Static bending of a twisted beam
For this benchmark problem, we examine the static tip deflection of a straight, but twisted beam. Details are provided in [@Wang-etal:2017]. The benchmark solution is a highly refined solid-element model solved in ANSYS. The following table shows the tip displacement calculated with a single Legendre Spectral Finite Element (LSFE) with the number of nodes shown. N-Point Gauss-Legendre quadrature was employed, where N is the number of nodes. The results show the expected spectral convergence to a solution that is in good agreement with the ANSYS solid-element solution. The results are also identical, within machine precision, to those produced with BeamDyn.
ANSYS Solid-Element Solution: u1=-1.134192, u2= -1.714467, u3=-3.58423
Number of Nodes (N) |
u1 |
u2 |
u3 |
|---|---|---|---|
3 |
-1.142067384519760E-01 |
-1.984490462570690E-01 |
-1.296500991573600E+00 |
6 |
-1.124292284062730E+00 |
-1.690365192280430E+00 |
-3.573215914495870E+00 |
9 |
-1.141513707963730E+00 |
-1.718037758175690E+00 |
-3.593187973051160E+00 |
12 |
-1.141525993948990E+00 |
-1.718053339951670E+00 |
-3.593213227112630E+00 |
15 |
-1.141525999539420E+00 |
-1.718053346463880E+00 |
-3.593213240269520E+00 |
18 |
-1.141525999540470E+00 |
-1.718053346464930E+00 |
-3.593213240271990E+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, 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