A generalized Vlasov theory for composite beams

An efficient beam element for the analysis of laminated composite beams of thin-walled open and closed cross sections

“…where ϕ is the warping function, = [16]. However, cross section warping has been included for both both closed and open cross section profiles in order develop a general formulation for both type of beam profiles.…”

“…In this context it should be mentioned that Hodges and co-workers (e.g., Volovoi et al [12], Volovoi and Hodges [13], Volovoi et al [14], Volovoi and Hodges [15], Ye et al [16]) further applied the concept introduced by the variational asymptotic method to two dimensional cross-sectional problem and derived closed-form expressions for the crosssectional stiffness coefficients of thin-walled beams. As the resulting theory [12][13][14][15][16] evolved through rigorous mathematical treatments, it involves some additional terms including those for in-plane warping of the section, which is found to be important in some specific situations.…”

“…As the resulting theory [12][13][14][15][16] evolved through rigorous mathematical treatments, it involves some additional terms including those for in-plane warping of the section, which is found to be important in some specific situations. Thus, the generality of the modelling has been enhanced in the asymptotic approach, but at the same time the mathematical formulation is very complex.…”

Variable-order finite elements for nonlinear, fully intrinsic beam equations

“…Although the work of [Volovoi and Hodges 2000] addresses both closed-and open-section beams, the present work pertains only to closed-section beams. The beam formulation of [Hodges 1990;2003] is not appropriate for beams with open cross-section, which require a separate warping displacement variable and associated boundary conditions [Simo and Vu-Quoc 1991;Yu et al 2005]. The book [Hodges 2006] gives a more comprehensive treatment for beams of all types.…”

Geometrically nonlinear analysis of thin-walled composite box beams

“…Atilgan and Hodges et al [4][5][6][7][8][9] pioneered the second approach, which was referred to as the so-called "Variational Asymptotic Beam Section Analysis". Hodges and co-workers (e.g., Cesnik et al [5], Volovoi et al [6], Yu et al [7][8][9] further applied the concept introduced by variational asymptotic method to two dimensional cross-sectional problem and derived closed-form expressions for the cross-sectional stiffness coefficients of thin-walled beams. In the present investigation, an analytical approach is adopted for the derivation of the cross-sectional stiffness matrix considering different effects and their coupling to yield a general formulation.…”