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

Abstract

The lateral-torsional buckling of tapered thin-walled beams with singly-symmetric cross-section
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.