Calculation of Linear Buckling Load for Frames Modeled with One-Finite-Element Beams and Columns

Abstract

Critical linear buckling load calculation is one of the possible ways to check structural stability. Structural analysis programs usually model beams and columns with just one element, but this is not enough to obtain an accurate value of the critical buckling load when the buckling mode is associated with an effective length that is less than twice the element length. This paper presents a method for the accurate calculation of the buckling load of frames modeled with only one finite element per structural element. For this purpose, a local correction is applied to some elements a few times until convergence is achieved. The validity of the presented method is confirmed by several examples ranging from simple canonical cases to large structures.

Improved FEM Natural Frequency Calculation for Structural Frames by Local Correction Procedure

“…The relative errors using a single element are excessive in all cases except CF. Errors larger than 1% are considered excessive from a structural engineering point of view [37]. Looking at Figure 1 and by analogy with the column buckling problem, we can interpret that a single element is not accurate enough to model more than a quarter of a sinusoidal deformation wavelength.…”

“…This approximation results in acceptable errors near those obtained in Table 1 with four elements. In our previous work on buckling [37] we used an auxiliary discretization of four subelements instead of two, but we will see that this approach is not possible when calculating multiple eigenvalues (or multiple frequencies) because of the override problem that is later explained.…”

“…It Is clear now that using a four subelement discretization for local element correction is not acceptable because it will be plagued by the override problem in the same way as the two-subelement one. Therefore, we will allow one or two elements per member at the coarse level and two subelements at the local level, which allows for a total of four subelements per member, roughly equivalent to what we did for buckling in [37].…”

“…Concerning the novelty of this work, the authors recently wrote a closely related paper [37] about calculating the critical buckling loads of structural frames using one element per member. This latest work presents some fundamentally novel developments.…”

“…Third, the method is extended to structural frames made up of more than one bar. Next, the devised algorithms are validated using 2D and 3D cases representative of realistic building structures taken from [10,37]. Finally, the results, discussion and conclusions are presented.…”