A derivation and solution of dynamic equilibrium equations of shear undeformable composite anisotropic beams using the DQEM

Chen, Chang New

doi:10.1016/s0307-904x(01)00075-0

Cited by 9 publications

(4 citation statements)

References 9 publications

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“…Differential quadrature method (DQM) as an alternative numerical method, which has simple formulation, low computational cost and high accuracy with respect to other conventional numerical methods, has been employed frequently in various engineering fields such as solid mechanics and heat transfer in the past three decades. A review of the early development of this method can be found in the paper of Bert and Malik .…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

Meraji

Ghaheri

Malekzadeh

2012

Numerical Methods in Fluids

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SUMMARYIn this paper, an approach to improve the application of the differential quadrature method for the solution of Navier–Stokes equations is presented. In using the conventional differential quadrature method for solving Navier–Stokes equations, difficulties such as boundary conditions' implementation, generation of an ill conditioned set of linear equations, large memory storage requirement to store data, and matrix coefficients, are usually encountered. Also, the solution of the generated set of equations takes a long running time and needs high computational efforts. An approach based on the point pressure–velocity iteration method, which is a variant of the Newton–Raphson relaxation technique, is presented to overcome these problems without losing accuracy. To verify its performance, four cases of two‐dimensional flows in single and staggered double lid‐driven cavity and flows past backward facing step and square cylinder, which have been often solved by researchers as benchmark solution, are simulated for different Reynolds numbers. The results are compared with existing solutions in the open literature. Very good agreement with low computational efforts of the approach is shown. It has been concluded that the method can be applied easily and is very time efficient. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

Meraji

Ghaheri

Malekzadeh

2012

Numerical Methods in Fluids

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“…A variety of structure problems have been solved with various proposed DQEMs since then 37–39. Chen solved the dynamic equilibrium equations of shear undeformable composite anisotropic beams using DQEM 40. A DQEM for free vibration analysis of arbitrary non‐uniform Timoshenko beams with attachments, that is, concentrated mass and rotary inertia and resting on elastic supports, was proposed by Karami et al 41.…”

Section: Introductionmentioning

confidence: 99%

DTM and DQEM for free vibration of axially loaded and semi-rigid-connected Reddy-Bickford beam

Yeşilce

2011

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYThe free vibration analysis of semi-rigid-connected Reddy-Bickford beams on elastic soil with/without axial force effect using the differential transform method (DTM) and the differential quadrature element method (DQEM) has not been investigated by any of the studies in the open literature so far. In this study, DTM and the recently proposed DQEM are employed in order to solve the governing differential equations of a Reddy-Bickford beam with two regions on elastic soil. The governing differential equations of motion of the rectangular beam in free vibration are derived using Hamilton's principle. Parameters for the relative stiffness, stiffness ratio and nondimensionalized multiplication factor for the axial compressive force are incorporated into the equations of motion in order to investigate their effects on the natural frequencies. An efficient and easy mathematical technique called DTM is used to solve the governing differential equations of the motion. The equilibrium equations are deduced, together with the boundary conditions, and then a recently proposed DQEM is employed, in order to solve the resulting boundary value problem. The calculated natural frequencies of semi-rigid-connected ReddyBickford beam with two regions on elastic soil using DTM and DQEM are tabulated in several tables and figures and are compared with the results of the analytical solution where a very good agreement is observed.

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“…Bert and Malik [10] in their review article covered a complete discussion of chronological development of the method. This method was successfully applied in structural analysis [11][12][13][14][15][16][17] and heat transfer [18]. Shu published several papers about generalized DQ for numerical simulation of NavierStokes (N-S) equations and boundary layer in the field of fluid mechanics [19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A differential quadrature analysis of unsteady open channel flow

Hashemi

Abedini

Malekzadeh

2007

Applied Mathematical Modelling

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A rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical simulation of unsteady open channel flow. To the best of authors' knowledge, this is the first attempt to use the DQM in open channel hydraulics. The Saint-Venant equations and the related nonhomogenous, time dependent boundary conditions are discretized in spatial and temporal domain by DQ rules. The unknowns in the entire domain are computed by satisfying governing equations, boundary and initial conditions simultaneously. By employing DQM, accurate results can be obtained using dramatically less grid points in spatial and time domain. The stability of DQM solution is not sensitive to choosing time step or Courant number unlike other methods. Although numerical problems such as instability, oscillation and underestimation near critical depth can be seen by using other methods but DQM solution is smooth and accurate in this case. The results are sensitive to grid distribution in time domain. In light of this, Chebyshev-Gauss-Lobatto distribution performance is excellent. To validate the DQM solutions, the obtained results are compared with those of the characteristic method. In conclusion, DQM is a potential powerful method with minimum computational effort for unsteady flow simulation.

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A derivation and solution of dynamic equilibrium equations of shear undeformable composite anisotropic beams using the DQEM

Cited by 9 publications

References 9 publications

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

An efficient algorithm based on the differential quadrature method for solving Navier–Stokes equations

DTM and DQEM for free vibration of axially loaded and semi-rigid-connected Reddy-Bickford beam

A differential quadrature analysis of unsteady open channel flow

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