Nonlinear flexural–torsional dynamic analysis of beams of variable doubly symmetric cross section—application to wind turbine towers

Efficient high-order implicit solvers for the dynamic of thin-walled beams with open cross section under external arbitrary loadings

“…The time evolution curves of components (u(L, t), v(L, t), w(L, t), θ x (L, t)) are reported in figure 9, compared to result computed by Abaqus code and those obtained by Spountzakis et al [27]. These response curves show a very good agreement with those obtained by the Abaqus code and by Spountzakis et al.…”

“…We also notice that the number of matrix inversions IM , the number of right hand sides RHS and the CP U time increase with the truncation order p. In this example, we analyze the nonlinear dynamic behavior of a cantilever bi-symmetrical beam with steel I section subjected to an eccentric trapezoidal load F z (t) applied at end B. The considered data are the same used in [27]; the Young's modulus E = 210GP a, the shear modulus µ = 8.0769 10 7 kP a, the mass density ρ = 7850kg/m 3 , the length L = 8m, the flange thickness t f = 0.03m, the web thickness t w = 0.012m, the section varies according to the relationship h(x) = (2t f + 0.5(1.5 − x/L)) (see figure 8a) and a constant width b = 0.30m (see figure 7a). The beam clamped-free is subjected at free end to an eccentric trapezoidal load F z (t) plotted in the figure 7b.…”

“…However, for thin-walled beams with open cross section, the research works which deal with nonlinear dynamics analysis has received less attention than thin-walled beams with constant open cross section. The research works are very limited concerning this topic [3,27].…”