equation is converted to algebraic equations using differential transformation methods (DT) which must be solved together with applied boundary conditions. The symbolic programming package, Mathematica is ideally suitable to solve such recursive equations by considering fairly large number of terms.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.387-395
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• 1991

Large deflection behavior of cylindrically orthotropic thin circular plates is investigated by the numerical technique of differential quadrature. Governing equations are derived in terms of transverse deflection and stress function and a Newton-Raphson technique is used to solve the nonlinear systems of equations. For small values of degree of differential quadrature (N.leq.13), as the degree of differential quadrature increases, the center deflection converges. However, as N increases further, the center deflection diverges by ill-conditioning in the weighting coefficients. As the orthotropic parameter increases, the center deflection decreases and behaves linear for the loads. At center, the stress is affected mainly by orthotropic parameter, while the stress is affected mainly by boundary condition at edge.

• Structural Engineering and Mechanics
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• v.17 no.1
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• pp.1-14
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• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.957-962
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• 2004

This paper deals with the free vibration analysis of beam-columns resting on Pasternak foundation by 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1005-1009
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• 2001

This paper deals with the free vibration analysis of beam-columns on elastic foundation using Differential Quadrature Method. Based on the dynamic equilibrium equation of a beam element acting the stress resultants and the inertia force, the governing differential equation is derived for the in-plane free vibration of such beam-columns. For calculating the natural frequencies, this equation is solved by the Differential Quadrature Method. It is expected that the results obtained herein can be used in application of Differential Quadrature Method to the field of civil engineering and practically in the structural engineering, the foundation engineering and the vibration control fields.

• Journal of Korean Tunnelling and Underground Space Association
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• v.6 no.4
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• pp.279-290
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• 2004

The differential quadrature method (DQM) for a system of coupled differential equations governing the elastic stability of thin-walled curved members is presented, and is applied to computation of the eigenvalues of out-of-plane buckling of curved beams subjected to uniformly distributed radial loads including a warping contribution. Critical loads with warping, which were found to be significant, are calculated for a single-span wide-flange beam with various end conditions, opening angles, and stiffness parameters. The results are compared with the exact methods available. New results are given for the case of both ends clamped and clamped-simply supported ends without comparison since no data are available The differential quadrature method gives good accuracy and stability compared with previous theoretical results.

• Structural Engineering and Mechanics
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• v.25 no.2
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• pp.201-217
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• 2007

A harmonic type differential quadrature approach for nonlinear dynamic analysis of multi-degree-of-freedom systems has been developed. A series of numerical examples is conducted to assess the performance of the HDQ method in linear and nonlinear dynamic analysis problems. Results are compared with the existing solutions available from other analytical and numerical methods. In all cases, the results obtained are quite accurate.

• Structural Engineering and Mechanics
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• v.41 no.1
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• pp.67-81
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• 2012

Differential Quadrature Method (DQM) is a powerful method which can be used to solve numerical problems in the analysis of structural and dynamical systems. In this study the governing equation which represents the free vibration of coupled shear walls is solved using the DQM method. A one-dimensional model has been used in this study. At the end of study various examples are presented to verify the accuracy of the method.

• Journal of the Korean Society of Safety
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• v.14 no.1
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• pp.199-207
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• 1999

The differential quadrature method (DQM) is applied to computation of eigenvalues of the equations of motion governing the free in-plane and out-of-plane vibrations for circular curved beams. Fundamental frequencies are calculated for the members with various end conditions and opening angles. The results are compared with existing exact solutions and numerical solutions by other methods (Rayleigh-Ritz, Galerkin or FEM) 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 Korean Society of Safety
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• v.13 no.3
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• pp.163-170
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• 1998

The differential quadrature method (D.Q.M.) is applied to computation of eigenvalues of small-amplitude free vibration for horizontally curved beams including a warping contribution. Fundamental frequencies are calculated for a single-span, curved, wide-flange beam with both ends simply supported or clamped, or simply supported-clamped end conditions. The results are compared with existing exact solutions and 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.