Static bending of a straight composite beam

In this benchmark problem we examine the tip deflection of a composite beam under a tip load. The problem is described in detail in [@Wang-etal:2017]. The problem was solved with a single Legendre Spectral Finite Element (LSFE) with N-point Gauss-Legendre quadrature where N is the number of nodes. The tip-displacement results, shown in the table below, are the same (to within machine precision) of those produced with BeamDyn.

# nodes

u1

u2

u3

3

-5.04479565690760E-02

-3.91038892649929E-02

9.11237052941376E-01

6

-9.02727162973492E-02

-6.47489265976265E-02

1.22973611590669E+00

9

-9.02726627568822E-02

-6.47488486249749E-02

1.22973648291939E+00

12

-9.02726627566302E-02

-6.47488486259037E-02

1.22973648292371E+00

15

-9.02726627566299E-02

-6.47488486259036E-02

1.22973648292371E+00

18

-9.02726627566296E-02

-6.47488486259039E-02

1.22973648292371E+00

Note

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

Wang, Q., M.A. Sprague, J. Jonkman, N. Johnson, B. Johnkman. 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