Lateral Stability of Bending Non-prismatic Thin-walled Beams Using Orthogonal Series

Ruta, P.; Szybiński, Józef

doi:10.1016/j.proeng.2015.07.134

Cited by 6 publications

(1 citation statement)

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“…In his work, the Ritz method has been adopted and the effects of simultaneous changes of the web height and flange width are taken into consideration. Recently, Ruta and Szybinski, 2015 [29] applied Chebyshev series to solve the torsion fourth order differential equation obtained by Asgarian et al, 2013 [5] and also to determine the critical lateraltorsional buckling of simply supported and cantilever beams with arbitrary open cross-sections. Based on nonlinear model, Mohri et al, 2015 [24] extended the tangent stiffness matrix and 3D beam element with seven degrees of freedom to the lateral buckling stability of thin-walled beams with consideration of large displacements and initial stresses.…”

Section: Introductionmentioning

confidence: 99%

Lateral stability analysis of steel tapered thin-walled beams under various boundary conditions

Soltani

Gharebaghi

Mohri

2018

NMCE

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The lateral-torsional buckling of tapered thin-walled beams with singly-symmetric crosssection has been investigated before. For instance, the power series method has been previously utilized to simulate the problem, as well as the finite element method. Although such methods are capable of predicting the critical buckling loads with the desired precision, they need a considerable amount of time to be accomplished. In this paper, the finite difference method is applied to investigate the lateral buckling stability of tapered thin-walled beams with arbitrary boundary conditions. Finite difference method, especially in its explicit formulation, is an extremely fast numerical method. Besides, it could be effectively tuned to achieve a desirable amount of accuracy. In the present study, all the derivatives of the dependent variables in the governing equilibrium equation are replaced with the corresponding forward, central and backward second order finite differences. Next, the discreet form of the governing equation is derived in a matrix formulation. The critical lateral-torsional buckling loads are then determined by solving the eigenvalue problem of the obtained matrix. In order to verify the accuracy of the method, several examples of tapered thin-walled beams are presented. The results are compared with their counterparts of finite element simulations using shell element of known commercial software. Additionally, the result of the power series method, which has been previously implemented by the authors, are considered to provide a comparison of both power series and finite element methods. The outcomes show that in some cases, the finite difference method not only finds the lateral buckling load more accurately, but outperforms the power series expansions and requires far less central processing unit time. Nevertheless, in some other cases, the power series approximation has less relative error. As a result, it is recommended that a hybrid method, based on a combination of the finite difference technique and the power series method, be employed for lateral buckling analysis. This hybrid method simultaneously inherits its performance and accuracy from both mentioned numerical methods.

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Section: Introductionmentioning

confidence: 99%