Abstract
The use of the Generalized Beam Theory (GBT) is extended to thin-walled beams with curvilinear cross-sections. After defining the kinematic features of the walls, where their curvature is consistently accounted for, the displacement of the points is assumed as linear combination of unknown amplitudes and pre-established trial functions. The latter, and specifically their in-plane components, are chosen as dynamic modes of a curved beam in the shape of the member cross-section. Moreover, the out-of-plane components come from the imposition of the Vlasov internal constraint of shear indeformable middle surface. For a case study of semi-annular cross-section, i.e., constant curvature, the modes are analytically evaluated and the procedure is implemented for two different load conditions. Outcomes are compared to those of a FEM model.
Highlights
Thin-walled beams are structural elements with three characteristic dimensions of different orders of magnitude: the thickness is small when compared to the dimensions of the cross-section, which in turn are small when compared to the beam length.Starting from the second half of the 19th century, slender thin-walled members have found applications in civil and naval engineering as beams, columns, frame-works etc
According to Generalized Beam Theory (GBT) framework, the displacements are considered as linear combinations of pre-established trial functions and kinematic descriptors which change along the axis line of the beam
Following the idea of the Kantorovitch semi-variational method the individual components of the mid-curve γpoints displacement are expressed as a linear combination of K triplets of trial functions (Uj (s), Vj (s), Wj (s)), j = 1, . . . , K, and unknown amplitude parameters a j ( x ): K
Summary
Thin-walled beams are structural elements with three characteristic dimensions of different orders of magnitude: the thickness is small when compared to the dimensions of the cross-section, which in turn are small when compared to the beam length. According to the original assumptions on beam profile kinematics the Vlasov theory fails to take into account the effects of cross-section distortion and any local in-plane deformations of the walls. Silvestre [26] investigated the buckling behavior of circular hollow section (CHS) members He postulated to extend the cross section analysis and include axisymmetric and torsional modes apart from the set of classical orthogonal shell-type deformations of the profile. The second stage consisted in selection just a few of natural nodes of this polyline to generate the independent DOFs for warping analysis while the intermediate nodes of the profile were treated like in classic procedure By this approach it was possible to describe the cross-section geometry accurately, without generating an excessive number of deformation modes.
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