Dynamic analysis of thin-walled members using Generalised Beam Theory (GBT)

GBT-Based Buckling Analysis Using the Exact Element Method

“…For the discretisation considered (involving 15 nodes), a total of = 3 × 15 = 45 deformation modes are obtained  the in-plane or out-of-plane configurations of the most relevant ones are depicted in Figure 3. They comprise: (i) the four classical rigid-body (or "global") modes (axial extension (1), major-and minor-axis bending (2-3) and torsion (4)), (ii) two distortional modes, associated with quasi-rigid body flange-lip motions (5-6), (iii) a sequence of local modes, involving transverse plate bending with increasing curvature (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), (iv) five global shear modes (18)(19)(20)(21)(22), consisting of the warping components of the Vlasov modes 2-6, (v) a set of local shear modes, (23)(24)(25)(26)(27)(28)(29)(30)(31), (vi) five global transverse extension modes (32)(33)(34)(35)(36) and (vii) the local transverse extension modes (37-45).…”

“…Recent progress concerning the cross-section analysis has made GBT applicable in the context of members exhibiting arbitrary flat-walled cross-sections [6][7] or circular/elliptical tubular cross-sections [8][9][10]. Concerning the member analysis, formulations/studies have been reported for various types of structural analysis, namely first-order [11,12], buckling [3,[13][14][15][16], vibration [17][18][19], post-buckling [20][21][22] and dynamic [23] analyses involving elastic members (mostly), frames and trusses. Recently, the second version of GBTUL [24], a GBT-based freeware code which performs linear buckling and vibration analyses of general thin-walled bars, has been released online [25].…”

Isogeometric Methods in Dynamic Analysis of Curved Beams Including Warping and Distortional Effects

“…However, this approach is only capable of handling problems that involve a limited range of deformation types due to the fact that the displacement field, which is based on, is not formulated in the most general way. In addition to these, Jang et al [28] and Bebiano et al [29] developed more refined beam models with open-or closed-shaped cross section for the vibration problem. However, their cross sectional analyses are based on beam-frame and plate models for the discretization of the cross section.…”

Free vibration of horizontally curved thin-walled beams with rectangular hollow sections considering two compatible displacement fields

“…There have been a number of good elements for the dynamic analysis of thin-walled beams, such as Bebiano, Camotim, and Silvestre (2013), Pagani et al (2013), Ramkumar and Kang (2013). Krishnan and Suresh (1998) obtained a cubic linear element for static and free vibration analysis of curved beams with the shear deformation effect and rotatory inertia taken into account.…”