Numerical solution for dynamic analysis of semicircular curved beams acted upon by moving loads

Abstract

The present study proposes a dynamic numerical solution for deflections of curved beam structures. In order to extract characteristic equations of an arch under an in-plane constant moving load, an analysis procedure based on the Euler–Bernoulli beam theory considering polar system is conducted. A prismatic semicircular arch with uniform cross section, in various boundary conditions, is assumed. Radial and tangential displacements, as well as bending moments are obtained using differential quadrature method as a well-known numerical method. In addition to parametric studies, a curved steel bridge as an actual application is analyzed by the mentioned method. By using this differential quadrature technique, the function values and some partial derivatives are approximated by weighting coefficients. Convergence study is carried out to demonstrate the stability of the present method. In order to confirm the high level of accuracy of this approach, some comparisons are made between the results obtained by selected methods such as differential quadrature method, Galerkin method, and finite element method. The results show that in the structural problems with specific geometry, using differential quadrature method, which is independent of domain discretization, is proven to be efficient.

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

“…But, no details were given how the time-dependent Diracdelta function was approximated or treated numerically in their study. Their numerical solutions also were not in a good agreement with the analytical and finite element solutions (Nikkhoo et al, 2012;Nikkhoo and Kananipour, 2014). The main source of error in their numerical results may be due to an incorrect approximate modeling of the Dirac-delta function.…”

“…In Eftekhari and Jafari (2012c) the capability of the DQM for handling the time-dependent Dirac-delta function was discussed at length and it was concluded that there are some major limitations in the choice of time steps and mesh sizes. Most recently, Nikkhoo et al (2012), Nikkhoo and Kananipour (2014) also Kananipour et al (2014) have proposed a formulation based on the DQM for transient dynamic analysis of curved beams traversed by moving concentrated loads. But, no details were given how the time-dependent Diracdelta function was approximated or treated numerically in their study.…”

Numerical ill-conditioning in evaluation of the dynamic response of structures with mode superposition method

“…The reason for this lies in the requirement that the generalised harmonic force in the new time interval should start at zero value. A cantilever uniform Euler-Bernoulli beam [5][6][7][8][9][10][11] is chosen as an example of this specific approach although it can be used for every structure whose response is calculated with the mode superposition method, and also when there is a need to evaluate the modal coordinate function at a high value of time. In practice, boundary conditions of slender structures are between clamped and simple supports and one has to carefully define the stiffness of supports to calculate the exact response of a structure.…”

A modified differential quadrature procedure for numerical solution of moving load problem

“…Most recently, Nikkhoo et al, 47 Nikkhoo and Kananipour, 48 and also Kananipour et al 49 have proposed a formulation based on the DQM for transient dynamic analysis of curved beams traversed by moving concentrated loads. But, no details were given how the time-dependent Dirac-delta function was approximated or treated numerically in their study.…”