Lateral buckling analysis of beams of arbitrary cross section by BEM

Abstract

In this paper, the lateral buckling analysis of beams of arbitrary cross section is presented taking into account moderate large displacements and employing nonlinear relationships between bending moments and curvatures. The beam is supported by the most general boundary conditions including elastic support or restraint. Starting from a displacement field without any simplifying assumptions about the angle of twist amplitude and based on the total potential energy principle, the stability criterion is formulated taking into account the warping effects, the prebuckling displacements and the Wagner's coefficients due to the asymmetric character of the cross section. The stability criterion is based on the positive definiteness of the second variation of the total potential energy and is established using the Analog Equation Method (AEM), a BEM based method. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section's torsional rigidity is evaluated exactly without using the so-called Saint-Venant's torsional constant. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The effects of both the load height and prebuckling deflections as well as the discrepancy of the Eurocode 3 standard solutions are discussed.

Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects

“…15(c). All translational DOFs are fixed at the clamped end (x = 0 m) while the above vertical loads are applied as It is required to consider the coupling effect of second order stress components in the beam formulation in order to predict this interesting phenomenon accurately [34,39,40]. Both the proposed beam model and the layerwise solid model predict almost the same bifurcation points for all k values.…”

Postbuckling analysis of beams of arbitrary cross section using BEM

“…In this final example, the influence of the axial load on the critical value of lateral beam buckling load is investigated, by employing the instability criterion based on the positive definiteness of the second variation of the total potential energy [36]. More specifically, a simply supported beam of a doubly symmetric HEA type cross section [19], as this is shown in Fig.…”

Nonlinear performance of continuum mechanics based beam elements focusing on large twisting behaviors

“…As a result, the modeling and analysis capabilities have been continuously improved; see Refs. [21][22][23][24][25][26][27][28][29] for examples. However, compared with other kinematics, relatively small improvements have been made in the large twisting kinematics of beams.…”

“…The total Lagrangian formulation is employed and, unlike other beam elements [22][23][24][25], the Wagner effect is automatically (implicitly) considered in the beam formulation due to the continuum mechanics based formulation, which results in the capability for large twisting analyses.…”