Discretization considerations in moving load finite element beam models

Rieker, J. R.; Lin, Yih‐Hwang; Trethewey, Martin W.

doi:10.1016/0168-874x(95)00029-s

Cited by 65 publications

(51 citation statements)

References 6 publications

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“…Note that these results are obtained using two different values of α. Excellent agreements are observed between the results of present analysis and those of Rieker et al (1996). Besides, the convergence behavior of solutions is more uniform in the case α = 0.025 as compared with the case α = 0.02.…”

Section: Vibration Of a Beam Due To A Moving Point Loadsupporting

confidence: 74%

“…The numerical results are given in Now, consider a moving point load on a beam with clamped-clamped boundary conditions. Although analytical solutions do not exist for this condition, accurate numerical solutions are available in the literature (Rieker et al, 1996). Therefore, the accuracy of the method can also be checked for this case.…”

Section: Vibration Of a Beam Due To A Moving Point Loadmentioning

confidence: 99%

“…Therefore, the accuracy of the method can also be checked for this case. The dynamic responses at the beam center are evaluated for different travel speeds (v) and normalized by the static deflection w cs = fL element solutions obtained by Rieker et al (1996). Note that these results are obtained using two different values of α.…”

Section: Vibration Of a Beam Due To A Moving Point Loadmentioning

confidence: 99%

“…Consider a simply supported beam with a span L of 10.16 cm, width b = 0.635 cm, thickness h = 0.635 cm, modulus of elasticity E = 2.068 × 10 11 Pa, mass density ρ = 10686.9 kg/m 3 , subjected to a f = 4.45 N moving force (Rieker et al, 1996). The dynamic responses at the beam center, w cd , are evaluated for different values of v (velocity of moving load) and normalized by the static deflection w cs = fL Our numerical experiments for the present problem showed that the value of α at which the convergence is attained depends considerably on the value of the beam length.…”

Section: Vibration Of a Beam Due To A Moving Point Loadmentioning

confidence: 99%

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A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

Eftekhari

2015

Lat. Am. j. solids struct.

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The differential quadrature method (DQM) is one of the most elegant and efficient methods for the numerical solution of partial differential equations arising in engineering and applied sciences. It is simple to use and also straightforward to implement. However, the DQM is well-known to have some difficulty when applied to partial differential equations involving singular functions like the Dirac-delta function. This is caused by the fact that the Dirac-delta function cannot be directly discretized by the DQM. To overcome this difficulty, this paper presents a simple differential quadrature procedure in which the Dirac-delta function is replaced by regularized smooth functions. By regularizing the Dirac-delta function, such singular function is treated as non-singular functions and can be easily and directly discretized using the DQM. To demonstrate the applicability and reliability of the proposed method, it is applied here to solve some moving load problems of beams and rectangular plates, where the location of the moving load is described by a time-dependent Dirac-delta function. The results generated by the proposed method are compared with analytical and numerical results available in the literature. Numerical results reveal that the proposed method can be used as an efficient tool for dynamic analysis of beam-and plate-type structures traversed by moving dynamic loads.

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Section: Vibration Of a Beam Due To A Moving Point Loadsupporting

confidence: 74%

Section: Vibration Of a Beam Due To A Moving Point Loadmentioning

confidence: 99%

Section: Vibration Of a Beam Due To A Moving Point Loadmentioning

confidence: 99%

Section: Vibration Of a Beam Due To A Moving Point Loadmentioning

confidence: 99%

See 2 more Smart Citations

A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

Eftekhari

2015

Lat. Am. j. solids struct.

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“…In more complex models numerical methods can be used. Numerical description of the loads travelling along a string, beams or plates have been widely presented in the literature [3,14,27]. This concerns both the classical FEM with spatial discretization as well as space-time discretization.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical approach to unbounded systems subjected to a moving load

Dyniewicz

2014

Comput Mech

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The present paper solves numerically the problem of vibrations of infinite structures under a moving load. A velocity formulation of the space-time finite element method was applied. In the case of simplex shaped space-time finite elements, the 'steady state' dynamic behaviour of the system was obtained. A properly performed discretization allowed of propagating information in a given direction at a limited velocity. The solutions were obtained under the assumption that the deformation is quasi-stationary, i.e., stationary in the coordinate system that moves with the load. The unbounded Timoshenko beam subjected to a distributed moving load was used as a test example. The dynamical system is placed on an elastic foundation. The matrices describing an infinite dynamical system subjected to a moving load are derived and the stability of the numerical scheme is analysed. The numerical results are compared with the analytical solutions in the literature and the classical numerical method.

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An adaptive algorithm in time domain for dynamic analysis of a simply supported beam subjected to a moving vehicle

Yang

2011

Math. Meth. Appl. Sci.

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Communicated by J. CashThis paper presents an adaptive algorithm in the time domain for the dynamic analysis of a simply supported beam subjected to the moving load and moving vehicle with/without varying surface roughness. By expanding variables at a discretized time interval, a coupled spatial-temporal problem can be converted into a series of recursive space problems that are solved by finite element method (FEM), and a piecewised adaptive computing procedure can be carried out for different sizes of time steps. The proposed approach is numerically verified via the comparison with analytical and the Runge-Kutta method-based solutions, and satisfactory results have been achieved.

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Discretization considerations in moving load finite element beam models

Cited by 65 publications

References 6 publications

A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

A Differential Quadrature Procedure with Regularization of the Dirac-delta Function for Numerical Solution of Moving Load Problem

Efficient numerical approach to unbounded systems subjected to a moving load

An adaptive algorithm in time domain for dynamic analysis of a simply supported beam subjected to a moving vehicle

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