|The authors propose a geometrically exact beam formulation (GEBF) which is able to the model mechanical behaviour of the structures having twist, taper and large center-line displacements. Although, GEBF is not a new method for wind turbine blade modeling, the existing models are not able to capture taper effects in strain (warping and stress) fields accurately. Wind turbine blades are long, slender, composite structures with initial twist and taper, and they go through large displacements in their operational life. Therefore, this study is highly related to wind turbine modeling and technology. Please see general comments on the new version of the manuscript.|
The authors elaborated the derivation of the equation compared to the previous version of the manuscript. They also added numerical examples including prismatic beam (5.1), blade structure (5.2) and elliptic cross-section (5.3) beam with taper, twist and curvature. They claim that the proposed method is able to capture large displacements, cross-sectional warping and small strains of curved, twisted and tapered beam-like structures. Although, existing numerical tools based on geometrically nonlinear beam theory are able to capture the curvature and twist effects accurately, the taper effects still need further research. Based on the authors' claim, the proposed method is able to capture the taper effects in strain field results. This feature is the most prominent contribution of the study. However, it is not demonstrated well in the results section. Strain results are given for analytical example only and numerical examples show only center-line displacement comparisons. Reviewer thinks, the effectiveness of the proposed model needs to be demonstrated by comparisons of strain (or warping) results with 3D FEM model, if the focus of the study is mechanical behaviour modeling of structures, which have particular geometrical characteristics such as twist, taper, in- and out-of-plane cross-section warping and large center-line displacements, as mentioned in the introduction.
1-) Authors can give comparison plots of the example in section 5.2, which shows only the beam model results in Figure 6-7-8.
2-) Authors use a load case with 250 kN tip load in section 5.3, and it results about 6 m tip displacement on a 90 m beam structure. This is a small displacement compared to a 90m wind turbine blade displacements occurring during its operational life. Hence, the reviewer recommends authors to use a load case which results much larger tip displacements (around 15% - 20% of span is a good number). The difference between linear and nonlinear models are apparent after the tip displacement with 16.7% of span length as shown in figure (4).
3-) Authors can consider adding an Appendix for long derivation or intermediate steps between equations (13-15) and warping fields of analytical example. It is not easy to go to all references (some of them are books and each one has different notations) to understand the intermediate steps. All derivation would be tracked with a consistent notation if they are given in the paper.
4-) "Rubin 1997" is cited in the manuscript but it is not in the reference list.
5-) Definition of "rho" is missing in equation (28) and (29).
6-) As mentioned before, the most significant feature of the proposed method is its ability to model taper effects in strain results. However, the numerical implementation of it is missing. This point should also be highlighted in all examples, showing comparisons of strain results with 3D FEM. It is not possible to say the proposed model can capture the taper effects accurately by Figure (11). The center-line displacements are so large compared to the deformations of cross-sections, so these effects cannot be seen in center line displacement results.