Dynamic bending of a straight composite beam

In this benchmark problem we examine the transient tip response of a straight composite beam subjected to a transverse tip load. The problem setup and sectional properties follow those of [@Wang-etal:2017]. The beam is modeled with a single Legendre Spectral Finite Element (LSFE) using \(n = 5\) nodes. The beam is clamped at the root and a point force \(P_z = 150\) lb is applied at the tip node in the global \(z\)-direction.

BeamDyn is used to provide a benchmark solution. The following figure compares the tip displacement components (\(u_1\), \(u_2\), \(u_3\)) for the dynamic response of the composite beam between Kynema and BeamDyn over 5 seconds of simulation time with a time step size of \(\Delta t = 0.005\) s. The comparison shows good agreement between the two solutions.

../_images/dynamic_beam_5nodes_0pt005s_comparison.png

8 Comparison of tip displacement components (\(u_1\), \(u_2\), \(u_3\)) for the dynamic composite beam between Kynema and BeamDyn for a single LSFE with \(n = 5\) nodes and time step \(\Delta t = 0.005\) s.

Note

This benchmark is included as a regression test in the Kynema code base. The test is implemented in:

https://github.com/kynema/kynema/blob/main/tests/regression_tests/regression/verification/dynamic_composite_beam_bending.cpp

Wang, Q., M. A. Sprague, J. Jonkman, N. Johnson, and B. Jonkman. 2017. “BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework.” Wind Energy 20: 1439–1462. https://onlinelibrary.wiley.com/doi/pdf/10.1002/we.2101